MikaStars39/nano-eval huggingface dataset:
We now define an algorithm: The definition of a(n) is the expansion of a modular function for Gamma_0(6), related to elliptic curves and modular forms. This sequence captures the coefficients in a specific q-expansion series used in the study of modular functions associated with the congruence subgroup Gamma_0(6). Given the input x_list (a series of values): [24, 25, 26, 27, 28, 29, 30, 31, 32, 33], determine the corresponding output sequence y_list.

Options:
A. [-3709670, -2354216, 3904694, 9931415, 6301127, -9983209, -25339627, -16057050, 24504586, 62033322]
B. [-3709689, -2354223, 3904701, 9931405, 6301109, -9983211, -25339628, -16057048, 24504581, 62033326]
C. [-3709678, -2354211, 3904697, 9931412, 6301130, -9983218, -25339635, -16057046, 24504590, 62033320]
D. [-3709674, -2354217, 3904700, 9931420, 6301128, -9983210, -25339630, -16057045, 24504589, 62033325]
E. [-3709685, -2354219, 3904702, 9931409, 6301125, -9983215, -25339640, -16057055, 24504578, 62033318]
F. [-3709672, -2354215, 3904696, 9931407, 6301120, -9983208, -25339626, -16057040, 24504584, 62033318]
G. [-3709682, -2354225, 3904703, 9931422, 6301123, -9983212, -25339632, -16057060, 24504582, 62033328]
H. [-3709673, -2354210, 3904695, 9931408, 6301119, -9983207, -25339625, -16057039, 24504585, 62033319]
I. [-3709676, -2354212, 3904698, 9931406, 6301126, -9983217, -25339624, -16057047, 24504588, 62033311]
J. [-3709680, -2354220, 3904690, 9931410, 6301122, -9983206, -25339620, -16057035, 24504580, 62033310]
Answer: F
We now define an algorithm: The definition of a(n) is the entry in the nth row and the kth column (0-based) of the coefficient triangle associated with specific polynomials that utilize rising powers, where these coefficients arise in the context of a generating function or a combinatorial construct. Given the input x_list (a series of values): [92, 93, 94, 95, 96, 97, 98, 99, 100, 101], determine the corresponding output sequence y_list.

Options:
A. [0, 0, 0, 0, 0, 0, 1, 19, -68, 86]
B. [0, 0, 0, 0, 0, 0, 0, 23, -70, 82]
C. [0, 0, 0, 0, 0, 0, -1, 20, -69, 85]
D. [0, 0, 0, 0, 0, 0, -1, 21, -70, 85]
E. [0, 0, 0, 0, 0, 0, -1, 20, -70, 83]
F. [0, 0, 0, 0, 0, 0, -1, 21, -69, 84]
G. [0, 0, 0, 0, 0, 0, -2, 22, -71, 83]
H. [0, 0, 0, 0, 0, 0, -3, 21, -72, 88]
I. [0, 0, 0, 0, 0, 0, 2, 21, -70, 80]
J. [0, 0, 0, 0, 0, 0, -1, 21, -70, 84]
Answer: J
We now define an algorithm: The definition of a(n) is: Numerators in a triangle formed from Bernoulli numbers. Bernoulli numbers are a sequence of rational numbers which are deeply connected to number theory and have applications in various fields such as calculus and algebra. In this context, the numerators are extracted from the rational numbers in the triangle arrangement of Bernoulli numbers. Given the input x_list (a series of values): [68, 69, 70, 71, 72, 73, 74, 75, 76, 77], determine the corresponding output sequence y_list.

Options:
A. [-6, 31, -27, 17, 16, -27, 33, -6, 5, 0]
B. [5, 31, -27, 15, 15, -27, 31, -4, 4, 1]
C. [-5, 31, -28, 17, 16, -29, 32, -5, 6, 0]
D. [-5, 33, -27, 17, 15, -29, 33, -4, 4, 0]
E. [-4, 33, -28, 16, 16, -27, 31, -5, 5, -1]
F. [-5, 32, -28, 16, 16, -28, 32, -5, 5, 0]
G. [-6, 33, -29, 17, 17, -29, 33, -6, 6, -1]
H. [-5, 32, -29, 15, 17, -28, 31, -5, 4, 1]
I. [-4, 32, -29, 16, 17, -27, 32, -6, 5, 1]
J. [4, 32, -28, 16, 15, -28, 32, -5, 6, 1]
Answer: F
We now define an algorithm: The definition of a(n) is the coefficients of the reciprocal of the 55th cyclotomic polynomial, φ(55)(x), which is the polynomial whose roots are the primitive 55th roots of unity. Given the input x_list (a series of values): [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], determine the corresponding output sequence y_list.

Options:
A. [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]
B. [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
C. [6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
D. [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
E. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
F. [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
G. [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]
H. [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]
I. [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
J. [8, 8, 8, 8, 8, 8, 8, 8, 8, 8]
Answer: E
We now define an algorithm: The definition of a(n) is the EULER transform of the sequence 3, 2, 2, 2, 2, 2, 2, 2, ... Given the input x_list (a series of values): [28, 29, 30, 31, 32, 33, 34, 35, 36, 37], determine the corresponding output sequence y_list.

Options:
A. [1200228, 1639418, 2228546, 3015360, 4062065, 5448995, 7280060, 9688718, 12846507, 16972577]
B. [1202928, 1639498, 2228666, 3015760, 4062995, 5449775, 7280960, 9689598, 12848507, 16984677]
C. [1200229, 1639419, 2228547, 3015361, 4062066, 5448996, 7280061, 9688719, 12846508, 16972578]
D. [1201229, 1639519, 2228647, 3015461, 4062166, 5449096, 7280161, 9688819, 12846608, 16972678]
E. [1234567, 1637890, 2229999, 3011111, 4062222, 5443333, 7284444, 9685555, 12866666, 16977777]
F. [1200328, 1639428, 2228556, 3015370, 4062075, 5449005, 7280070, 9688728, 12846517, 16972587]
G. [1200227, 1639417, 2228545, 3015359, 4062064, 5448994, 7280059, 9688717, 12846506, 16972576]
H. [1201228, 1639518, 2228646, 3015460, 4062165, 5449095, 7280160, 9688818, 12846607, 16972677]
I. [1200327, 1639317, 2228536, 3015341, 4062045, 5448975, 7280040, 9688708, 12846516, 16972567]
J. [1209218, 1639818, 2229446, 3016360, 4063265, 5449995, 7281160, 9689818, 12847607, 16983677]
Answer: A
We now define an algorithm: The definition of a(n) is entries in Pascal's tetrahedron, which is a 3-dimensional version of Pascal's triangle, also known as trinomial coefficients. Given the input x_list (a series of values): [74, 75, 76, 77, 78, 79, 80, 81, 82, 83], determine the corresponding output sequence y_list.

