MikaStars39/nano-eval huggingface dataset:
We now define an algorithm: The definition of a(n) is shifts left when INVERT transform applied thrice. An INVERT transform, in basic terms, rearranges the sequence according to a specific permutation pattern. Given the input x_list (a series of values): [13, 14, 15, 16, 17, 18, 19, 20, 21, 22], determine the corresponding output sequence y_list.

Options:
A. [1373830307, 9004186191, 67015411391, 356192767396, 3122028221934, 21467779499863, 158246598341017, 1027656662676600, 7148589698592955, 49884563176689583]
B. [1573830308, 9905186192, 67015411393, 556192667396, 3122028122934, 21467769499864, 148246598241118, 1027656663576600, 7148588697992956, 49884553176689564]
C. [1473839308, 9904187192, 68015401391, 456192667496, 3122028223934, 21467769488864, 148246598349018, 1027656663677600, 7148588699592956, 49884553176689594]
D. [1473833308, 9903186192, 67015420391, 456162667396, 3122028223934, 21467769599864, 148246598341438, 1027656663673600, 7148588698591956, 49884553176689284]
E. [1473831308, 9904186192, 67015411391, 456182667396, 3122028232934, 21467769499844, 148246598341018, 1027656663876600, 7148588698592956, 49882553176689584]
F. [1473831308, 9904286192, 67014501391, 256192567396, 3122028221934, 21467769499874, 148256598341018, 1027656664676600, 7148588697792956, 49884553176689684]
G. [1473840308, 8904186190, 57015401392, 456192767396, 2122028222934, 21467769489864, 118246598341019, 92756663676600, 8148588698592956, 59884553176689584]
H. [1473830308, 9904186192, 67015401391, 456192667396, 3122028222934, 21467769499864, 148246598341018, 1027656663676600, 7148588698592956, 49884553176689584]
I. [2383830309, 9805186193, 67015391391, 556192567396, 3122029222934, 21467759499865, 138246598241018, 1027656664676601, 7148587698592957, 49884543176689585]
J. [1473810308, 9903156192, 67015411392, 456192667797, 3122028222944, 21467769497864, 148246598341918, 1027656663876600, 7148588698593956, 49884553176689574]
Answer: H
We now define an algorithm: The definition of a(n) is: Let Cn(x) be the n-th cyclotomic polynomial; a(n) is the least positive integer k > 1 such that the evaluation of Cn(k) yields a prime number. Given the input x_list (a series of values): [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], determine the corresponding output sequence y_list.

Options:
A. [19, 63, 39, 9, 4, 4, 6, 7, 4, 4]
B. [22, 60, 42, 6, 3, 3, 9, 4, 3, 3]
C. [27, 55, 47, 15, 10, 10, 14, 10, 10, 10]
D. [23, 59, 43, 11, 6, 6, 10, 3, 6, 6]
E. [25, 57, 45, 13, 8, 8, 12, 1, 8, 8]
F. [20, 62, 40, 8, 1, 1, 7, 6, 1, 1]
G. [18, 64, 38, 10, 5, 5, 5, 8, 5, 5]
H. [24, 58, 44, 12, 7, 7, 11, 2, 7, 7]
I. [21, 61, 41, 7, 2, 2, 8, 5, 2, 2]
J. [26, 56, 46, 14, 9, 9, 13, 9, 9, 9]
Answer: I
We now define an algorithm: The definition of a(n) is: Sorting numbers: the number of comparisons needed for merge insertion sort when sorting n elements, a method combining merge sort and insertion sort. 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. [215, 221, 227, 233, 239, 245, 251, 257, 263, 269]
B. [207, 213, 219, 225, 231, 237, 243, 249, 255, 261]
C. [213, 219, 225, 231, 237, 243, 249, 255, 261, 267]
D. [211, 217, 223, 229, 235, 241, 247, 253, 259, 265]
E. [201, 207, 213, 219, 225, 231, 237, 243, 249, 255]
F. [199, 205, 211, 217, 223, 229, 235, 241, 247, 253]
G. [197, 203, 209, 215, 221, 227, 233, 239, 245, 251]
H. [203, 209, 215, 221, 227, 233, 239, 245, 251, 257]
I. [209, 215, 221, 227, 233, 239, 245, 251, 257, 263]
J. [205, 211, 217, 223, 229, 235, 241, 247, 253, 259]
Answer: E
We now define an algorithm: The definition of a(n) is: Continued fraction representation for the sum of the infinite series Sum_{n>=0} 1/2^(2^n) = 0.8164215090218931... Given the input x_list (a series of values): [89, 90, 91, 92, 93, 94, 95, 96, 97, 98], determine the corresponding output sequence y_list.

Options:
A. [7, 5, 3, 2, 6, 5, 5, 3, 7, 4]
B. [2, 4, 6, 2, 8, 4, 4, 6, 2, 4]
C. [1, 2, 3, 6, 1, 2, 3, 9, 2, 5]
D. [9, 5, 4, 7, 9, 8, 5, 4, 7, 5]
E. [2, 5, 3, 7, 2, 5, 7, 3, 2, 5]
F. [8, 6, 4, 2, 8, 6, 4, 5, 8, 4]
G. [3, 9, 2, 3, 5, 1, 5, 9, 3, 2]
H. [8, 7, 5, 3, 9, 7, 5, 3, 8, 9]
I. [6, 4, 2, 4, 6, 4, 4, 2, 6, 4]
J. [5, 3, 1, 6, 5, 3, 7, 1, 4, 6]
Answer: I
We now define an algorithm: The definition of a(n) is the number of ternary search trees that can be formed using n distinct keys, where a ternary search tree is a type of tree data structure used for locating specific keys from within a set. Given the input x_list (a series of values): [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], determine the corresponding output sequence y_list.

