MikaStars39/nano-eval huggingface dataset:
What is the founder of the Beaverbrook newspaper group known as in the history of journalism?

Options:
A. Chandler of Norway
B. Murdoch of Ireland
C. Hearst of England
D. Graham of Finland
E. Ochs of Germany
F. Knight of Sweden
G. Harmsworth of Belgium
H. Pulitzer of Wales
I. Sulzberger of Denmark
J. Scripps of Scotland
Answer: C
In a common-orbit laser, what phenomenon causes energy loss in the beam?

Options:
A. Internal refraction
B. Amplified dispersion
C. Wave divergence
D. Quantum deflagration
E. Spectral inversion
F. Photon imbalance
G. Self-absorption
H. Thermal oscillation
I. Optical leakage
J. Polarization decay
Answer: G
Which of the following is a primary goal of forest ecological engineering?

Options:
A. Support the construction of industrial facilities
B. Accelerate desertification processes
C. Reduce the rate of deforestation
D. Enhance agricultural output
E. Reduce the use of renewable resources
F. Decrease the protected habitats for wildlife
G. Promote urban development zones
H. Improve soil erosion rates
I. Increase pesticide application in agriculture
J. Expand mining operations near forests
Answer: C
What are the reasons for limiting fish meal in waterfowl feed?

Options:
A. Because fish meal has low protein content
B. Because fish meal increases water pollution
C. Because of high cost
D. Because fish meal harms beak structure
E. Because fish meal attracts predators
F. Because fish meal contains anti-nutritional factors
G. Because fish meal may contain heavy metals
H. Because fish meal is difficult to preserve
I. Because fish meal is prone to fungal infections
J. Because fish meal reduces feed efficiency
Answer: C
In the heat exchanger, the water inlet temperature is 35°C, the flow rate is 0.667 kg/s, the oil inlet temperature is 110°C, and the total heat transfer coefficient of the heat exchanger is 320 W/(m²·°C). Find the water outlet temperature.

Options:
A. 89.8°C
B. 78.3°C
C. 85.7°C
D. 79.6°C
E. 87.9°C
F. 90.0°C
G. 65.4°C
H. 92.5°C
I. 88.1°C
J. 93.2°C
Answer: A
The rotor of the LZB-40I rotor flowmeter is made of stainless steel (specific gravity: 7.92), the scale value is based on water, and the range is $0.25\\sim2.5m^3/h$. If this rotor flowmeter is used to measure the flow of alcohol (specific gravity: 0.8), the actual flow value of alcohol is greater than the scale value_, and the correction coefficient is. When measuring alcohol, what is the maximum flow value of this flowmeter?

Options:
A. Lower; 0.850: 2.000 $m^3/h$
B. Small; 0.882: 2.205 $m^3/h$"
C. Lesser; 0.825: 2.250 $m^3/h$
D. Identical; 0.870: 2.050 $m^3/h$
E. Moderate; 0.775: 2.300 $m^3/h$
F. Equal; 0.950: 3.000 $m^3/h$
G. Greater; 0.900: 2.700 $m^3/h$
H. Higher; 0.800: 2.400 $m^3/h$
I. Reduced; 0.650: 1.800 $m^3/h$
J. Larger; 0.750: 2.000 $m^3/h$
Answer: B
$\rho=1000kg/m^{3}$ Fluid flows through a smooth horizontal circular tube at a laminar flow rate of $1 m/s$, $Re=1600$, what is the friction stress $ps$ on the wall?

Options:
A. 1.2 Pa
B. 0.5 Pa
C. 0.8 Pa
D. 3 Pa
E. 1.5 Pa
F. 2 Pa
G. 2.5 Pa
H. 1 Pa
I. 0.7 Pa
J. 1.8 Pa
Answer: H
What does the maximum load refer to in terms of the highest power load within an electric power system for a specified period (a day, a month, or a year)?