Options:
A. [61, 29, 7, 1, 6, 14, 19, 17, 5, 2]
B. [64, 31, 5, 1, 7, 14, 21, 16, 5, 1]
C. [58, 31, 7, 3, 4, 18, 21, 13, 7, 0]
D. [66, 29, 4, 0, 9, 11, 20, 14, 5, 3]
E. [65, 32, 5, 1, 8, 12, 23, 15, 6, 2]
F. [60, 30, 6, 1, 6, 15, 20, 15, 6, 1]
G. [57, 30, 6, 2, 7, 13, 18, 14, 8, 1]
H. [62, 28, 7, 2, 5, 16, 22, 15, 7, 0]
I. [59, 33, 8, 1, 5, 17, 19, 14, 6, 0]
J. [63, 34, 5, 0, 5, 15, 18, 16, 7, 1]
Answer: F
We now define an algorithm: The definition of a(n) is the sequence of weak numbers (i.e., not powerful numbers): a number n is in the sequence if there exists a prime number p such that p divides n but p squared does not divide n. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_list.

Options:
A. [72, 73, 76, 77, 78, 81, 82, 83, 84, 85]
B. [72, 75, 76, 77, 78, 80, 81, 82, 84, 85]
C. [74, 75, 76, 77, 80, 81, 82, 83, 86, 87]
D. [73, 74, 76, 77, 78, 79, 80, 83, 84, 85]
E. [74, 76, 77, 78, 79, 81, 82, 83, 84, 85]
F. [75, 76, 77, 78, 79, 80, 81, 82, 83, 85]
G. [74, 75, 76, 78, 79, 80, 82, 83, 84, 85]
H. [74, 75, 76, 77, 78, 79, 80, 82, 83, 84]
I. [74, 75, 77, 78, 79, 80, 81, 82, 83, 86]
J. [73, 75, 76, 77, 78, 79, 80, 82, 84, 85]
Answer: H
We now define an algorithm: The definition of a(n) is: Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers. These are composite numbers \\( n \\) such that \\( 2^{n-1} \\equiv 1 \\ (\\text{mod} \\ n) \\). Given the input x_list (a series of values): [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], determine the corresponding output sequence y_list.

Options:
A. [15709, 15841, 16705, 18705, 18721, 19951, 23001, 23377, 25761, 29341]
B. [15707, 15837, 16701, 18703, 18717, 19947, 22998, 23373, 25757, 29338]
C. [15712, 15839, 16703, 18706, 18719, 19949, 23004, 23375, 25759, 29344]
D. [15711, 15842, 16707, 18708, 18723, 19953, 23002, 23379, 25763, 29343]
E. [15698, 15835, 16699, 18701, 18715, 19945, 22996, 23371, 25755, 29336]
F. [15710, 15840, 16706, 18709, 18722, 19950, 23000, 23378, 25760, 29342]
G. [15697, 15834, 16698, 18700, 18714, 19944, 22995, 23370, 25754, 29335]
H. [15708, 15843, 16704, 18707, 18720, 19952, 23003, 23376, 25762, 29340]
I. [15713, 15838, 16702, 18704, 18718, 19948, 22999, 23374, 25758, 29339]
J. [15699, 15836, 16700, 18702, 18716, 19946, 22997, 23372, 25756, 29337]
Answer: A
We now define an algorithm: The definition of a(n) is the least nontrivial exponent e such that the decimal representation of n is a substring of the decimal representation of n raised to the power of e. Given the input x_list (a series of values): [78, 79, 80, 81, 82, 83, 84, 85, 86, 87], determine the corresponding output sequence y_list.

Options:
A. [16, 8, 2, 13, 19, 11, 8, 28, 16, 4]
B. [19, 10, 4, 9, 12, 6, 11, 25, 19, 5]
C. [14, 6, 0, 15, 21, 2, 7, 30, 14, 2]
D. [22, 12, 6, 7, 15, 5, 12, 23, 23, 8]
E. [18, 9, 3, 8, 13, 7, 10, 24, 20, 6]
F. [23, 14, 8, 11, 17, 9, 14, 26, 18, 10]
G. [20, 13, 7, 10, 16, 8, 13, 21, 21, 9]
H. [21, 11, 5, 6, 14, 4, 11, 22, 22, 7]
I. [17, 15, 9, 12, 18, 10, 0, 27, 17, 11]
J. [15, 7, 1, 14, 20, 3, 9, 29, 15, 3]
Answer: H
We now define an algorithm: The definition of a(n) is the number of self-dual 2-colored necklaces with 2n beads, where a self-dual necklace is one that is identical to its reverse цвет pattern.\n Given the input x_list (a series of values): [27, 28, 29, 30, 31, 32, 33, 34, 35, 36], determine the corresponding output sequence y_list.

Options:
A. [1246000, 2400000, 4636000, 8956000, 17330000, 33570000, 65108000, 126355300, 245492200, 477284100]
B. [1240000, 2400000, 4630000, 8950000, 17300000, 33500000, 65100000, 126000000, 245000000, 477000000]
C. [1234567, 2398765, 4630000, 8954321, 17300000, 33560000, 65100000, 126355000, 245492000, 477284000]
D. [1246800, 2400800, 4636300, 8956000, 17334000, 33570000, 65108000, 126355000, 245492000, 477284000]
E. [1246860, 2400840, 4636390, 8956060, 17334800, 33570800, 65108060, 126355330, 245492240, 477284180]
F. [1246863, 2400842, 4636395, 8956065, 17334810, 33570817, 65108070, 126355340, 245492250, 477284185]
G. [1246800, 2400800, 4636000, 8956000, 17334000, 33570000, 65108000, 126000000, 245492000, 477284000]
H. [1200000, 2400000, 4630000, 8950000, 17300000, 33500000, 65100000, 126000000, 245000000, 477000000]
I. [1246863, 2400843, 4636390, 8956061, 17334801, 33570817, 65108062, 126355336, 245492245, 477284182]
J. [1246863, 2400842, 4636390, 8956060, 17334801, 33570816, 65108062, 126355336, 245492244, 477284182]
Answer: J
We now define an algorithm: The definition of a(n) is: Fundamental discriminants of real quadratic fields; indices of primitive positive Dirichlet L-series. Fundamental discriminants are discriminants of quadratic fields that are square-free and congruent to 0 or 1 mod 4. The discriminant of a quadratic field \\(\\mathbb{Q}(\\sqrt{d})\\) for a square-free integer \\(d\\) is \\(d\\) if \\(d \\equiv 1 (mod~4)\\) or \\(4d\\) if \\(d \\equiv 2, 3 (mod~4)\\). Given the input x_list (a series of values): [52, 53, 54, 55, 56, 57, 58, 59, 60, 61], determine the corresponding output sequence y_list.

Options:
A. [167, 172, 176, 180, 182, 185, 188, 193, 196, 198]
B. [166, 170, 173, 178, 181, 183, 187, 189, 193, 196]
C. [168, 172, 173, 177, 181, 184, 185, 188, 193, 197]
D. [170, 174, 176, 179, 183, 186, 188, 191, 195, 199]
E. [166, 171, 173, 176, 181, 184, 186, 189, 192, 194]
F. [165, 170, 172, 175, 178, 182, 185, 187, 191, 195]
G. [164, 168, 172, 177, 179, 183, 185, 188, 192, 196]
H. [169, 173, 175, 178, 182, 185, 187, 189, 194, 198]
I. [167, 171, 174, 176, 180, 183, 186, 190, 192, 196]
J. [163, 169, 175, 178, 181, 184, 186, 191, 194, 197]
Answer: C
We now define an algorithm: The definition of a(n) is the sum of odd Fermat coefficients rounded to the nearest integer. Given the input x_list (a series of values): [22, 23, 24, 25, 26, 27, 28, 29, 30, 31], determine the corresponding output sequence y_list.