Options:
A. [587689948, 1850692503, 5845013530, 18509607750, 58759391015, 186958014762, 596108115401, 1904387243799, 6095040222190, 19540540075822]
B. [587689940, 1850692499, 5845013540, 18509607800, 58759391020, 186958014760, 596108115400, 1904387243795, 6095040222195, 19540540075820]
C. [587689947, 1850692506, 5845013538, 18509607753, 58759391013, 186958014766, 596108115402, 1904387243796, 6095040222192, 19540540075824]
D. [587689949, 1850692504, 5845013539, 18509607754, 58759391014, 186958014761, 596108115404, 1904387243793, 6095040222191, 19540540075826]
E. [587689944, 1850692502, 5845013535, 18509607756, 58759391019, 186958014763, 596108115406, 1904387243794, 6095040222194, 19540540075823]
F. [587689945, 1850692501, 5845013531, 18509607751, 58759391016, 186958014767, 596108115400, 1904387243797, 6095040222196, 19540540075829]
G. [587689946, 1850692505, 5845013537, 18509607755, 58759391011, 186958014765, 596108115405, 1904387243792, 6095040222189, 19540540075827]
H. [587689941, 1850692507, 5845013536, 18509607752, 58759391018, 186958014764, 596108115398, 1904387243798, 6095040222193, 19540540075825]
I. [587689943, 1850692498, 5845013534, 18509607757, 58759391017, 186958014768, 596108115403, 1904387243790, 6095040222197, 19540540075821]
J. [587689950, 1850692500, 5845013533, 18509607802, 58759391012, 186958014766, 596108115399, 1904387243791, 6095040222188, 19540540075828]
Answer: C
We now define an algorithm: The definition of a(n) is the reversion transform of x*(x - 1)^2/(1 - x + x^3). 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. [68437032, 287910046, 1217627175, 5173854025, 22077273855, 94564541168, 406451008388, 1752472631366, 7577758539860, 32852955892195]
B. [68437029, 287910035, 1217627165, 5173854008, 22077273808, 94564541162, 406451008382, 1752472631358, 7577758539828, 32852955892189]
C. [68437040, 287910060, 1217627190, 5173854030, 22077273870, 94564541175, 406451008395, 1752472631375, 7577758539880, 32852955892220]
D. [68437025, 287910030, 1217627160, 5173854005, 22077273790, 94564541155, 406451008375, 1752472631340, 7577758539780, 32852955892170]
E. [68437028, 287910044, 1217627174, 5173854009, 22077273820, 94564541161, 406451008381, 1752472631354, 7577758539818, 32852955892188]
F. [68437030, 287910040, 1217627170, 5173854015, 22077273850, 94564541165, 406451008385, 1752472631362, 7577758539840, 32852955892185]
G. [68437033, 287910048, 1217627176, 5173854018, 22077273858, 94564541166, 406451008386, 1752472631360, 7577758539846, 32852955892191]
H. [68437031, 287910042, 1217627172, 5173854012, 22077273812, 94564541164, 406451008383, 1752472631364, 7577758539842, 32852955892192]
I. [68437035, 287910050, 1217627180, 5173854020, 22077273860, 94564541170, 406451008390, 1752472631365, 7577758539850, 32852955892200]
J. [68437021, 287910036, 1217627164, 5173854010, 22077273800, 94564541160, 406451008380, 1752472631350, 7577758539800, 32852955892180]
Answer: G
We now define an algorithm: The definition of a(n) is the number of 3 X n binary matrices that avoid simultaneously the right-angled numbered polyomino patterns (ranpp) (00;1) and (11;0). Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [11534336, 23068672, 46137344, 92274680, 184549354, 369098736, 738197498, 1476394988, 2952790018, 5905580008]
B. [11534332, 23068654, 46137340, 92274678, 184549356, 369098746, 738197484, 1476395004, 2952790014, 5905580016]
C. [11534324, 23068660, 46137332, 92274676, 184549364, 369098740, 738197492, 1476394996, 2952790004, 5905580020]
D. [11534340, 23068674, 46137346, 92274660, 184549350, 369098734, 738197482, 1476394984, 2952790020, 5905580014]
E. [11534330, 23068668, 46137338, 92274666, 184549370, 369098744, 738197486, 1476395000, 2952790000, 5905580024]
F. [11534320, 23068658, 46137330, 92274670, 184549362, 369098730, 738197490, 1476394990, 2952790002, 5905580010]
G. [11534328, 23068662, 46137328, 92274672, 184549368, 369098738, 738197496, 1476394998, 2952790008, 5905580022]
H. [11534322, 23068664, 46137334, 92274668, 184549366, 369098742, 738197494, 1476394992, 2952790010, 5905580018]
I. [11534326, 23068666, 46137336, 92274674, 184549360, 369098748, 738197488, 1476395002, 2952790006, 5905580026]
J. [11534338, 23068670, 46137326, 92274664, 184549352, 369098732, 738197480, 1476394986, 2952790012, 5905580028]
Answer: C
We now define an algorithm: The definition of a(n) is the expansion of the square root of 2 in base 2. Given the input x_list (a series of values): [90, 91, 92, 93, 94, 95, 96, 97, 98, 99], determine the corresponding output sequence y_list.

Options:
A. [1, 0, 1, 1, 0, 0, 1, 1, 0, 1]
B. [0, 0, 1, 0, 1, 1, 0, 0, 1, 0]
C. [1, 1, 0, 1, 1, 0, 0, 1, 0, 1]
D. [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
E. [0, 0, 1, 1, 0, 0, 1, 1, 0, 1]
F. [1, 0, 1, 0, 1, 1, 1, 0, 0, 1]
G. [0, 1, 0, 0, 1, 1, 1, 0, 1, 0]
H. [1, 0, 0, 1, 1, 0, 0, 1, 0, 0]
I. [0, 1, 1, 0, 0, 1, 1, 0, 1, 1]
J. [1, 1, 0, 0, 1, 0, 1, 1, 0, 0]
Answer: I
We now define an algorithm: The definition of a(n) is the nth term of the sequence formed by reading the triangle T(n,k), where T(n,k) represents the coefficients of the Lucas (or Cardan) polynomials, row by row, from left to right. Given the input x_list (a series of values): [65, 66, 67, 68, 69, 70, 71, 72, 73, 74], determine the corresponding output sequence y_list.

Options:
A. [14, 89, 276, 451, 377, 139, 14, 0, 15, 103]
B. [13, 88, 277, 452, 376, 138, 13, 3, 14, 102]
C. [15, 90, 275, 450, 378, 140, 15, 1, 16, 104]
D. [18, 93, 272, 447, 381, 143, 18, 6, 19, 107]
E. [17, 92, 273, 448, 380, 142, 17, 4, 18, 106]
F. [11, 86, 279, 454, 374, 136, 11, 7, 12, 100]
G. [19, 94, 271, 446, 382, 144, 19, 8, 20, 108]
H. [10, 85, 280, 455, 373, 135, 10, 9, 11, 99]
I. [12, 87, 278, 453, 375, 137, 12, 5, 13, 101]
J. [16, 91, 274, 449, 379, 141, 16, 2, 17, 105]
Answer: C
We now define an algorithm: The definition of a(n) is square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of the inverse of the k-th cyclotomic polynomial. Given the input x_list (a series of values): [95, 96, 97, 98, 99, 100, 101, 102, 103, 104], determine the corresponding output sequence y_list.