Options:
A. Total standby power
B. Total rated power
C. Highest apparent power
D. Total apparent powe
E. Highest demand charge
F. Total active power
G. Peak system voltage
H. Total reactive power
I. Maximum energy output
Answer: F
A laboratory conducted an experiment to determine the permeability of a cylindrical core. The core has a radius of 1 cm and a length of 5 cm. A pressure difference is established at both ends of the core so that a liquid with a viscosity of 1 mPa-s passes through the core, and the amount of liquid that passes through is measured to be 15 cm³ and the pressure difference to be 157 mmHg in 2 min, so try to calculate the permeability of the core K. What is the value of K?

Options:
A. 2.89 × 10-³ m²
B. 8.15 × 10-³ m²
C. 1.95 × 10-³ m²
D. 3.76 × 10-³ m²
E. 7.53 × 10-³ m²
F. 4.88 × 10-³ m²
G. 5.67 × 10-³ m²
H. 6.14 × 10-³ m²
I. 8.42 × 10-³ m²
J. 9.51 × 10-³ m²
Answer: J
Which defect is most likely to occur during the wood drying process?

Options:
A. resin pocketing
B. insect bites
C. mold growth
D. warping
E. blue discoloration
F. knots forming
G. sap leakage
H. cracks
I. discoloration
J. swelling
Answer: H
Which of the following options appears in the plot of the seventh play?

Options:
A. Hidden Lobby
B. Closed Passage
C. Grateful Favor
D. Distant Honor
E. Silent Eclipse
F. Peeping Bath
G. The Bower
H. Night Grievance
I. Shadow Command
J. Mourning Duel
Answer: F
Who proposed the slogan "Everyone plays themselves"?

Options:
A. Taviani
B. De Sica
C. Visconti
D. Rossellini
E. Olmi
F. Pasolini
G. Cecchi D'Amico
H. Antonioni
I. Bertolucci
J. Fellini
Answer: D
What is the balanced half-reaction for the oxidation of acetate at pH=8?

Options:
A. $$
1 / 6 \ {\mathrm{ H C O_{3}}^{-}+9 / 8 ~ H^{+}+e^{-}=1 / 8 ~ a c e t a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 2 2
$$
B. $$
1 / 6 \ {\mathrm{ S O_{4}}^{2-}+6 / 8 ~ H^{+}+e^{-}=1 / 8 ~ s u c c i n a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 0 4
$$
C. $$
1 / 6 \ {\mathrm{ H S O_{3}}^{-}+8 / 8 ~ H^{+}+e^{-}=1 / 8 ~ l a c t a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 4 6
$$
D. $$
1 / 6 \ {\mathrm{ H C O_{2}}^{2-}+6 / 8 ~ H^{+}+e^{-}=1 / 8 ~ p r o p i o n a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=2. 6 5
$$
E. $$
1 / 6 \ {\mathrm{ C O_{2}}+7 / 8 ~ H^{+}+e^{-}=1 / 8 ~ o x a l a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 8 4
$$
F. $$
1 / 6 \ {\mathrm{ H P O_{4}}^{2-}+5 / 8 ~ H^{+}+e^{-}=1 / 8 ~ f u m a r a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 9 0
$$
G. $$
1 / 6 \ {\mathrm{ H C O_{3}}^{-}+5 / 8 ~ H^{+}+e^{-}=1 / 8 ~ b u t y r a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=3. 5 7
$$
H. $$
1 / 6 \ {\mathrm{ H C O_{2}}^{-}+4 / 8 ~ H^{+}+e^{-}=1 / 8 ~ p y r u v a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=2. 7 1
$$
I. $$
1 / 6 \ {\mathrm{ C O_{3}}^{2-}+7 / 8 ~ H^{+}+e^{-}=1 / 8 ~ f o r m a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=4. 5 1
$$
J. $$
1 / 6 \ {\mathrm{ N O_{3}}^{-}+8 / 8 ~ H^{+}+e^{-}=1 / 8 ~ m a l o n a t e^{-}+1 / 2 ~ H_{2} O}
$$
$$
\mathrm{p e}^{\circ}=2. 8 9
$$
Answer: A
calculate the [Cr] concentration in the molten iron under basic slag with $w(\mathrm{CaO}) / w(\mathrm{SiO}_{2}) = 2.5$ at the temperature of $1600~\degree\mathrm{C}$.