Options:
A. [28196900, 70679142, 177487719, 446446565, 1124706149, 2837445504, 7167878632, 18129622765, 45907772904, 116372614255]
B. [28196896, 70679137, 177487714, 446446560, 1124706145, 2837445500, 7167878628, 18129622761, 45907772900, 116372614251]
C. [28196899, 70679141, 177487718, 446446564, 1124706148, 2837445503, 7167878631, 18129622764, 45907772903, 116372614254]
D. [28196898, 70679140, 177487717, 446446563, 1124706147, 2837445502, 7167878630, 18129622763, 45907772902, 116372614253]
E. [28196897, 70679139, 177487716, 446446562, 1124706146, 2837445501, 7167878629, 18129622762, 45907772901, 116372614252]
F. [28196895, 70679136, 177487713, 446446559, 1124706144, 2837445499, 7167878627, 18129622760, 45907772899, 116372614250]
G. [28196903, 70679145, 177487722, 446446568, 1124706153, 2837445507, 7167878635, 18129622768, 45907772907, 116372614258]
H. [28196902, 70679144, 177487721, 446446567, 1124706152, 2837445506, 7167878634, 18129622767, 45907772906, 116372614257]
I. [28196896, 70679138, 177487715, 446446561, 1124706150, 2837445510, 7167878638, 18129622770, 45907772910, 116372614261]
J. [28196901, 70679143, 177487720, 446446566, 1124706151, 2837445505, 7167878633, 18129622766, 45907772905, 116372614256]
Answer: B
We now define an algorithm: The definition of a(n) is: Kolakoski sequence: a(n) is the length of the n-th run in a self-describing sequence that consists only of 1's and 2's, starting with a(1) = 1. Given the input x_list (a series of values): [99, 100, 101, 102, 103, 104, 105, 106, 107, 108], determine the corresponding output sequence y_list.

Options:
A. [2, 1, 1, 2, 1, 2, 2, 1, 1, 2]
B. [1, 2, 2, 1, 2, 1, 1, 2, 1, 2]
C. [2, 2, 1, 2, 1, 1, 2, 1, 2, 2]
D. [1, 2, 2, 1, 2, 1, 2, 1, 2, 1]
E. [1, 2, 1, 1, 2, 1, 2, 2, 1, 2]
F. [2, 1, 2, 1, 1, 2, 2, 1, 2, 1]
G. [2, 1, 2, 2, 1, 1, 2, 1, 1, 2]
H. [1, 2, 1, 2, 2, 1, 1, 2, 2, 1]
I. [1, 1, 2, 1, 2, 2, 1, 2, 1, 2]
J. [2, 1, 1, 2, 2, 1, 2, 2, 1, 1]
Answer: C
We now define an algorithm: The definition of a(n) is the number of n-element posets which are unions of 2 chains, where a poset (partially ordered set) is defined as a set combined with a partial order, and a chain is a subset of the poset where every pair of elements is comparable. Given the input x_list (a series of values): [22, 23, 24, 25, 26, 27, 28, 29, 30, 31], determine the corresponding output sequence y_list.

Options:
A. [36320186415, 135548135850, 507434502469, 1904982684102, 7170113287578, 27051804890642, 102287657120458, 387558371409610, 1471212825012495, 5594771416613715]
B. [36320086420, 135548135853, 507434502471, 1904982684104, 7170113287576, 27051804890640, 102287657120456, 387558371409608, 1471212825012497, 5594771416613718]
C. [36320186416, 135548235851, 507434502477, 1904982684109, 7170113287571, 27051804890635, 102287657120451, 387558371409603, 1471212825012502, 5594771416613716]
D. [36320186418, 135548235854, 507434502475, 1904982684105, 7170113287575, 27051804890639, 102287657120453, 387558371409605, 1471212825012500, 5594771416613722]
E. [36320086419, 135548135855, 507434502473, 1904982684107, 7170113287573, 27051804890637, 102287657120455, 387558371409607, 1471212825012498, 5594771416613720]
F. [36320086418, 135548135854, 507434502474, 1904982684106, 7170113287574, 27051804890638, 102287657120454, 387558371409606, 1471212825012499, 5594771416613721]
G. [36320186414, 135548235848, 507434502479, 1904982684110, 7170113287570, 27051804890634, 102287657120450, 387558371409602, 1471212825012503, 5594771416613713]
H. [36320086421, 135548135852, 507434502470, 1904982684103, 7170113287577, 27051804890641, 102287657120457, 387558371409609, 1471212825012496, 5594771416613717]
I. [36320086422, 135548135849, 507434502468, 1904982684101, 7170113287579, 27051804890643, 102287657120459, 387558371409611, 1471212825012494, 5594771416613714]
J. [36320186417, 135548135856, 507434502476, 1904982684108, 7170113287572, 27051804890636, 102287657120452, 387558371409604, 1471212825012501, 5594771416613719]
Answer: F
We now define an algorithm: The definition of a(n) is the arithmetic mean of two consecutive balanced primes of order one. Given the input x_list (a series of values): [36, 37, 38, 39, 40, 41, 42, 43, 44, 45], determine the corresponding output sequence y_list.

Options:
A. [4525, 4625, 4673, 4840, 5048, 5108, 5206, 5343, 5388, 5475]
B. [4515, 4615, 4660, 4832, 5042, 5102, 5202, 5332, 5382, 5462]
C. [4530, 4630, 4680, 4850, 5060, 5120, 5210, 5350, 5400, 5480]
D. [4534, 4634, 4678, 4848, 5056, 5116, 5214, 5351, 5396, 5484]
E. [4520, 4620, 4670, 4830, 5040, 5100, 5200, 5340, 5390, 5470]
F. [4550, 4640, 4690, 4860, 5070, 5130, 5230, 5370, 5415, 5500]
G. [4522, 4622, 4672, 4838, 5046, 5106, 5204, 5341, 5380, 5468]
H. [4518, 4618, 4666, 4835, 5045, 5105, 5205, 5335, 5385, 5465]
I. [4540, 4635, 4685, 4855, 5065, 5125, 5225, 5360, 5410, 5490]
J. [4527, 4627, 4674, 4842, 5050, 5110, 5208, 5345, 5390, 5478]
Answer: J
We now define an algorithm: The definition of a(n) is: Array A(n, k) = lunar sum n + k (n >= 0, k >= 0) read by antidiagonals. Given the input x_list (a series of values): [87, 88, 89, 90, 91, 92, 93, 94, 95, 96], determine the corresponding output sequence y_list.

Options:
A. [13, 16, 15, 16, 17, 16, 16, 17, 13, 12]
B. [9, 12, 11, 12, 13, 12, 12, 13, 9, 8]
C. [5, 8, 7, 8, 9, 8, 8, 9, 5, 4]
D. [6, 9, 8, 9, 10, 9, 9, 10, 6, 5]
E. [10, 13, 12, 13, 14, 13, 13, 14, 10, 9]
F. [12, 15, 14, 15, 16, 15, 15, 16, 12, 11]
G. [8, 11, 10, 11, 12, 11, 11, 12, 8, 7]
H. [7, 10, 9, 10, 11, 10, 10, 11, 7, 6]
I. [11, 14, 13, 14, 15, 14, 14, 15, 11, 10]
J. [14, 17, 16, 17, 18, 17, 17, 18, 14, 13]
Answer: B
We now define an algorithm: The definition of a(n) is generated by a sieve: keep the first number (0), drop every 2nd number, keep the new first number (1), drop every 3rd number, keep the new first number (3), drop every 4th number, and so on. Given the input x_list (a series of values): [48, 49, 50, 51, 52, 53, 54, 55, 56, 57], determine the corresponding output sequence y_list.