Options:
A. [-1, -1, 0, 0, 1, 0, 0, 0, 0, 1]
B. [1, 0, 0, 0, -1, -1, -1, 0, 0, 0]
C. [0, 1, -1, 0, 0, 0, 0, 1, -1, 0]
D. [1, 0, 0, 0, 1, 0, -1, -1, 0, 0]
E. [0, -1, 1, 0, 0, 0, -1, 0, 0, -1]
F. [0, 1, 0, 0, 0, -1, -1, 0, 1, 0]
G. [-1, 0, 0, -1, 0, 1, 0, 0, 1, 0]
H. [1, 0, 0, -1, 0, 0, 1, 0, -1, 0]
I. [0, 0, 0, 1, 0, 0, -1, -1, -1, 0]
J. [0, 0, 1, 0, -1, 0, 0, -1, 0, 0]
Answer: I
We now define an algorithm: The definition of a(n) is the number of comparisons needed for Batcher's odd-even mergesort algorithm when applied to sort 2^n items. This algorithm is a parallel comparison-based sorting algorithm that minimizes the number of comparisons. 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. [488636416, 1069547518, 2332033029, 5066719230, 10972299269, 23689428990, 51002736636, 109521666046, 234612588541, 501437431809]
B. [488636414, 1069547517, 2332033027, 5066719235, 10972299264, 23689428989, 51002736635, 109521666043, 234612588538, 501437431803]
C. [488636417, 1069547515, 2332033029, 5066719239, 10972299261, 23689428996, 51002736633, 109521666044, 234612588537, 501437431801]
D. [488636415, 1069547519, 2332033023, 5066719231, 10972299263, 23689428991, 51002736639, 109521666047, 234612588543, 501437431807]
E. [488636412, 1069547523, 2332033020, 5066719238, 10972299260, 23689428994, 51002736630, 109521666042, 234612588549, 501437431812]
F. [488636421, 1069547524, 2332033022, 5066719237, 10972299268, 23689428993, 51002736631, 109521666049, 234612588548, 501437431805]
G. [488636420, 1069547520, 2332033024, 5066719236, 10972299262, 23689428992, 51002736640, 109521666048, 234612588544, 501437431808]
H. [488636413, 1069547516, 2332033026, 5066719232, 10972299266, 23689428995, 51002736638, 109521666041, 234612588539, 501437431804]
I. [488636418, 1069547522, 2332033026, 5066719234, 10972299266, 23689428994, 51002736642, 109521666050, 234612588546, 501437431810]
J. [488636419, 1069547521, 2332033028, 5066719233, 10972299267, 23689428988, 51002736637, 109521666040, 234612588540, 501437431806]
Answer: D
We now define an algorithm: The definition of a(n) is the coefficients of x^n in the Hermite polynomial $H_{n+4}$. Hermite polynomials $H_n(x)$ are a classical orthogonal polynomial sequence that are used in probability, physics, and numerical analysis, defined by the recurrence relation $H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}(x)$ with initial conditions $H_0(x) = 1$ and $H_1(x) = 2x$. 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. [1524105221, 3810263051, 9413591051, 23011000351, 55710842891, 133706022921, 318347673621, 752458137621, 1766640844821, 4122161971221]
B. [1524105217, 3810263041, 9413591041, 23011000321, 55710842881, 133706022913, 318347673601, 752458137601, 1766640844801, 4122161971201]
C. [1524105220, 3810263050, 9413591050, 23011000350, 55710842890, 133706022920, 318347673620, 752458137620, 1766640844820, 4122161971220]
D. [1524105223, 3810263053, 9413591053, 23011000353, 55710842893, 133706022923, 318347673623, 752458137623, 1766640844823, 4122161971223]
E. [1524105225, 3810263055, 9413591055, 23011000355, 55710842895, 133706022925, 318347673625, 752458137625, 1766640844825, 4122161971225]
F. [1524105226, 3810263056, 9413591056, 23011000356, 55710842896, 133706022926, 318347673626, 752458137626, 1766640844826, 4122161971226]
G. [1524105215, 3810263039, 9413591039, 23011000319, 55710842879, 133706022911, 318347673599, 752458137599, 1766640844799, 4122161971199]
H. [1524105228, 3810263058, 9413591058, 23011000358, 55710842898, 133706022928, 318347673628, 752458137628, 1766640844828, 4122161971228]
I. [1524105216, 3810263040, 9413591040, 23011000320, 55710842880, 133706022912, 318347673600, 752458137600, 1766640844800, 4122161971200]
J. [1524105230, 3810263060, 9413591060, 23011000360, 55710842900, 133706022930, 318347673630, 752458137630, 1766640844830, 4122161971230]
Answer: I
We now define an algorithm: The definition of a(n) is: Safe primes p: (p-1)/2 is also prime, meaning both p and (p-1)/2 are prime numbers. Given the input x_list (a series of values): [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], determine the corresponding output sequence y_list.

Options:
A. [2067, 2103, 2211, 2451, 2463, 2583, 2823, 2883, 2907, 2967]
B. [2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963]
C. [2072, 2108, 2216, 2456, 2468, 2588, 2828, 2888, 2912, 2972]
D. [2069, 2105, 2213, 2453, 2465, 2585, 2825, 2885, 2909, 2969]
E. [2064, 2100, 2208, 2448, 2460, 2580, 2820, 2880, 2904, 2964]
F. [2070, 2106, 2214, 2454, 2466, 2586, 2826, 2886, 2910, 2970]
G. [2068, 2104, 2212, 2452, 2464, 2584, 2824, 2884, 2908, 2968]
H. [2071, 2107, 2215, 2455, 2467, 2587, 2827, 2887, 2911, 2971]
I. [2066, 2102, 2210, 2450, 2462, 2582, 2822, 2882, 2906, 2966]
J. [2065, 2111, 2209, 2449, 2461, 2581, 2821, 2881, 2905, 2965]
Answer: B
We now define an algorithm: The definition of a(n) is: Signature-permutation of a Catalan automorphism. Reflect a rooted plane binary tree, and consider Deutsch's 1998 involution on Dyck paths. Given the input x_list (a series of values): [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], determine the corresponding output sequence y_list.