Options:
A. $$
0. 4 3 \%
$$
B. $$
0. 7 1 \%
$$
C. $$
1. 1 7 \%
$$
D. $$
0. 6 2 \%
$$
E. $$
1. 5 0 \%
$$
F. $$
0. 5 4 \%
$$
G. $$
1. 3 4 \%
$$
H. $$
0. 8 9 \%
$$
I. $$
1. 2 5 \%
$$
J. $$
0. 9 8 \%
$$
Answer: F
Individual dose limits generally do not include ___

Options:
A. Medical Diagnostic Radiation Dose
B. Non-Ionizing Radiation Safety Dose
C. Controlled Area Radiation Dose
D. Occupational Internal Radiation Dose
E. Occupational External Radiation Dose
F. Public Background Exposure Dose
G. Cosmic Background Radiation Dose
H. Environmental Radiation Mitigation Dose
I. Natural Radiation Exposure Dose
J. Occupational Radiation Dose
Answer: I
Rank the following groups of compounds in order of basicity from strongest to weakest: acetamide, ethylamine, diethylaminomide. The result is ().

Options:
A. Ethanamine > Acetamide > Diacetamide
B. Acetamide > Diacetamide > Ethanamine
C. Ethanamine > Diethylaminomide > Acetamide
D. Diacetamide > Acetamide > Ethanamide
E. Ethanamide > Diacetamide > Ethylamine
F. Acetamide > Ethylamine > Diethylaminomide
G. Diethylamine > Ethylamine > Acetamide
H. Ethylamide > Ethanamine > Diacetamide
I. Diethylaminomide > Acetamide > Ethanamine
J. Acetamide > Diethylamide > Ethanamide
Answer: A
The outer walls of a certain warehouse use a strip brick foundation with a wall thickness of 240mm and a foundation depth of 2.0m. The known standard combined value of the upper structure load acting at the foundation top level is 240kN/m. The foundation is artificially compacted fill, with a characteristic bearing capacity of 160kPa and a density of 19kN/m³. According to the current "Code for Design of Building Foundation" , which of the following options is closest to the minimum height of the foundation?

Options:
A. 1.04m
B. 1.75m
C. 1.90m
D. 0.92m
E. 1.50m
F. 1.68m
G. 2.30m
H. 2.15m
I. 2.37m
J. 0.87m
Answer: A
We now define an algorithm: The definition of a(n) is the number of columns in all directed column-convex polyominoes of area n+1, where a directed column-convex polyomino is a connected arrangement of cells on the square grid such that in every column the cells are contiguous and the leftmost cell in each row is connected. 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. [223410563, 609468951, 1677042776, 4548235818, 12481157715, 33600126297, 92130468259, 253570040499, 678844474322, 1843289002640]
B. [225610563, 607468851, 1657041776, 4550234018, 12411118715, 33100136287, 92780468249, 250970020499, 678844578822, 1832280093640]
C. [220604563, 606988451, 1653040776, 4531204088, 12341155715, 34010136297, 92830469242, 254571013499, 670044584322, 1822280001630]
D. [229010763, 601468851, 1684042776, 4538234018, 12631155715, 33720136297, 92650468259, 251570090499, 675844574322, 1843286003640]
E. [227195872, 613607451, 1646075776, 4508234128, 12411155795, 33650836297, 92750468239, 252570011499, 667844564312, 1862285003640]
F. [231250172, 602515634, 1691232509, 4675290019, 12049000456, 34451811566, 90540711478, 242778001542, 681254601388, 1883350043120]
G. [224110763, 604968451, 1669042776, 4528234018, 12461155750, 33670136247, 92430468269, 257570000499, 679844584322, 1852281003640]
H. [213164523, 615780784, 1689040472, 4609234866, 12681678909, 33211478081, 91450368121, 257653004239, 669044122311, 1835020029599]
I. [221610563, 608468451, 1667040776, 4558234018, 12441155715, 33900136297, 92230468249, 250570010499, 679844574322, 1842280003640]
J. [226510563, 605468451, 1672040776, 4548234018, 12349155705, 33090136297, 92080468289, 250570050499, 679844504322, 1845280007640]
Answer: I
We now define an algorithm: The definition of a(n) is the number of distinct shapes formed by connecting n cells (polycubes) in a (n-1)-dimensional space such that one cell is labeled, considering that two shapes are identical if one can be transformed into the other through rotations and reflections (chiral symmetry). Given the input x_list (a series of values): [25, 26, 27, 28, 29, 30, 31, 32, 33, 34], determine the corresponding output sequence y_list.