Options:
A. [784, 806, 844, 874, 922, 934, 994, 1006, 1058, 1072]
B. [781, 803, 841, 871, 919, 931, 991, 1003, 1055, 1069]
C. [775, 797, 835, 865, 913, 925, 985, 997, 1049, 1063]
D. [783, 805, 843, 873, 921, 933, 993, 1005, 1057, 1071]
E. [778, 800, 838, 868, 916, 928, 988, 1000, 1052, 1066]
F. [780, 802, 840, 870, 918, 930, 990, 1002, 1054, 1068]
G. [777, 799, 837, 867, 915, 927, 987, 999, 1051, 1065]
H. [782, 804, 842, 872, 920, 932, 992, 1004, 1056, 1070]
I. [779, 801, 839, 869, 917, 929, 989, 1001, 1053, 1067]
J. [776, 798, 836, 866, 914, 926, 986, 998, 1050, 1064]
Answer: I
We now define an algorithm: The definition of a(n) is a unique monotonic sequence of nonnegative integers satisfying a(a(n)) = 3n, where "monotonic" implies the sequence is either entirely non-decreasing or non-increasing. Given the input x_list (a series of values): [58, 59, 60, 61, 62, 63, 64, 65, 66, 67], determine the corresponding output sequence y_list.

Options:
A. [94, 97, 100, 103, 106, 109, 112, 115, 118, 121]
B. [88, 91, 94, 97, 100, 103, 106, 109, 112, 115]
C. [90, 93, 96, 99, 102, 105, 108, 111, 114, 117]
D. [87, 90, 93, 96, 99, 102, 105, 108, 111, 114]
E. [93, 96, 99, 102, 105, 108, 111, 114, 117, 120]
F. [96, 99, 102, 105, 108, 111, 114, 117, 120, 123]
G. [95, 98, 101, 104, 107, 110, 113, 116, 119, 122]
H. [92, 95, 98, 101, 104, 107, 110, 113, 116, 119]
I. [91, 94, 97, 100, 103, 106, 109, 112, 115, 118]
J. [89, 92, 95, 98, 101, 104, 107, 110, 113, 116]
Answer: E
We now define an algorithm: The definition of a(n) is: Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime. These are primes that do not form a twin prime pair with another prime number. Given the input x_list (a series of values): [45, 46, 47, 48, 49, 50, 51, 52, 53, 54], determine the corresponding output sequence y_list.

Options:
A. [478, 484, 492, 498, 500, 508, 540, 546, 556, 564]
B. [480, 486, 490, 500, 502, 510, 542, 548, 558, 562]
C. [474, 492, 498, 503, 508, 516, 544, 542, 559, 567]
D. [477, 488, 494, 496, 504, 512, 539, 549, 553, 565]
E. [479, 487, 491, 499, 503, 509, 541, 547, 557, 563]
F. [476, 489, 495, 501, 505, 507, 537, 544, 554, 566]
G. [483, 486, 494, 497, 499, 515, 535, 547, 556, 564]
H. [482, 483, 489, 495, 506, 513, 538, 550, 555, 569]
I. [481, 485, 493, 497, 501, 511, 543, 545, 559, 561]
J. [475, 490, 496, 502, 507, 514, 536, 548, 546, 568]
Answer: E
We now define an algorithm: The definition of a(n) is the Jordan function J_2(n), a generalization of Euler's totient function phi(n), which is used in number theory to count the number of certain types of lattice points within an n-dimensional space. Given the input x_list (a series of values): [39, 40, 41, 42, 43, 44, 45, 46, 47, 48], determine the corresponding output sequence y_list.

Options:
A. [1144, 1452, 1680, 1352, 1848, 1440, 1828, 1584, 2208, 1536]
B. [1244, 1152, 1780, 1252, 1848, 1440, 1728, 1584, 2108, 1536]
C. [1344, 1252, 1580, 1352, 1748, 1440, 1728, 1684, 2108, 1636]
D. [1344, 1152, 1680, 1152, 1848, 1440, 1728, 1584, 2208, 1536]
E. [1244, 1352, 1580, 1152, 1848, 1340, 1728, 1484, 2208, 1536]
F. [1144, 1252, 1780, 1352, 1948, 1440, 1628, 1584, 2008, 1636]
G. [1244, 1252, 1780, 1252, 1748, 1540, 1628, 1484, 2108, 1636]
H. [1444, 1352, 1580, 1252, 1948, 1340, 1728, 1684, 2008, 1436]
I. [1444, 1152, 1680, 1252, 1848, 1540, 1828, 1684, 2108, 1436]
J. [1344, 1352, 1680, 1152, 1948, 1440, 1728, 1684, 2208, 1536]
Answer: D
We now define an algorithm: The definition of a(n) is: Numbers whose ternary expansion contains no 1's. Ternary expansion is the representation of a number in base 3. In this context, ensure that the digits in the base 3 representation are only 0's and 2's. Given the input x_list (a series of values): [47, 48, 49, 50, 51, 52, 53, 54, 55, 56], determine the corresponding output sequence y_list.

Options:
A. [560, 564, 646, 650, 654, 656, 664, 668, 672, 676]
B. [562, 564, 649, 651, 653, 657, 665, 667, 673, 675]
C. [561, 567, 649, 651, 653, 657, 665, 667, 673, 679]
D. [565, 567, 649, 651, 655, 657, 667, 668, 670, 674]
E. [560, 562, 646, 652, 653, 655, 665, 667, 673, 675]
F. [563, 565, 647, 649, 653, 657, 667, 669, 671, 675]
G. [563, 565, 648, 650, 653, 655, 667, 669, 671, 673]
H. [561, 563, 647, 651, 653, 655, 665, 669, 671, 673]
I. [564, 566, 648, 650, 654, 656, 666, 668, 672, 674]
J. [566, 568, 648, 650, 654, 656, 668, 670, 674, 676]
Answer: I
We now define an algorithm: The definition of a(n) is the sequence obtained by applying the inverse Moebius transform twice to the sequence of perfect squares. Given the input x_list (a series of values): [32, 33, 34, 35, 36, 37, 38, 39, 40, 41], determine the corresponding output sequence y_list.

Options:
A. [1916, 1253, 1844, 1375, 2653, 1464, 2179, 1783, 2922, 1781]
B. [1717, 1455, 1845, 1374, 2654, 1367, 2279, 1784, 2923, 1784]
C. [2819, 1252, 1642, 1278, 2655, 1472, 2075, 1878, 3125, 1589]
D. [1819, 1251, 1743, 1378, 2755, 1272, 2175, 1780, 3226, 1689]
E. [1915, 1453, 1745, 1370, 2756, 1273, 2073, 1785, 3127, 1685]
F. [1918, 1354, 1645, 1275, 2856, 1463, 2277, 1982, 3025, 1583]
G. [1818, 1353, 1746, 1377, 2754, 1371, 2178, 1881, 3024, 1683]
H. [2019, 1452, 1744, 1177, 2657, 1374, 2076, 1879, 2723, 1483]
I. [2018, 1255, 1843, 1276, 2649, 1372, 2177, 1984, 3022, 1582]
J. [1817, 1350, 1643, 1379, 2855, 1269, 2176, 1983, 2921, 1682]
Answer: G
We now define an algorithm: The definition of a(n) is the sequence of consecutive internal states generated by the IMSL pseudo-random number generator RNUN when it is initialized with the seed ISEED=1. Given the input x_list (a series of values): [16, 17, 18, 19, 20, 21, 22, 23, 24, 25], determine the corresponding output sequence y_list.