Options:
A. [37, 28, 25, 24, 23, 196, 195, 194, 190, 189]
B. [37, 29, 24, 26, 22, 199, 196, 193, 191, 188]
C. [39, 27, 26, 22, 21, 197, 198, 193, 192, 188]
D. [36, 28, 25, 23, 21, 199, 198, 193, 191, 187]
E. [38, 28, 26, 23, 24, 197, 196, 194, 191, 188]
F. [39, 28, 27, 22, 23, 195, 197, 195, 192, 190]
G. [38, 30, 25, 23, 21, 198, 195, 194, 191, 189]
H. [37, 27, 26, 25, 22, 194, 195, 196, 192, 189]
I. [36, 29, 24, 25, 22, 195, 196, 193, 191, 190]
J. [35, 30, 27, 24, 23, 198, 197, 195, 189, 191]
Answer: A
We now define an algorithm: The definition of a(n) is the number of dyslexic planted planar trees with n nodes, where a dyslexic planted planar tree is a rooted tree embedded in the plane that is indistinguishable if its left and right children are swapped. 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. [21068877928, 70133571795, 234043258805, 782831380624, 2624022529695, 8813080348892, 29654400681972, 99953565213651, 337447946046901, 1140961171059557]
B. [21068877925, 70133571796, 234043258803, 782831380628, 2624022529689, 8813080348896, 29654400681968, 99953565213647, 337447946046905, 1140961171059561]
C. [21068877929, 70133571799, 234043258806, 782831380622, 2624022529696, 8813080348891, 29654400681973, 99953565213652, 337447946046900, 1140961171059556]
D. [21068877923, 70133571800, 234043258800, 782831380625, 2624022529693, 8813080348894, 29654400681970, 99953565213649, 337447946046903, 1140961171059559]
E. [21068877935, 70133571717, 234043258872, 782831380726, 2624022529650, 8813080348997, 29654400681876, 99953565213625, 337447946046906, 1140961171059564]
F. [21068877924, 70133571798, 234043258801, 782831380627, 2624022529692, 8813080348895, 29654400681969, 99953565213648, 337447946046904, 1140961171059560]
G. [21068877926, 70133571797, 234043258802, 782831380626, 2624022529691, 8813080348898, 29654400681967, 99953565213646, 337447946046907, 1140961171059562]
H. [21068877927, 70133571794, 234043258804, 782831380623, 2624022529694, 8813080348893, 29654400681971, 99953565213650, 337447946046902, 1140961171059558]
I. [21068877930, 70133571793, 234043258807, 782831380621, 2624022529697, 8813080348890, 29654400681974, 99953565213653, 337447946046909, 1140961171059555]
J. [21068877925, 70133571797, 234043258802, 782831380626, 2624022529690, 8813080348897, 29654400681966, 99953565213645, 337447946046906, 1140961171059563]
Answer: J
We now define an algorithm: The definition of a(n) is: Left Fibonacci row-sum array, where each row represents the sum of a subset of Fibonacci numbers from the sequence, starting from n >= 0 and summing for 0 <= k <= n. 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. [17, 34, 59, 66, 39, 9, 3, 3, 3, 4]
B. [15, 30, 55, 60, 35, 12, 2, 2, 2, 3]
C. [18, 35, 58, 67, 38, 11, 0, 0, 0, 1]
D. [23, 37, 50, 65, 29, 3, 9, 9, 9, 0]
E. [20, 36, 56, 68, 34, 7, 5, 5, 5, 7]
F. [19, 31, 54, 62, 36, 8, 4, 4, 4, 5]
G. [14, 38, 52, 69, 31, 5, 7, 7, 7, 8]
H. [16, 32, 57, 64, 37, 10, 1, 1, 1, 2]
I. [21, 33, 53, 63, 32, 6, 6, 6, 6, 6]
J. [22, 39, 51, 61, 30, 4, 8, 8, 8, 9]
Answer: H
We now define an algorithm: The definition of a(n) is given by the Hurwitz-Radon function evaluated at powers of 2. This function is significant in various areas of number theory and algebra, particularly in the context of quadratic forms and Clifford algebras. Given the input x_list (a series of values): [53, 54, 55, 56, 57, 58, 59, 60, 61, 62], determine the corresponding output sequence y_list.

Options:
A. [102, 108, 113, 114, 116, 117, 120, 121, 124, 125]
B. [106, 108, 112, 113, 114, 116, 120, 121, 122, 124]
C. [106, 107, 111, 114, 115, 118, 121, 123, 125, 126]
D. [104, 109, 113, 115, 116, 119, 120, 122, 123, 126]
E. [107, 108, 110, 114, 115, 117, 119, 123, 125, 126]
F. [106, 109, 111, 115, 116, 119, 120, 123, 124, 127]
G. [105, 109, 112, 115, 116, 118, 120, 122, 124, 126]
H. [105, 109, 111, 113, 115, 116, 119, 122, 123, 127]
I. [105, 108, 112, 113, 117, 118, 121, 123, 124, 125]
J. [104, 107, 110, 113, 115, 117, 119, 121, 123, 125]
Answer: B
We now define an algorithm: The definition of a(n) is the number of partitions of n of the form a_1*b_1^2 + a_2*b_2^2 + ...; number of semisimple rings with p^n elements for any prime p. 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. [53442, 65943, 81423, 100036, 122991, 150481, 184149, 224448, 273617, 332290]
B. [53447, 65943, 81422, 100034, 122990, 150482, 184150, 224450, 273613, 332292]
C. [53448, 65940, 81425, 100035, 122989, 150479, 184151, 224447, 273616, 332289]
D. [53443, 65944, 81424, 100030, 122988, 150480, 184148, 224447, 273614, 332289]
E. [53449, 65945, 81420, 100036, 122988, 150478, 184152, 224446, 273617, 332288]
F. [53446, 65942, 81423, 100033, 122991, 150481, 184149, 224449, 273614, 332291]
G. [53440, 65944, 81421, 100031, 122993, 150483, 184147, 224451, 273612, 332293]
H. [53441, 65939, 81419, 100029, 122987, 150477, 184153, 224445, 273618, 332287]
I. [58346, 66542, 82523, 100133, 123091, 151481, 185149, 225449, 274614, 333291]
J. [53445, 65941, 81424, 100032, 122992, 150480, 184148, 224448, 273615, 332290]
Answer: F
We now define an algorithm: The definition of a(n) is the integers which, when written in binary form, contain exactly one or two bits set to 1. Given the input x_list (a series of values): [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], determine the corresponding output sequence y_list.

Options:
A. [528, 544, 576, 640, 768, 1024, 1025, 1026, 1028, 1032]
B. [529, 545, 577, 641, 769, 1025, 1026, 1027, 1029, 1033]
C. [527, 543, 575, 639, 767, 1023, 1024, 1025, 1027, 1031]
D. [531, 547, 579, 643, 771, 1027, 1028, 1029, 1031, 1035]
E. [524, 540, 572, 636, 764, 1020, 1021, 1022, 1024, 1028]
F. [525, 541, 573, 637, 765, 1021, 1022, 1023, 1025, 1029]
G. [530, 546, 578, 642, 770, 1026, 1027, 1028, 1030, 1034]
H. [526, 542, 574, 638, 766, 1022, 1023, 1024, 1026, 1030]
I. [523, 539, 571, 635, 763, 1019, 1020, 1021, 1023, 1027]
J. [532, 548, 580, 644, 772, 1028, 1029, 1030, 1032, 1036]
Answer: A
We now define an algorithm: The definition of a(n) is: Square array A(x,y), read by antidiagonals, where A(x,y) = 0 if (x AND y) = 0, otherwise A(x,y) = 1+A(x XOR y, 2*(x AND y)). Given the input x_list (a series of values): [110, 111, 112, 113, 114, 115, 116, 117, 118, 119], determine the corresponding output sequence y_list.

Options:
A. [0, 1, 0, 1, 1, 0, 1, 0, 1, 0]
B. [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
C. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
D. [1, 0, 1, 1, 0, 1, 0, 1, 0, 0]
E. [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
F. [1, 0, 0, 1, 0, 0, 1, 0, 0, 1]
G. [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
H. [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
I. [1, 0, 0, 0, 1, 0, 0, 0, 1, 0]
J. [1, 1, 0, 1, 0, 1, 0, 1, 0, 1]
Answer: B
We now define an algorithm: The definition of a(n) is the CIK (necklace, indistinct, unlabeled) transform of the sequence 1, 2, 3, 4,... 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. [4600205, 11442087, 28527440, 71292599, 178526885, 447919416, 1125750149, 2833906685, 7144450560, 18036423975]
B. [4600217, 11442073, 28527441, 71292604, 178526880, 447919419, 1125750130, 2833906680, 7144450569, 18036423976]
C. [4600207, 11442089, 28527442, 71292607, 178526887, 447919410, 1125750141, 2833906687, 7144450562, 18036423977]
D. [4600201, 11442085, 28527446, 71292603, 178526881, 447919418, 1125750145, 2833906683, 7144450566, 18036423973]
E. [4600213, 11442077, 28527438, 71292597, 178526893, 447919417, 1125750153, 2833906684, 7144450565, 18036423972]
F. [4600215, 11442075, 28527439, 71292602, 178526882, 447919411, 1125750120, 2833906686, 7144450563, 18036423970]
G. [4600219, 11442071, 28527443, 71292608, 178526884, 447919415, 1125750125, 2833906688, 7144450567, 18036423978]
H. [4600203, 11442083, 28527448, 71292601, 178526883, 447919420, 1125750143, 2833906681, 7144450568, 18036423971]
I. [4600209, 11442081, 28527444, 71292609, 178526889, 447919412, 1125750147, 2833906689, 7144450564, 18036423979]
J. [4600211, 11442079, 28527436, 71292605, 178526891, 447919414, 1125750151, 2833906682, 7144450561, 18036423974]
Answer: D
We now define an algorithm: The definition of a(n) is the product of three positive integer solutions of the Diophantine equation \\( x^3 - y^3 = z^2 \\). Given the input x_list (a series of values): [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], determine the corresponding output sequence y_list.