Options:
A. [66102921, 161417867, 395042562, 968791315, 2380383481, 5859176855, 14446043494, 35672895787, 88219204394, 218466647493]
B. [66102922, 161417864, 395042564, 968791314, 2380383479, 5859176853, 14446043491, 35672895785, 88219204399, 218466647490]
C. [66102920, 161417868, 395042561, 968791316, 2380383482, 5859176854, 14446043493, 35672895786, 88219204393, 218466647492]
D. [66102918, 161417869, 395042560, 968791311, 2380383484, 5859176852, 14446043496, 35672895788, 88219204392, 218466647496]
E. [66102925, 161417862, 395042558, 968791320, 2380383476, 5859176850, 14446043497, 35672895780, 88219204395, 218466647487]
F. [66102919, 161417870, 395042559, 968791318, 2380383480, 5859176857, 14446043495, 35672895784, 88219204397, 218466647491]
G. [66102926, 161417866, 395042563, 968791313, 2380383477, 5859176860, 14446043488, 35672895781, 88219204396, 218466647488]
H. [66102924, 161417863, 395042566, 968791317, 2380383478, 5859176858, 14446043490, 35672895783, 88219204391, 218466647489]
I. [66102923, 161417865, 395042565, 968791312, 2380383483, 5859176856, 14446043492, 35672895789, 88219204390, 218466647495]
J. [66102917, 161417871, 395042557, 968791319, 2380383485, 5859176859, 14446043489, 35672895782, 88219204398, 218466647494]
Answer: A
We now define an algorithm: The definition of a(n) is the number of one-sided triangulations of the disk, which refers to the ways to divide a polygon into triangles by drawing non-intersecting diagonals within the polygon. Alternatively, it can be interpreted as the number of flexagons of order n, which are flat folded paper constructions that can be flexed to reveal hidden faces. Additionally, a(n) represents the count of unlabeled plane trivalent trees with (n-2) internal vertices, where each internal vertex has a degree of 3, resulting in n leaves. 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. [299999999, 1070000000, 4000000000, 13800000000, 49800000000, 181000000000, 659999999999, 2400000000000, 8799999999999, 32400000000000]
B. [301245120, 1074421900, 3912847620, 13945751200, 50182300300, 181245300000, 659874530270, 2401236500000, 8823091048000, 32412390000000]
C. [298377508, 1063750740, 3811803164, 13722384546, 49611801980, 180072089896, 655977266884, 2397708652276, 8791599732140, 32330394085528]
D. [298377509, 1063750751, 3811803201, 13722384547, 49611801981, 180072089897, 655977266885, 2397708652277, 8791599732141, 32330394085529]
E. [299000000, 1065000000, 3820000000, 13750000000, 49650000000, 180100000000, 656500000000, 2398000000000, 8792000000000, 32340000000000]
F. [310000000, 1075000000, 3999999999, 14000000000, 50000000000, 181000000000, 660000000000, 2400000000000, 8800000000000, 32400000000000]
G. [298400000, 1063800000, 3811900000, 13723000000, 49612000000, 180080000000, 655980000000, 2397720000000, 8791600000000, 32330400000000]
H. [300000000, 1070000000, 3900000000, 13800000000, 49800000000, 181000000000, 658000000000, 2400000000000, 8800000000000, 32350000000000]
I. [298500000, 1064000000, 3812000000, 13724000000, 49615000000, 180090000000, 656000000000, 2397800000000, 8791700000000, 32331000000000]
J. [298377510, 1063750750, 3811803200, 13722384650, 49611802100, 180072090000, 655977270000, 2397708700000, 8791600000000, 32330394100000]
Answer: C
We now define an algorithm: The definition of a(n) is the coordination sequence for "cab" 3D uniform tiling formed from octahedra and truncated cubes, representing the number of vertices of the tiling at a given distance from a fixed vertex. Given the input x_list (a series of values): [46, 47, 48, 49, 50, 51, 52, 53, 54, 55], determine the corresponding output sequence y_list.