Options:
A. [214807987, 2237522503, 2441282327, 26531729, 923378840, 243542612, 996544303, 2474833169, 2264817709, 2998097157]
B. [114807987, 1137522513, 1441292327, 1531729, 823378840, 163542612, 823544303, 1714833169, 1944817709, 1798091557]
C. [111807987, 1177522503, 1401282327, 16931729, 853378850, 14542612, 496544303, 1874833169, 1364817709, 1928097157]
D. [16140798, 107522503, 441282327, 651729, 2378840, 7342612, 96544303, 84833169, 481776709, 98097157]
E. [114807987, 1137522503, 1441282327, 16531729, 823378840, 143542612, 896544303, 1474833169, 1264817709, 1998097157]
F. [214803987, 1337522503, 1741182327, 15531729, 933378840, 134542612, 196514303, 1614853169, 1564317709, 1498887157]
G. [117807987, 1337522503, 1111282327, 16531792, 844378840, 543542612, 1236544303, 184833169, 1464817709, 188097157]
H. [12807987, 1137522503, 11344282327, 1631729, 803378840, 113542612, 89654433, 4724833169, 1764817709, 1498097157]
I. [104807987, 1037522503, 1341282327, 7531729, 723378840, 93542612, 796544303, 174833169, 1264817709, 198097157]
J. [124807987, 1397522503, 1241282327, 16531719, 831178840, 24542612, 896547303, 174831169, 1764817709, 2224567157]
Answer: E
We now define an algorithm: The definition of a(n) is the number of elements at distance n in the Cayley graph of the modular group with a standard generating set. Given the input x_list (a series of values): [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], determine the corresponding output sequence y_list.

Options:
A. [98765, 87654, 76543, 65432, 54321, 43210, 32109, 21098, 10987, 9876]
B. [67890, 78901, 89012, 90123, 12345, 23456, 34567, 45678, 56789, 67890]
C. [24680, 35791, 46802, 57913, 68024, 79135, 80246, 91357, 102468, 113579]
D. [12345, 23456, 34567, 45678, 56789, 67890, 78901, 89012, 90123, 12345]
E. [11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111110]
F. [98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152]
G. [54321, 65432, 76543, 87654, 98765, 109876, 120987, 131098, 142109, 153210]
H. [192837, 293847, 394857, 495867, 596877, 697887, 798897, 899907, 910017, 1011127]
I. [13579, 24680, 35791, 46802, 57913, 68024, 79135, 80246, 91357, 102468]
J. [112233, 223344, 334455, 445566, 556677, 667788, 778899, 889900, 990011, 1001222]
Answer: F
We now define an algorithm: The definition of a(n) is the length of the longest chain of subgroups in the symmetric group S_n, where S_n denotes the group of all permutations on n elements. Given the input x_list (a series of values): [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], determine the corresponding output sequence y_list.

Options:
A. [45, 46, 47, 53, 54, 55, 56, 58, 59, 60]
B. [72, 73, 74, 80, 81, 82, 83, 85, 86, 87]
C. [96, 97, 98, 104, 105, 106, 107, 109, 110, 111]
D. [39, 40, 41, 47, 48, 49, 50, 52, 53, 54]
E. [92, 93, 94, 100, 101, 102, 103, 105, 106, 107]
F. [86, 87, 88, 94, 95, 96, 97, 99, 100, 101]
G. [56, 57, 58, 64, 65, 66, 67, 69, 70, 71]
H. [82, 83, 84, 90, 91, 92, 93, 95, 96, 97]
I. [66, 67, 68, 74, 75, 76, 77, 79, 80, 81]
J. [76, 77, 78, 84, 85, 86, 87, 89, 90, 91]
Answer: F
We now define an algorithm: The definition of a(n) is the number of equivalence classes of Boolean functions of n variables under the action of the symmetry group that consists of all variable permutations and negations. Given the input x_list (a series of values): [17, 18, 19, 20, 21, 22, 23, 24, 25, 26], determine the corresponding output sequence y_list.

Options:
A. [3221225472, 12884901824, 51539607680, 206158430208, 824633720896, 3298534883328, 13194139561984, 52776558133248, 211106232532992, 844424930131968]
B. [10737428224, 42949644800, 171798691840, 687194779136, 2748779069440, 10995116277760, 43980465111040, 175921860444160, 703687441776640, 2814749767106560]
C. [12884901888, 51539607552, 206499606528, 825741107200, 3302943238144, 13211565581952, 52846339645440, 211385485844480, 845095942815744, 3380383776894976]
D. [1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465066496]
E. [8589934592, 34359738368, 137438953472, 549755813888, 2199023255552, 8796093022208, 35184372072448, 140737488495616, 562949953421312, 2251799813685248]
F. [7340032000, 29360128000, 117440512000, 469762048000, 1879048192000, 7516192768000, 30064771072000, 120259084288000, 481036337152000, 1924145348608000]
G. [2147483648, 8589934592, 34359738368, 137438953472, 549755813888, 2199023255552, 8796093022208, 35184372072448, 140737488495616, 562949953421312]
H. [4295032832, 17180000256, 68719738880, 274878431232, 1099512676352, 4398048608256, 17592190238720, 70368752566272, 281474993487872, 1125899940397056]
I. [5368709120, 21474836544, 85899345920, 343597384704, 1374389531648, 5497558165504, 21990232586240, 87960930345984, 351843721416704, 1407374883553280]
J. [6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465065984, 1688849860263936]
Answer: H
We now define an algorithm: The definition of a(n) is the dimensions of the n-th multiple of the minimal representation of the complex Lie algebra E7. Given the input x_list (a series of values): [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], determine the corresponding output sequence y_list.