Options:
A. [7285000000, 14195000000, 26095000000, 45695000000, 76795000000, 124380000000, 195470000000, 298770000000, 445770000000, 650770000000]
B. [7310000000, 14220000000, 26120000000, 45720000000, 76820000000, 124430000000, 195530000000, 298830000000, 445830000000, 650830000000]
C. [7290000000, 14190000000, 26080000000, 45660000000, 76750000000, 124370000000, 195450000000, 298750000000, 445750000000, 650725000000]
D. [7270000000, 14180000000, 26070000000, 45650000000, 76700000000, 124350000000, 195400000000, 298700000000, 445700000000, 650700000000]
E. [7300000000, 14200000000, 26100000000, 45700000000, 76800000000, 124400000000, 195500000000, 298800000000, 445800000000, 650800000000]
F. [7260000000, 14170000000, 26060000000, 45640000000, 76650000000, 124340000000, 195390000000, 298660000000, 445600000000, 650600000000]
G. [7305000000, 14210000000, 26110000000, 45710000000, 76850000000, 124410000000, 195510000000, 298810000000, 445810000000, 650810000000]
H. [7295000000, 14203000000, 26103000000, 45703000000, 76803000000, 124390000000, 195480000000, 298790000000, 445790000000, 650790000000]
I. [7280000000, 14186660488, 26085556224, 45680920376, 76741030912, 124385625000, 195421011968, 298726553944, 445696183296, 650738625992]
J. [7275000000, 14185000000, 26075000000, 45675000000, 76725000000, 124360000000, 195420000000, 298720000000, 445720000000, 650720000000]
Answer: I
We now define an algorithm: The definition of a(n) is: "Magic" integers: a(n+1) is the smallest integer m such that there is no overlap between the sets {m, m-a(i), m+a(i): 1 <= i <= n} and {a(i), a(i)-a(j), a(i)+a(j): 1 <= j < i <= n}, where a(i) represents the previously defined terms of the sequence. 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. [4533, 4771, 4898, 5022, 5377, 5834, 6212, 6498, 6709, 7223]
B. [4513, 4791, 4878, 5002, 5357, 5814, 6192, 6478, 6689, 7203]
C. [4573, 4742, 4938, 5062, 5417, 5874, 6252, 6538, 6749, 7263]
D. [4583, 4731, 4948, 5072, 5427, 5884, 6262, 6548, 6759, 7273]
E. [4543, 4761, 4908, 5032, 5387, 5844, 6222, 6508, 6719, 7233]
F. [4563, 4741, 4928, 5052, 5407, 5864, 6242, 6528, 6739, 7253]
G. [4613, 4701, 4978, 5102, 5457, 5914, 6292, 6578, 6789, 7293]
H. [4523, 4781, 4888, 5012, 5367, 5824, 6202, 6488, 6699, 7213]
I. [4593, 4721, 4958, 5082, 5437, 5894, 6272, 6558, 6769, 7283]
J. [4553, 4751, 4918, 5042, 5397, 5854, 6232, 6518, 6729, 7243]
Answer: F
We now define an algorithm: The definition of a(n) is the sequence of integers representing the first column of the spectral array W(sqrt(2)), which arises in the study of the spectral properties of recurrent sequences connected to quadratic irrationalities. Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [113, 115, 117, 118, 121, 123, 125, 127, 128, 131]
B. [322, 324, 326, 329, 331, 333, 336, 338, 341, 343]
C. [1046, 1048, 1050, 1053, 1055, 1057, 1060, 1062, 1065, 1067]
D. [941, 943, 945, 948, 950, 952, 955, 957, 960, 962]
E. [528, 530, 532, 535, 537, 539, 542, 544, 547, 549]
F. [839, 841, 843, 846, 848, 850, 853, 855, 858, 860]
G. [424, 426, 428, 431, 433, 435, 438, 440, 443, 445]
H. [736, 738, 740, 743, 745, 747, 750, 752, 755, 757]
I. [216, 218, 220, 223, 225, 227, 230, 232, 235, 237]
J. [632, 634, 636, 639, 641, 643, 646, 648, 651, 653]
Answer: A
We now define an algorithm: The definition of a(n) is: Nearest integer to the imaginary part of the n-th nontrivial zero of the Riemann zeta function, listed with positive imaginary parts in ascending order. Given the input x_list (a series of values): [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], determine the corresponding output sequence y_list.

Options:
A. [141, 144, 145, 148, 149, 151, 154, 156, 157, 159]
B. [140, 143, 144, 147, 148, 150, 153, 155, 156, 158]
C. [147, 150, 151, 154, 155, 157, 160, 162, 163, 165]
D. [143, 146, 147, 150, 151, 153, 156, 158, 159, 161]
E. [139, 142, 143, 146, 147, 149, 152, 154, 155, 157]
F. [145, 148, 149, 152, 153, 155, 158, 160, 161, 163]
G. [142, 145, 146, 149, 150, 152, 155, 157, 158, 160]
H. [144, 147, 148, 151, 152, 154, 157, 159, 160, 162]
I. [148, 151, 152, 155, 156, 158, 161, 163, 164, 166]
J. [146, 149, 150, 153, 154, 156, 159, 161, 162, 164]
Answer: D
We now define an algorithm: The definition of a(n) is Lucas and Lehmer numbers with parameters (1 ± sqrt(-7))/2, represented as a sequence. 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. [-84915, 104399, 364129, -24599, -753227, -703889, 802105, 2209943, 605513, -3814373]
B. [95873, -204576, 375912, 27649, 763028, 714120, -811876, -2212754, -606764, 3875223]
C. [-84919, 194599, 374229, -24769, -753047, -713889, 802185, 2208943, 605613, -3814272]
D. [-84912, 194369, 364239, -24561, -753127, -703789, 801165, 2209941, 605603, -3814263]
E. [-74715, 194309, 365129, -24579, -752127, -703879, 802125, 2209947, 605612, -3814275]
F. [-84915, 194399, 364229, -24569, -753027, -703889, 802165, 2209943, 605613, -3814273]
G. [-84815, 194299, 363229, -24549, -752927, -703889, 802165, 2209942, 605613, -3814263]
H. [-75815, 204786, 364919, 23659, -754127, -703999, 802265, 2219353, 604713, -3813278]
I. [-75915, 204799, 376229, 23469, -752027, -704889, 802175, 2209843, 605673, -3815283]
J. [-85915, 194409, 365229, -24549, -753137, -703989, 803165, 2209944, 605623, -3814283]
Answer: F
We now define an algorithm: The definition of a(n) is the "class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes, which classifies primes based on certain properties related to their factorization and divisors. Given the input x_list (a series of values): [96, 97, 98, 99, 100, 101, 102, 103, 104, 105], determine the corresponding output sequence y_list.