Options:
A. [4765, 4997, 5182, 5381, 5629, 5878, 6085, 6297, 6562, 6837]
B. [4766, 4997, 5183, 5381, 5630, 5878, 6085, 6297, 6563, 6836]
C. [4765, 4998, 5181, 5383, 5630, 5877, 6085, 6298, 6563, 6838]
D. [4766, 4996, 5181, 5382, 5629, 5879, 6086, 6296, 6563, 6837]
E. [4766, 4997, 5182, 5380, 5630, 5879, 6084, 6298, 6563, 6836]
F. [4765, 4998, 5183, 5382, 5629, 5880, 6085, 6298, 6563, 6837]
G. [4764, 4997, 5183, 5383, 5630, 5878, 6086, 6297, 6563, 6838]
H. [4764, 4996, 5182, 5380, 5628, 5879, 6085, 6296, 6563, 6837]
I. [4765, 4996, 5182, 5381, 5628, 5877, 6084, 6296, 6562, 6837]
J. [4765, 4997, 5181, 5381, 5629, 5878, 6086, 6297, 6562, 6838]
Answer: A
We now define an algorithm: The definition of a(n) is the maximal number of linearly independent smooth nowhere-zero vector fields on a (2n+1)-sphere, where the (2n+1)-sphere refers to a high-dimensional sphere embedded in Euclidean space, representing the set of all points that are equidistant from a common center.\n 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. [1, 3, 2, 11, 2, 3, 2, 7, 2, 3]
B. [2, 4, 1, 12, 1, 4, 1, 8, 1, 4]
C. [2, 4, 2, 12, 2, 4, 2, 8, 2, 4]
D. [2, 3, 2, 11, 2, 3, 2, 7, 2, 3]
E. [1, 3, 1, 11, 1, 3, 1, 7, 1, 3]
F. [1, 2, 1, 9, 1, 2, 1, 5, 1, 2]
G. [0, 3, 0, 10, 0, 3, 0, 6, 0, 3]
H. [0, 2, 0, 10, 0, 2, 0, 6, 0, 2]
I. [0, 2, 1, 9, 1, 2, 1, 6, 1, 2]
J. [1, 4, 1, 12, 1, 4, 1, 8, 1, 4]
Answer: E
We now define an algorithm: The definition of a(n) is the number of toothpicks present after n stages of a process where toothpicks are continuously added according to specific geometric rules, starting with a single toothpick. Given the input x_list (a series of values): [44, 45, 46, 47, 48, 49, 50, 51, 52, 53], determine the corresponding output sequence y_list.