Options:
A. [96265194240, 354992859975, 1369301331000, 4642249264625, 15473017267200, 46398364338250, 143897996890800, 392822534859750, 1139290591104000, 2854459117589400]
B. [87265194239, 345992859974, 1279301330999, 4442249264624, 14573017267199, 45398364338249, 134897996890799, 383822534859749, 1049290591103999, 2764459117589399]
C. [86265194240, 344992859975, 1269301331000, 4432249264625, 14573017267100, 45298364338250, 133897996890800, 382822534859750, 1039290591104000, 2754459117589400]
D. [87265194241, 345992859976, 1279301331001, 4442249264626, 14573017267201, 45398364338251, 134897996890801, 383822534859751, 1049290591104001, 2764459117589401]
E. [77265194240, 335992859975, 1179301331000, 4142249264625, 13573017267200, 43398364338250, 124897996890800, 373822534859750, 964290591104000, 2564459117589400]
F. [97265194240, 355992859975, 1379301331000, 4742249264625, 15573017267200, 47398364338250, 144897996890800, 393822534859750, 1149290591104000, 2864459117589400]
G. [74265194240, 315992859975, 1079301331000, 4042249264625, 12573017267200, 41398364338250, 114897996890800, 353822534859750, 924290591104000, 2364459117589400]
H. [87265194240, 345992859975, 1279301331000, 4442249264625, 14573017267200, 45398364338250, 134897996890800, 383822534859750, 1049290591104000, 2764459117589400]
I. [87265194238, 345992859974, 1279301330998, 4442249264623, 14573017267198, 45398364338248, 134897996890798, 383822534859748, 1049290591103998, 2764459117589398]
J. [88265194241, 346992859976, 1289301331001, 4452249264626, 14673017267201, 45498364338251, 135897996890801, 384822534859751, 1059290591104001, 2774459117589401]
Answer: H
We now define an algorithm: The definition of a(n) is the number of rooted trees with leaves colored using two different colors (e.g., red and blue). Each tree must have at least one leaf of each color. Given the input x_list (a series of values): [19, 20, 21, 22, 23, 24, 25, 26, 27, 28], determine the corresponding output sequence y_list.

Options:
A. [774226545, 2758043730, 9862357694, 35387662263, 127374191686, 459783039105, 1664042970920, 6037070913562, 21951214425143, 79981665585026]
B. [774226552, 2758043724, 9862357693, 35387662260, 127374191683, 459783039103, 1664042970917, 6037070913563, 21951214425147, 79981665585024]
C. [774226554, 2758043722, 9862357691, 35387662269, 127374191681, 459783039110, 1664042970915, 6037070913565, 21951214425138, 79981665585027]
D. [774226546, 2758043729, 9862357695, 35387662264, 127374191689, 459783039107, 1664042970923, 6037070913560, 21951214425142, 79981665585025]
E. [774226550, 2758043726, 9862357696, 35387662261, 127374191685, 459783039104, 1664042970919, 6037070913559, 21951214425145, 79981665585031]
F. [774226553, 2758043723, 9862357692, 35387662268, 127374191682, 459783039102, 1664042970916, 6037070913564, 21951214425139, 79981665585032]
G. [774226549, 2758043727, 9862357697, 35387662266, 127374191687, 459783039109, 1664042970924, 6037070913558, 21951214425140, 79981665585029]
H. [774226555, 2758043721, 9862357690, 35387662267, 127374191680, 459783039101, 1664042970914, 6037070913566, 21951214425137, 79981665585022]
I. [774226551, 2758043725, 9862357699, 35387662262, 127374191684, 459783039106, 1664042970918, 6037070913561, 21951214425144, 79981665585028]
J. [774226548, 2758043728, 9862357698, 35387662265, 127374191688, 459783039108, 1664042970925, 6037070913557, 21951214425141, 79981665585030]
Answer: G
We now define an algorithm: The definition of a(n) is the triangle of the number of rooted trees with \\( n \\ge 2 \\) nodes and a given height \\( h \\ge 1 \\), formatted such that the entry T(n, h) represents the number of rooted trees with exactly \\( n \\) nodes and height \\( h \\). Given the input x_list (a series of values): [58, 59, 60, 61, 62, 63, 64, 65, 66, 67], determine the corresponding output sequence y_list.

Options:
A. [56, 510, 1199, 1322, 942, 488, 187, 52, 9, 2]
B. [52, 515, 1195, 1313, 936, 482, 195, 57, 15, 6]
C. [54, 508, 1197, 1324, 940, 486, 189, 54, 11, 0]
D. [59, 506, 1210, 1300, 948, 492, 186, 50, 12, 4]
E. [51, 512, 1208, 1340, 943, 493, 182, 55, 13, 5]
F. [55, 509, 1198, 1323, 941, 487, 188, 53, 10, 1]
G. [53, 501, 1201, 1299, 921, 480, 191, 56, 18, 8]
H. [60, 503, 1189, 1327, 930, 495, 180, 58, 16, 7]
I. [57, 507, 1190, 1330, 945, 490, 185, 51, 8, 3]
J. [61, 500, 1175, 1345, 950, 485, 179, 59, 19, 9]
Answer: F
We now define an algorithm: The definition of a(n) is the number of hexagonal (hex) trees with n edges and no branches of length 1. Hex trees are a type of spanning tree used in graph theory, often visualized within a hexagonal lattice structure, ensuring that no single edge forms a branch of just one edge length. Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [214525024, 865041613, 3502806370, 14237599842, 58069495195, 237583710556, 974819569102, 4010205424876, 16536842688274, 68344258564987]
B. [214525022, 865041611, 3502806368, 14237599840, 58069495193, 237583710554, 974819569100, 4010205424874, 16536842688272, 68344258564985]
C. [214525021, 865041610, 3502806367, 14237599839, 58069495192, 237583710553, 974819569099, 4010205424873, 16536842688271, 68344258564984]
D. [214525018, 865041607, 3502806364, 14237599836, 58069495189, 237583710550, 974819569096, 4010205424870, 16536842688268, 68344258564981]
E. [214525025, 865041614, 3502806371, 14237599843, 58069495196, 237583710557, 974819569103, 4010205424877, 16536842688275, 68344258564988]
F. [214525019, 865041608, 3502806365, 14237599837, 58069495190, 237583710551, 974819569097, 4010205424871, 16536842688269, 68344258564982]
G. [214525026, 865041615, 3502806372, 14237599844, 58069495197, 237583710558, 974819569104, 4010205424878, 16536842688276, 68344258564989]
H. [214525023, 865041612, 3502806369, 14237599841, 58069495194, 237583710555, 974819569101, 4010205424875, 16536842688273, 68344258564986]
I. [214525017, 865041606, 3502806363, 14237599635, 58069495188, 237583710549, 974819569095, 4010205424869, 16536842688267, 68344258564980]
J. [214525020, 865041609, 3502806366, 14237599838, 58069495191, 237583710552, 974819569098, 4010205424872, 16536842688270, 68344258564983]
Answer: I
We now define an algorithm: The definition of a(n) is the number of rooted connected graphs where every block is a complete graph. A block is a maximal connected subgraph without a cut-vertex, and a complete graph is a simple undirected graph in which a unique edge connects every pair of distinct vertices. Given the input x_list (a series of values): [16, 17, 18, 19, 20, 21, 22, 23, 24, 25], determine the corresponding output sequence y_list.