Options:
A. [3, 3, 2, 3, 2, 2, 4, 2, 2, 1]
B. [2, 2, 4, 3, 3, 2, 1, 2, 2, 4]
C. [3, 3, 5, 3, 1, 4, 5, 2, 3, 2]
D. [3, 3, 2, 3, 2, 2, 5, 3, 3, 2]
E. [5, 5, 4, 5, 4, 4, 7, 5, 5, 4]
F. [2, 2, 1, 2, 1, 1, 4, 2, 2, 1]
G. [4, 4, 3, 4, 3, 3, 6, 4, 4, 3]
H. [2, 2, 5, 4, 4, 2, 2, 3, 3, 5]
I. [1, 1, 3, 2, 2, 3, 2, 1, 1, 3]
J. [4, 4, 6, 3, 5, 3, 3, 4, 4, 5]
Answer: D
We now define an algorithm: The definition of a(n) is integers expressible as sums of distinct even-subscripted Fibonacci numbers, where even-subscripted Fibonacci numbers are those in the Fibonacci sequence that appear at even positions (F(0), F(2), F(4), etc.). 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. [204, 210, 211, 213, 217, 222, 223, 226, 229, 232]
B. [205, 209, 212, 213, 222, 223, 225, 226, 230, 231]
C. [200, 208, 213, 216, 217, 222, 223, 228, 229, 230]
D. [206, 209, 213, 214, 217, 220, 224, 225, 231, 233]
E. [204, 206, 209, 215, 216, 222, 224, 230, 231, 233]
F. [208, 209, 214, 215, 218, 219, 222, 225, 226, 232]
G. [207, 208, 210, 211, 220, 221, 223, 224, 228, 229]
H. [202, 207, 211, 214, 217, 219, 221, 225, 227, 232]
I. [201, 207, 209, 214, 221, 222, 226, 227, 230, 232]
J. [203, 206, 209, 212, 218, 223, 227, 228, 230, 234]
Answer: G
We now define an algorithm: The definition of a(n) is primes whose base-2 representation is also the base-3 representation of a prime, considering base-2 and base-3 representations as whole numbers without leading zeroes. Given the input x_list (a series of values): [55, 56, 57, 58, 59, 60, 61, 62, 63, 64], determine the corresponding output sequence y_list.

Options:
A. [1447, 1487, 1553, 1587, 1611, 1647, 1675, 1691, 1717, 1771]
B. [1439, 1517, 1543, 1561, 1593, 1631, 1653, 1689, 1747, 1753]
C. [1471, 1531, 1567, 1571, 1657, 1667, 1669, 1697, 1709, 1759]
D. [1417, 1447, 1559, 1583, 1601, 1649, 1673, 1687, 1711, 1793]
E. [1423, 1481, 1529, 1577, 1609, 1659, 1671, 1703, 1729, 1777]
F. [1469, 1511, 1539, 1591, 1621, 1661, 1683, 1701, 1739, 1769]
G. [1509, 1513, 1537, 1549, 1613, 1637, 1651, 1681, 1707, 1741]
H. [1453, 1499, 1573, 1589, 1619, 1643, 1677, 1699, 1733, 1783]
I. [1493, 1523, 1579, 1597, 1627, 1663, 1679, 1693, 1723, 1763]
J. [1477, 1501, 1541, 1579, 1617, 1639, 1679, 1727, 1739, 1791]
Answer: C
We now define an algorithm: The definition of a(n) is a self-inverse permutation of the positive integers where 1 is fixed, followed by an infinite number of adjacent transpositions (n, n+1). Given the input x_list (a series of values): [63, 64, 65, 66, 67, 68, 69, 70, 71, 72], determine the corresponding output sequence y_list.

Options:
A. [62, 63, 66, 65, 68, 67, 70, 69, 71, 72]
B. [63, 64, 66, 65, 68, 67, 70, 69, 72, 71]
C. [62, 64, 65, 66, 68, 67, 69, 71, 70, 73]
D. [63, 64, 65, 67, 68, 66, 69, 71, 70, 72]
E. [63, 65, 64, 68, 66, 69, 67, 71, 70, 72]
F. [64, 63, 65, 67, 66, 68, 70, 69, 71, 73]
G. [62, 65, 66, 64, 68, 67, 69, 71, 70, 72]
H. [62, 65, 64, 67, 66, 69, 68, 71, 70, 73]
I. [62, 63, 65, 67, 66, 68, 70, 71, 69, 73]
J. [62, 65, 63, 67, 64, 69, 66, 71, 68, 73]
Answer: H
We now define an algorithm: The definition of a(n) is the nth term in the Molien series of the 4-dimensional representation of the cyclic group of order 4 over the finite field GF(2), which is not Cohen-Macaulay. Given the input x_list (a series of values): [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], determine the corresponding output sequence y_list.

Options:
A. [3198, 3444, 3694, 3950, 4215, 4499, 4792, 5108, 5429, 5775]
B. [3300, 3538, 3772, 4032, 4310, 4600, 4889, 5220, 5537, 5872]
C. [3160, 3386, 3651, 3925, 4191, 4477, 4765, 5063, 5379, 5712]
D. [3234, 3491, 3717, 3993, 4258, 4541, 4840, 5151, 5468, 5811]
E. [3311, 3553, 3795, 4060, 4324, 4612, 4900, 5213, 5525, 5863]
F. [3282, 3520, 3740, 4045, 4292, 4570, 4856, 5169, 5489, 5830]
G. [3165, 3407, 3649, 3921, 4185, 4469, 4757, 5052, 5364, 5703]
H. [3215, 3460, 3682, 3972, 4223, 4502, 4788, 5097, 5410, 5752]
I. [3122, 3389, 3618, 3885, 4157, 4425, 4720, 5018, 5330, 5671]
J. [3246, 3503, 3733, 4020, 4277, 4555, 4855, 5167, 5483, 5827]
Answer: E
We now define an algorithm: The definition of a(n) is: Number of irreducible polynomials of degree n over the finite field GF(4); also, the dimensions of free Lie algebras over a 4-element field. Given the input x_list (a series of values): [14, 15, 16, 17, 18, 19, 20, 21, 22, 23], determine the corresponding output sequence y_list.