Options:
A. [931, 992, 1086, 1161, 1204, 1222, 1247, 1281, 1316, 1382]
B. [938, 993, 1087, 1167, 1200, 1219, 1246, 1275, 1317, 1381]
C. [939, 1001, 1084, 1159, 1196, 1212, 1248, 1273, 1324, 1374]
D. [935, 995, 1083, 1163, 1199, 1215, 1243, 1279, 1319, 1379]
E. [934, 994, 1081, 1164, 1197, 1221, 1244, 1277, 1322, 1376]
F. [937, 998, 1082, 1166, 1201, 1213, 1242, 1274, 1318, 1377]
G. [932, 997, 1080, 1165, 1202, 1216, 1241, 1278, 1321, 1378]
H. [930, 996, 1085, 1160, 1198, 1220, 1245, 1280, 1320, 1380]
I. [936, 999, 1079, 1162, 1203, 1214, 1240, 1276, 1323, 1375]
J. [933, 1000, 1088, 1168, 1205, 1217, 1239, 1282, 1325, 1373]
Answer: D
We now define an algorithm: The definition of a(n) is the binary expansion of Thue constant (or Roth's constant), a number associated with combinatorics on words and Diophantine approximation. 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. [1, 1, 1, 1, 0, 1, 1, 0, 1, 1]
B. [1, 0, 0, 1, 0, 1, 1, 0, 0, 1]
C. [0, 0, 1, 1, 0, 1, 1, 1, 0, 0]
D. [0, 1, 0, 1, 1, 1, 0, 1, 0, 0]
E. [1, 0, 0, 1, 1, 1, 0, 0, 1, 1]
F. [0, 0, 1, 0, 1, 0, 1, 1, 0, 1]
G. [1, 1, 0, 1, 0, 0, 1, 1, 1, 0]
H. [0, 1, 1, 1, 1, 0, 0, 0, 1, 1]
I. [1, 0, 1, 1, 0, 0, 0, 1, 1, 1]
J. [0, 1, 1, 0, 1, 1, 0, 0, 1, 0]
Answer: A
We now define an algorithm: The definition of a(n) is the number of ways of partitioning n points on a circle into subsets only of sizes 2 and 3, where the order of the points within each subset matters, and the circle's rotation symmetry is taken into account. Given the input x_list (a series of values): [26, 27, 28, 29, 30, 31, 32, 33, 34, 35], determine the corresponding output sequence y_list.

Options:
A. [269766659, 667224482, 1653266560, 4103910936, 10203669281, 25408828062, 63364046195, 158229645726, 395632288592, 990419552732]
B. [269766653, 667224485, 1653266566, 4103910927, 10203669284, 25408828061, 63364046191, 158229645719, 395632288595, 990419552737]
C. [269766657, 667224483, 1653266568, 4103910929, 10203669283, 25408828070, 63364046186, 158229645718, 395632288594, 990419552739]
D. [269766658, 667224481, 1653266563, 4103910925, 10203669280, 25408828067, 63364046185, 158229645725, 395632288596, 990419552731]
E. [269766656, 667224488, 1653266564, 4103910928, 10203669282, 25408828069, 63364046187, 158229645727, 395632288588, 990419552733]
F. [269766650, 667224480, 1653266567, 4103910932, 10203669286, 25408828066, 63364046192, 158229645722, 395632288591, 990419552735]
G. [269766651, 667224484, 1653266569, 4103910935, 10203669287, 25408828063, 63364046188, 158229645721, 395632288590, 990419552734]
H. [269766652, 667224487, 1653266558, 4103910933, 10203669288, 25408828068, 63364046183, 158229645723, 395632288593, 990419552736]
I. [269766655, 667224480, 1653266565, 4103910930, 10203669285, 25408828065, 63364046190, 158229645720, 395632288590, 990419552730]
J. [269766654, 667224486, 1653266562, 4103910937, 10203669289, 25408828064, 63364046189, 158229645724, 395632288589, 990419552738]
Answer: I
We now define an algorithm: The definition of a(n) is: Generalized ballot numbers, which are the first differences of Motzkin numbers. Given the input x_list (a series of values): [23, 24, 25, 26, 27, 28, 29, 30, 31, 32], determine the corresponding output sequence y_list.