Options:
A. [28486075, 108809501, 417862339, 1612440611, 6248778650, 24309992574, 94905791604, 371691137829, 1459935388205, 5749666477459]
B. [28486074, 108809502, 417862344, 1612440614, 6248778645, 24309992575, 94905791609, 371691137825, 1459935388204, 5749666477458]
C. [28486079, 108809510, 417862334, 1612440606, 6248778636, 24309992568, 94905791600, 371691137822, 1459935388209, 5749666477463]
D. [28486070, 108809505, 417862342, 1612440610, 6248778640, 24309992578, 94905791608, 371691137829, 1459935388200, 5749666477456]
E. [28486072, 108809504, 417862341, 1612440613, 6248778643, 24309992577, 94905791607, 371691137828, 1459935388203, 5749666477455]
F. [28486078, 108809509, 417862336, 1612440607, 6248778637, 24309992569, 94905791601, 371691137823, 1459935388208, 5749666477462]
G. [28486077, 108809508, 417862337, 1612440608, 6248778638, 24309992570, 94905791602, 371691137830, 1459935388207, 5749666477461]
H. [28486076, 108809507, 417862338, 1612440609, 6248778639, 24309992573, 94905791603, 371691137824, 1459935388206, 5749666477460]
I. [28486073, 108809506, 417862343, 1612440615, 6248778644, 24309992579, 94905791605, 371691137826, 1459935388201, 5749666477457]
J. [28486071, 108809503, 417862340, 1612440612, 6248778642, 24309992576, 94905791606, 371691137827, 1459935388202, 5749666477454]
Answer: J
We now define an algorithm: The definition of a(n) is the number of 2-matchings of the n X n grid graph. In graph theory, a k-matching is a set of k independent edges, meaning no two edges share a common vertex. Here, we specifically refer to 2-matchings, which are sets of 2 independent edges in the n X n grid graph. Given the input x_list (a series of values): [27, 28, 29, 30, 31, 32, 33, 34, 35, 36], determine the corresponding output sequence y_list.

Options:
A. [980900, 1137950, 1313150, 1507850, 1723450, 1961350, 2223050, 2510150, 2824050, 3166550]
B. [981050, 1137960, 1313180, 1507880, 1723460, 1961360, 2223060, 2510160, 2824060, 3166570]
C. [981100, 1137990, 1313160, 1507890, 1723490, 1961390, 2223090, 2510090, 2824090, 3166590]
D. [980852, 1137944, 1313174, 1507886, 1723472, 1961372, 2223074, 2510114, 2824076, 3166592]
E. [980700, 1137930, 1313130, 1507830, 1723430, 1961330, 2223030, 2510030, 2824030, 3166530]
F. [980800, 1137900, 1313100, 1507800, 1723400, 1961300, 2223000, 2510000, 2824000, 3166500]
G. [980902, 1137952, 1313152, 1507852, 1723452, 1961352, 2223052, 2510052, 2824052, 3166552]
H. [980750, 1137920, 1313120, 1507820, 1723420, 1961320, 2223020, 2510020, 2824020, 3166520]
I. [981000, 1138000, 1313200, 1507900, 1723500, 1961400, 2223100, 2510100, 2824100, 3166600]
J. [980650, 1137970, 1313140, 1507840, 1723440, 1961340, 2223080, 2510040, 2824040, 3166540]
Answer: D
We now define an algorithm: The definition of a(n) is the number of series-parallel networks with n unlabeled edges, where a series-parallel network is a two-terminal graph that can be constructed from a single edge by recursively applying two operations: series composition and parallel composition. These networks are also referred to as yoke-chains by Cayley and MacMahon. Given the input x_list (a series of values): [18, 19, 20, 21, 22, 23, 24, 25, 26, 27], determine the corresponding output sequence y_list.

Options:
A. [47633487, 156047204, 513477403, 1696305727, 5623993943, 18706733127, 62408176763, 208769240139, 700129713629, 2353386723913]
B. [47833486, 156147204, 513477602, 1695305728, 5622993944, 18606733128, 63408176762, 209769240140, 690129713630, 2353286723912]
C. [46633486, 156037204, 503477402, 1697305728, 5624993944, 18706733118, 61408176762, 208879240140, 700219713630, 2353486723912]
D. [47633486, 156047204, 513477502, 1696305728, 5623993944, 18706733128, 62408176762, 208769240140, 700129713630, 2353386723912]
E. [47633476, 156047104, 513477402, 1696306728, 5623993945, 18706733129, 62408176761, 208769240141, 700129713631, 2353386723911]
F. [49633486, 166037204, 553477502, 1596305728, 5823993944, 17706733128, 63408176762, 198769240140, 720129713630, 2253386723912]
G. [48632486, 158047204, 503477502, 1606305728, 5523993944, 16706733128, 60408176762, 188769240140, 730129713630, 2153386723912]
H. [47632486, 150047204, 513477402, 1686305728, 5624993944, 18716733128, 62418176762, 208869240140, 700119713630, 2353286723912]
I. [45632486, 146042304, 523477502, 1796305728, 5723993944, 19706733128, 61408176762, 218769240140, 710129713630, 2453386723912]
J. [47633488, 156047203, 513477501, 1696305729, 5623993945, 18706733129, 62408176764, 208769240141, 700129713632, 2353386723910]
Answer: D
There are two types of Darwin's finches, whose beak shape and size show significant differences within the same distribution area. However, in different distribution areas, the beaks of the two types exhibit similar shapes and sizes. Which option provides the most reasonable theoretical explanation for this phenomenon?

Options:
A. Convergent evolution pressure
B. Adaptive radiation theory
C. Gradient Group
D. Genetic drift hypothesis
E. Niche Differentiation
F. Likelihood Competition
G. Sympatric speciation model
H. Mutual interference and competition
I. Evolutionary parallelism
J. Phenotypic plasticity dynamics
Answer: E
Which of the following statements about Spirogyra is incorrect?

Options:
A. The chloroplasts of Spirogyra are long and ribbon-shaped, coiled in a spiral pattern.
B. The life cycle of Spirogyra involves gametic meiosis.
C. Spirogyra forms roots to anchor itself to substrates.
D. Spirogyra reproduces asexually only through sporulation.
E. The life cycle of Spirogyra includes binary fission exclusively.
F. The sexual reproduction of Spirogyra is conjugation.
G. Spirogyra is an unbranched filamentous organism.
H. The chloroplasts of Spirogyra are spherical and randomly arranged.
I. The life cycle of Spirogyra involves vegetative meiosis stages.
J. Spirogyra uses pollination for sexual reproduction purposes.
Answer: B
Which of the following statements about the emergence of eukaryotic cells is incorrect?

Options:
A. The origin of eukaryotic cells triggered the elimination of complex multicellular forms.
B. The origin of eukaryotic cells facilitated the formation of the tri-polar ecosystem of animals, plants, and fungi.
C. The origin of eukaryotic cells induced the breakdown of ecological networks and ecosystems.
D. The origin of eukaryotic cells laid the foundation for the emergence of sexual reproduction.
E. The origin of eukaryotic cells favored the dissolution of genetic material into simplified states.
F. The origin of eukaryotic cells drove the diversification of animals and plants.
G. The origin of eukaryotic cells resulted in the loss of intracellular compartmentalization.
H. The origin of eukaryotic cells led to the simplification of organism structures and the convergence of functions.
I. The origin of eukaryotic cells promoted the independence of organelles and halted collaboration.
J. The origin of eukaryotic cells caused the decline of metabolic diversity in organisms.
Answer: H
What is the most important meristem for plants to complete their life cycle?

Options:
A. Secondary Xylem Tissue
B. Vascular Cambium
C. Axillary Meristem Zone
D. Apical meristem
E. Root Cap Meristem
F. Primary Meristem Tissue
G. Epidermal Growth Meristem
H. Lateral Meristem
I. Intercalary Meristem
J. Cambial Layer Tissue
Answer: H
The ascending limb of the nephron loop in a certain child is permeable to water due to a genetic mutation. What is the most likely minimum/maximum urinary osmolarity (mmol/L)?