Options:
A. [19172800, 71582726, 268431370, 1010580550, 3817733930, 14467258270, 54975528958, 209430785470, 799644629560, 3059510616430]
B. [19172793, 71582719, 268431363, 1010580543, 3817733923, 14467258263, 54975528951, 209430785463, 799644629553, 3059510616423]
C. [19172794, 71582720, 268431364, 1010580544, 3817733924, 14467258264, 54975528952, 209430785464, 799644629554, 3059510616424]
D. [19172789, 71582715, 268431359, 1010580539, 3817733919, 14467258259, 54975528947, 209430785459, 799644629549, 3059510616419]
E. [19172791, 71582717, 268431361, 1010580541, 3817733921, 14467258261, 54975528949, 209430785461, 799644629551, 3059510616421]
F. [19172790, 71582716, 268431360, 1010580540, 3817733920, 14467258260, 54975528948, 209430785460, 799644629550, 3059510616420]
G. [19172795, 71582721, 268431365, 1010580545, 3817733925, 14467258265, 54975528953, 209430785465, 799644629555, 3059510616425]
H. [19172797, 71582723, 268431367, 1010580547, 3817733927, 14467258267, 54975528955, 209430785467, 799644629557, 3059510616427]
I. [19172792, 71582718, 268431362, 1010580542, 3817733922, 14467258262, 54975528950, 209430785462, 799644629552, 3059510616422]
J. [19172796, 71582722, 268431366, 1010580546, 3817733926, 14467258266, 54975528954, 209430785466, 799644629556, 3059510616426]
Answer: F
We now define an algorithm: The definition of a(n) is the coefficients in the expansion of the Molien series for the invariants of the 3-dimensional group [3,4]+ = 432. Given the input x_list (a series of values): [59, 60, 61, 62, 63, 64, 65, 66, 67, 68], determine the corresponding output sequence y_list.

Options:
A. [66, 92, 71, 97, 76, 103, 81, 109, 86, 115]
B. [68, 94, 73, 99, 78, 105, 83, 111, 88, 117]
C. [65, 91, 70, 96, 75, 102, 80, 108, 85, 114]
D. [61, 87, 66, 92, 71, 98, 76, 104, 81, 110]
E. [67, 93, 72, 98, 77, 104, 82, 110, 87, 116]
F. [70, 96, 75, 101, 80, 107, 85, 113, 90, 119]
G. [64, 90, 69, 95, 74, 101, 79, 107, 84, 113]
H. [62, 88, 67, 93, 72, 99, 77, 105, 82, 111]
I. [69, 95, 74, 100, 79, 106, 84, 112, 89, 118]
J. [63, 89, 68, 94, 73, 100, 78, 106, 83, 112]
Answer: C
We now define an algorithm: The definition of a(n) is the number of rooted identity trees with n nodes, where a rooted identity tree is a rooted tree whose automorphism group is the identity group, meaning it has no non-trivial symmetries. Given the input x_list (a series of values): [29, 30, 31, 32, 33, 34, 35, 36, 37, 38], determine the corresponding output sequence y_list.

Options:
A. [974662479, 2325443076, 5589508647, 13346130437, 32234837885, 77763375116, 186737499012, 452203435318, 1085295264856, 2639957419340]
B. [965662479, 2225443066, 5499508637, 13346130427, 32234837875, 76763375015, 176737499002, 452203434308, 1085295254746, 2639957409240]
C. [973662477, 2315443075, 5579508646, 13246130436, 32134837884, 77663375125, 185737499011, 451203435317, 1075295264855, 2629957419339]
D. [975662480, 2335443077, 5599508648, 13446130438, 32334837886, 77863375126, 187737500013, 453203435319, 1095295264857, 2649957419351]
E. [976662482, 2345443079, 5609508650, 13546130440, 32434837888, 77963375128, 188737500015, 454203435321, 1105295264859, 2659957419353]
F. [975662481, 2335443078, 5599508649, 13446130439, 32334837887, 77863375127, 187737500014, 453203435320, 1095295264858, 2649957419352]
G. [986662481, 2445443088, 5699508759, 13546130549, 32434837997, 78963375237, 198737511024, 454203446430, 1105295374968, 2659957520462]
H. [985662490, 2435443087, 5699508748, 13546130538, 32434837986, 78863375226, 197737511013, 454203446419, 1105295374957, 2659957520451]
I. [964662478, 2215443065, 5489508636, 13246130426, 32134837874, 76663375014, 175737498001, 451203434307, 1075295254745, 2629957409239]
J. [977662483, 2355443080, 5619508651, 13646130441, 32534837889, 78063375129, 189737500016, 455203435322, 1115295264860, 2669957419354]
Answer: D
We now define an algorithm: The definition of a(n) is: Number of non-root branch nodes in all non-crossing rooted trees on n nodes, placed on a circle such that no branches cross each other. Given the input x_list (a series of values): [13, 14, 15, 16, 17, 18, 19, 20, 21, 22], determine the corresponding output sequence y_list.

Options:
A. [129585457, 856703849, 5663913531, 37454912048, 247778648883, 1639890119020, 10858731869163, 71939098633181, 476841658085112, 3162310375905470]
B. [129585459, 856703847, 5663913523, 37454912042, 247778648886, 1639890119019, 10858731869164, 71939098633176, 476841658085102, 3162310375905445]
C. [129585452, 856703842, 5663913532, 37454912038, 247778648881, 1639890119026, 10858731869167, 71939098633179, 476841658085109, 3162310375905490]
D. [129585459, 856703848, 5663913528, 37454912045, 247778648889, 1639890119023, 10858731869165, 71939098633175, 476841658085103, 3162310375905440]
E. [129585455, 856703845, 5663913530, 37454912043, 247778648888, 1639890119028, 10858731869161, 71939098633170, 476841658085108, 3162310375905430]
F. [129585456, 856703848, 5663913528, 37454912040, 247778648880, 1639890119016, 10858731869160, 71939098633185, 476841658085100, 3162310375905450]
G. [129585453, 856703850, 5663913526, 37454912041, 247778648884, 1639890119015, 10858731869166, 71939098633183, 476841658085101, 3162310375905400]
H. [129585458, 856703846, 5663913527, 37454912038, 247778648887, 1639890119024, 10858731869169, 71939098633189, 476841658085106, 3162310375905480]
I. [129585476, 856703848, 5663913528, 37454912040, 247778648880, 1639890119316, 10858731869160, 71939198633185, 476841658085100, 3162310375905450]
J. [129585454, 856703852, 5663913520, 37454912044, 247778648882, 1639890119017, 10858731869162, 71939098633190, 476841658085110, 3162310375905460]
Answer: F
We now define an algorithm: The definition of a(n) is the number of nonisomorphic systems of catafusenes for the unsymmetrical schemes (group \\(C_s\\)) with two appendages, as described in the mathematical chemistry literature concerning polycyclic aromatic hydrocarbons. 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. [50234016880, 67731093715, 623273611810, 1947265325255, 1424606035900, 53211459517120, 109642275853176, 318959629394294, 1460993383491632, 21691102386417575]
B. [40234016880, 27731093715, 223273611910, 1547265325255, 5924606035900, 43211459517120, 109642675853176, 318959629394294, 2460993383491632, 11691102386417575]
C. [10234016880, 47731093715, 223273611810, 1047265325255, 4924606035900, 23211459517120, 109642275853176, 518959629394294, 2460993383491632, 11691102386417575]
D. [20234016880, 37731093715, 423273611810, 1047265325265, 3924606035900, 33211459517120, 209642275853176, 618959629394294, 11691102386417575, 1460993383491632]
E. [30234016880, 57731093715, 523273611820, 1247265325255, 1924606035900, 13211459517120, 109642275853176, 218959629394294, 21691102386417575, 1460993383491632]
F. [19234016880, 47731093716, 323273611810, 1147265325255, 5924606035900, 24211459517120, 209642275853176, 418959629394294, 11691102386417575, 3460993383491632]
G. [60234016880, 47731093718, 723273611810, 1047265325255, 2924606035900, 22211459517120, 119642275853176, 418959629394294, 2460993383491632, 13691102386417575]
H. [70234016880, 57731093715, 227273611810, 1847265325255, 6924606035900, 22211459517120, 129642275853176, 518959629394294, 3460993383491632, 11691102386417575]
I. [80234016880, 46731093715, 127273611810, 1047265325253, 1924606035900, 12211459517120, 109642275853176, 618959629394294, 2960993383491632, 11691102386417575]
J. [10234016881, 47731093714, 223273611809, 1047265325254, 4924606035899, 23211459517121, 109642275853177, 518959629394295, 2460993383491633, 11691102386417576]
Answer: C
We now define an algorithm: The definition of a(n) is the coordination sequence for the planar net 3.3.3.3.6, also known as the fsz net, which describes the number of vertices at each distance from an arbitrary starting vertex in this two-dimensional structure. Given the input x_list (a series of values): [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], determine the corresponding output sequence y_list.