Options:
A. [2042967300, 5800674500, 16636415999, 47137954320, 135015505000, 382719506670, 1100672687000, 3122376205000, 9074807670300, 26098895429400]
B. [2083967395, 5840674709, 16696415960, 47427954321, 135415505413, 385519506622, 1107642686372, 3169376205290, 9089807670380, 26118895429390]
C. [2072967389, 5844674703, 16606415977, 47237954329, 135815505432, 383719506603, 1105642686399, 3152376205105, 9063807670319, 26138895429310]
D. [2034879381, 5780473630, 16437492855, 47048498523, 134274594387, 384590603920, 1093672643120, 3142877384183, 9034896740123, 25928498375768]
E. [2062967382, 5850674704, 16626415975, 47337954326, 135015505407, 385719506620, 1103642686382, 3162376205180, 9073807670316, 26068895429376]
F. [2061967380, 5854674710, 16646416000, 47397954340, 135115505410, 384619506610, 1100642686300, 3160376205100, 9071807670320, 26028895429400]
G. [2102973384, 5920874730, 16526876002, 47367500300, 136595505401, 386719507100, 1112642680000, 3178376205001, 9079907670201, 26168895429070]
H. [2064967394, 5865674708, 16696416100, 47467954370, 135515505430, 385819506610, 1109642686350, 3163376205200, 9078907670390, 26108895429500]
I. [2092967380, 5870674712, 16726415979, 47587954335, 136315505423, 385919506630, 1111642686385, 3189376205390, 9074807670309, 26088895429600]
J. [2063967392, 5860674700, 16616415900, 47347954350, 135125505420, 384719506600, 1104642686320, 3161376205100, 9072807670310, 26058895429300]
Answer: E
We now define an algorithm: The definition of a(n) is the Stirling numbers of the second kind S(n,3) which count the number of ways to partition a set of n elements into exactly 3 non-empty subsets. 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. [64321000, 193000000, 583000000, 1730000000, 5210000000, 15700000000, 47200000000, 141000000000, 425000000000, 1280000000000]
B. [64400000, 193000000, 580000000, 1740000000, 5200000000, 15600000000, 47000000000, 142000000000, 423000000000, 1260000000000]
C. [64600000, 197000000, 585000000, 1750000000, 5270000000, 15900000000, 47500000000, 143000000000, 426000000000, 1290000000000]
D. [65432109, 199999999, 570000000, 1700000000, 5100000000, 15000000000, 45000000000, 140000000000, 420000000000, 1200000000000]
E. [64500000, 194000000, 582000000, 1740000000, 5220000000, 15600000000, 47100000000, 141000000000, 424000000000, 1270000000000]
F. [64900000, 192000000, 584000000, 1710000000, 5180000000, 15800000000, 47300000000, 144000000000, 422000000000, 1250000000000]
G. [64439010, 193448101, 580606446, 1742343625, 5228079450, 15686335501, 47063200806, 141197991025, 423610750290, 1270865805301]
H. [64800000, 198000000, 581000000, 1750000000, 5240000000, 15600000000, 46800000000, 139000000000, 421000000000, 1230000000000]
I. [65000000, 190000000, 579000000, 1720000000, 5210000000, 15500000000, 46900000000, 140000000000, 422000000000, 1260000000000]
J. [64000000, 195000000, 581000000, 1730000000, 5230000000, 15700000000, 47100000000, 142000000000, 424000000000, 1280000000000]
Answer: G
We now define an algorithm: The definition of a(n) is the number of ways to arrange n indistinguishable coins into non-empty piles where each pile is allowed to have a fountain (a sequence of coins forming a triangular number). Given the input x_list (a series of values): [34, 35, 36, 37, 38, 39, 40, 41, 42, 43], determine the corresponding output sequence y_list.