Options:
A. 300/300
B. 300/1000
C. 200/300
D. 100/100
E. 300/1200
F. 100/1200
G. 1200/1200
H. 500/500
I. 100/300
J. 1200/100
Answer: A
What is the most obvious trait used to determine whether small animals are adapted to arid environments in the given options?

Options:
A. Bone Density
B. The Structure of the Nasal Cavity
C. The Morphology of the Digestive Tract
D. The Size of Ears
E. Body Color
F. Brown Adipose Tissue
G. Basal Metabolic Rate
Answer: B
Which of the following descriptions about niche theory is incorrect?

Options:
A. Environmental pressure can cause species to narrow their realized niche.
B. When lacking competitors, a species can expand its realized niche.
C. Niche overlap typically leads to intensified competition among species.
D. Niche shifts typically occur during periods of significant environmental change.
E. Niche differentiation can reduce conflicts between competitors.
F. Niche refers to the position of a population in terms of time and space within a system, as well as its functional relationships with related populations.
G. Mutualistic symbiosis tends to expand the fundamental niche.
H. Species with strong adaptability typically expand their fundamental niche.
I. The ecological niche of a species can change with its development.
J. Population dynamics can alter the niche breadth of a species.
Answer: G
Scientists have determined the osmotic pressure of the living environment, blood, and urine of a certain fish species, measured in degrees of freezing-point depression. The results are 1.85, 0.8, and 0.7, respectively. What is the most likely type of fish?

Options:
A. Angelfish
B. Grass Carp
C. Shark
D. Catfish
E. Ribbonfish
F. Goldfish
G. Trout
H. Carp
I. Salmon
J. Halibut
Answer: E
A week prior to the long-distance transportation of fish fry, which of the following procedures can most effectively enhance their survival rate during transportation?

Options:
A. Herbal Bath
B. Change Water Temperature
C. Increase Aeration Time
D. Dragnet Training
E. Inject oxygen into the nursery pond.
F. Frequent Feeding
G. Use Synthetic Hormones
H. Reduce Water Level
I. Aerate the nursery pond
J. Add Salt to Water
Answer: D
If your living room, having a volume of $6 m \times 6m \times 3m \approx 100 m^{3}$, were perfectly insulated, how much energy would be needed to raise the temperature inside the room from $T_{\mathrm{i n i t i a l}}=0^{\circ} \mathrm{C}$ to $T_{\mathrm{f i n a l}}=2 5^{\circ} \mathrm{C}$ ? Note that $C_{V}=C_{p}$ - n$R$. for an ideal gas.

Options:
A. $$
4 7 0 \ \mathrm{k c a l}
$$
B. $$
4 6 0 \ \mathrm{k c a l}
$$
C. $$
5 0 8 \ \mathrm{k c a l}
$$
D. $$
5 2 0 \ \mathrm{k c a l}
$$
E. $$
4 8 5 \ \mathrm{k c a l}
$$
F. $$
5 6 0 \ \mathrm{k c a l}
$$
G. $$
4 9 2 \ \mathrm{k c a l}
$$
H. $$
4 7 8 \ \mathrm{k c a l}
$$
I. $$
5 3 5 \ \mathrm{k c a l}
$$
J. $$
5 5 0 \ \mathrm{k c a l}
$$
Answer: C
What is the translational entropy for carbon monoxide CO (C has mass $m=1 2$ amu, O has mass $m=1 6 \, \mathrm{a m u} )$ at $T=3 0 0 \, \mathrm{K}, \, p=1$ atm?

Options:
A. $$
1 4 7. 3 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
B. $$
1 5 4. 6 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
C. $$
1 5 8. 2 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
D. $$
1 4 9. 8 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
E. $$
1 5 0. 3 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}
$$
F. $$
1 4 5. 9 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
G. $$
1 5 2. 1 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
H. $$
1 6 3. 5 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
I. $$
1 4 2. 7 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
J. $$
1 6 0. 7 \; {\frac{\mathrm{J}} {\mathrm{K \; m o l}}}$$
Answer: E
Freezing temperature depression is a usefu the molecular weights of some molecules. One g of protein of molecular weight 100, 000 $\mathrm{g} \ \mathrm{m o l}^{-1}$ is in 1 g of water. What is the freezing temperature of the solution?

Options:
A. $$
0 . 0 1 5 2 \mathrm{~ K}
$$
B. $$
0 . 0 1 2 0 \mathrm{~ K}
$$
C. $$
0 . 0 0 6 3 \mathrm{~ K}
$$
D. $$
0 . 0 0 9 8 \mathrm{~ K}
$$
E. $$
0 . 0 1 8 9 \mathrm{~ K}
$$
F. $$
0 . 0 1 4 5 \mathrm{~ K}
$$
G. $$
0 . 0 2 0 1 \mathrm{~ K}
$$
H. $$
0 . 0 2 3 7 \mathrm{~ K}
$$
I. $$
0. 0 1 1 4 \mathrm{~ K}
$$
J. $$
0 . 0 0 7 6 \mathrm{~ K}
$$
Answer: I
842 emal loy aow o aecriaicontnihinelecrmobliyawevo $1. 2 \times1 0^{7}$ (Q-m) and 0.0050 m?r's, respectively $A$ curentof4 spased thougha specimen t his aly thtis 5 m thick What mageticfied wouded obeimpasd io yied Hal voluwe f $- 3. 5 \times1 0^{-7}$ V?

Options:
A. $$
3. 6 5 0 \mathrm{~ t e s l a}
$$
B. $$
5. 3 7 5 \mathrm{~ t e s l a}
$$
C. $$
1. 2 5 0 \mathrm{~ t e s l a}
$$
D. $$
0. 7 3 5 \mathrm{~ t e s l a}
$$
E. $$
0. 8 5 1 \mathrm{~ t e s l a}
$$
F. $$
2. 8 4 0 \mathrm{~ t e s l a}
$$
G. $$
4. 1 5 0 \mathrm{~ t e s l a}
$$
H. $$
1. 9 8 0 \mathrm{~ t e s l a}
$$
I. $$
0. 6 2 5 \mathrm{~ t e s l a}
$$
J. $$
0. 4 9 0 \mathrm{~ t e s l a}
$$
Answer: D
Which of the following is the most likely cause of a buzzing sound when a beginner snare drum student plays fast?

Options:
A. The student is playing multiple strokes on the drum.
B. The student is hammering the drumstick onto the drum.
C. The student is dropping the drumstick onto the drum.
D. The student is playing single strokes on the drum.
Answer: B
Which option matches the following scale?
L:1/4
M:none
K:C
^C,4 | D,4 | E,4 | ^F,4 | G,4 | A,4 | B,4 | ^C4 |] %8

Options:
A. Dorian mode with Si as the leading tone
B. Locrian mode with Sol as the dominant tone
C. Phrygian mode with ♯F as the VI degree
D. Phrygian mode with D as the II degree
Answer: B
Which of the following is NOT a main characteristic of Debussy's musical compositions?

Options:
A. Frequently using parallel chords; Often using whole-tone scales
B. Mainly using the twelve-tone technique for pitch logic; Highly chromatic harmony; Often using whole-tone scales
C. Mainly using the twelve-tone technique for pitch logic; Often using whole-tone scales
D. Frequently using parallel chords; Mainly using the twelve-tone technique for pitch logic; Highly chromatic harmony; Often using whole-tone scales
Answer: A