Options:
A. [194, 199, 203, 209, 213, 218, 223, 227, 233, 237]
B. [191, 196, 200, 206, 211, 215, 220, 224, 230, 238]
C. [189, 193, 198, 204, 209, 214, 219, 223, 229, 234]
D. [188, 194, 199, 206, 212, 217, 222, 229, 233, 238]
E. [190, 195, 200, 205, 210, 215, 220, 224, 230, 234]
F. [193, 198, 202, 208, 212, 217, 222, 226, 232, 236]
G. [192, 197, 201, 207, 211, 216, 221, 225, 231, 235]
H. [195, 200, 204, 210, 214, 219, 224, 228, 234, 239]
I. [196, 199, 205, 208, 215, 218, 223, 227, 230, 240]
J. [191, 195, 202, 206, 214, 218, 222, 228, 230, 237]
Answer: G
We now define an algorithm: The definition of a(n) is the length of the longest possible arrangement of domino tiles, known as a "domino snake," where each tile in the snake is a [i:j] domino (with 0 ≤ i ≤ j ≤ n) and where each tile connects to its predecessor by matching one number. The tile set used includes all possible dominoes up to the [n:n] tile. 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. [1034, 1060, 1127, 1152, 1226, 1250, 1327, 1352, 1430, 1460]
B. [1041, 1051, 1134, 1146, 1232, 1247, 1334, 1345, 1439, 1450]
C. [1029, 1054, 1132, 1149, 1229, 1248, 1331, 1348, 1436, 1453]
D. [1039, 1053, 1133, 1148, 1230, 1255, 1332, 1347, 1437, 1452]
E. [1040, 1052, 1125, 1147, 1231, 1256, 1333, 1346, 1438, 1451]
F. [1038, 1056, 1131, 1150, 1228, 1254, 1329, 1349, 1435, 1454]
G. [1035, 1059, 1128, 1153, 1225, 1251, 1326, 1353, 1431, 1459]
H. [1033, 1057, 1130, 1155, 1223, 1249, 1328, 1351, 1433, 1457]
I. [1036, 1058, 1129, 1154, 1224, 1252, 1325, 1354, 1432, 1458]
J. [1037, 1055, 1126, 1151, 1227, 1253, 1330, 1350, 1434, 1455]
Answer: G
We now define an algorithm: The definition of a(n) is the diameter (i.e., largest distance between two vertices) of the rooted tree with Matula-Goebel number n, a unique number associated with the tree encoding its structure. Given the input x_list (a series of values): [111, 112, 113, 114, 115, 116, 117, 118, 119, 120], determine the corresponding output sequence y_list.

Options:
A. [5, 3, 4, 4, 6, 5, 5, 5, 4, 5]
B. [5, 3, 5, 4, 6, 5, 5, 5, 5, 5]
C. [5, 3, 4, 4, 6, 5, 4, 5, 5, 5]
D. [5, 4, 5, 4, 6, 4, 5, 5, 5, 5]
E. [5, 3, 5, 5, 6, 5, 4, 5, 5, 5]
F. [4, 3, 5, 4, 6, 5, 5, 4, 5, 5]
G. [5, 3, 5, 4, 5, 5, 5, 5, 5, 5]
H. [5, 2, 5, 4, 6, 5, 5, 5, 5, 4]
I. [5, 3, 5, 3, 6, 5, 5, 5, 5, 5]
J. [5, 3, 5, 4, 6, 4, 5, 5, 5, 5]
Answer: B
Which of the following options is not conducive to people adapting to long-term life in high-altitude regions?

Options:
A. Lower hemoglobin levels
B. Reduced oxygen uptake in tissues
C. Increased respiratory rate
D. Enhanced digestion efficiency
E. Decreased blood circulation
F. The kidneys produce more erythropoietin.
G. The number of red blood cells in the blood increases
H. Increase iron intake
I. Increase muscle mass significantly
J. Reduced lung capacity
Answer: C
In a certain primary spermatocyte, the gene sequence of one chromatid in a pair of chromosomes is 1234.5678, and the other is 1265.4378 (the "." indicates the centromere). If a crossover occurs between 3 and 4 during meiosis, what is the composition of this chromosome in the four gametes it forms?

Options:
A. 1234.5678 1265.4312 8735.5648 1267.4321
B. 1234.5678 1256.3478 8734.5678 1264.5321
C. 1234.5678 1267.4351 8734.5678 1256.4321
D. 1234.5678 1235.4261 8734.5678 1267.4321
E. 1234.5678 1265.4312 8734.5687 1267.4321
F. 1234.5678 1265.4321 1234.5678 8765.4387
G. 1234.5678 1265.4321 8734.5678 1265.4378
H. 1234.5678 1256.4378 8734.5612 1265.4321
I. 1234.5678 1256.3421 8734.5678 1265.4321
J. 1234.5678 1276.4351 8734.5612 1265.4378
Answer: G
Most scientists believe that the unit of natural selection is what?

Options:
A. Biome
B. Individual
C. Population
D. Ecosystem
E. Species
F. Niche
G. Community
H. Family
I. Genome
J. Habitat
Answer: C
What type of connection exists between the pectoral girdle and the neurocranium in mammals?

Options:
A. Cervico-anchored type
B. Vertebro-connective type
C. Skeletally-fixed type
D. Neuro-bound type
E. Scapulo-bound type
F. Tongue-and-groove type
G. Self-conjugated type
H. Bipolar Type
I. Thoraco-binding type
J. Cranio-connective type
Answer: J