Options:
A. [43299500, 75253200, 130440000, 226400000, 392950000, 682030000, 1183700000, 2054600000, 3566100000, 6189700000]
B. [43299484, 75153285, 130440741, 226401111, 392955955, 682038998, 1183789678, 2054659668, 3566196322, 6189714275]
C. [43299495, 75153295, 130440795, 226401195, 392955995, 682039095, 1183789695, 2054659695, 3566196395, 6189714395]
D. [43299495, 75153296, 130440750, 226401212, 392955966, 682039099, 1183789678, 2054659679, 3566196321, 6189714275]
E. [43299485, 75153286, 130440740, 226401112, 392955956, 682038999, 1183789679, 2054659669, 3566196321, 6189714276]
F. [43299489, 75153288, 130440749, 226401118, 392955960, 682039005, 1183789680, 2054659670, 3566196329, 6189714279]
G. [43299400, 75153200, 130440700, 226400100, 392955900, 682038900, 1183789600, 2054659600, 3566196300, 6189714200]
H. [43399485, 75163286, 130441740, 226402112, 392956956, 682039999, 1183789689, 2054659699, 3566196320, 6189714280]
I. [43299480, 75153280, 130440730, 226401102, 392955946, 682038989, 1183789669, 2054659659, 3566196311, 6189714265]
J. [43299586, 75253286, 130450740, 226411112, 393955956, 683038999, 1183799679, 2054669669, 3576196321, 6199714276]
Answer: E
We now define an algorithm: The definition of a(n) is the number of different shapes of balanced binary trees with n nodes. The tree is balanced if the total number of nodes in the left and right branch of every node differ by at most one. A balanced binary tree is a rooted binary tree where the difference in height between the left and right subtree of any node is at most one. 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. [65536, 131072, 262144, 524288, 262144, 524288, 262144, 131072, 65536, 131072]
B. [65536, 524288, 1048576, 2097152, 1048576, 2097152, 1048576, 524288, 65536, 524288]
C. [32768, 262144, 524288, 1048576, 524288, 1048576, 524288, 262144, 32768, 262144]
D. [512, 4096, 8192, 16384, 8192, 16384, 8192, 4096, 512, 4096]
E. [16384, 131072, 262144, 524288, 262144, 524288, 262144, 131072, 16384, 131072]
F. [8192, 65536, 131072, 262144, 131072, 262144, 131072, 65536, 8192, 65536]
G. [256, 2048, 4096, 8192, 4096, 8192, 4096, 2048, 256, 2048]
H. [131072, 1048576, 2097152, 4194304, 2097152, 4194304, 2097152, 1048576, 131072, 1048576]
I. [2048, 16384, 32768, 65536, 32768, 65536, 32768, 16384, 2048, 16384]
J. [4096, 32768, 65536, 131072, 65536, 131072, 65536, 32768, 4096, 32768]
Answer: B
We now define an algorithm: The definition of a(n) is: Square array of pyramidal numbers in three dimensions, read by antidiagonals. Note that pyramidal numbers, also known as square pyramidal numbers, represent sums of squares of natural 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. [40, 88, 153, 229, 306, 370, 403, 383, 284, 76]
B. [46, 94, 159, 235, 312, 376, 409, 389, 290, 82]
C. [43, 91, 156, 232, 309, 373, 406, 386, 287, 79]
D. [41, 89, 154, 230, 307, 371, 404, 384, 285, 77]
E. [44, 92, 157, 233, 310, 374, 407, 387, 288, 80]
F. [42, 90, 155, 231, 308, 372, 405, 385, 286, 78]
G. [47, 95, 160, 236, 313, 377, 410, 390, 291, 83]
H. [38, 86, 151, 227, 304, 368, 401, 381, 282, 74]
I. [45, 93, 158, 234, 311, 375, 408, 388, 289, 81]
J. [39, 87, 152, 228, 305, 369, 402, 382, 283, 75]
Answer: F
We now define an algorithm: The definition of a(n) is numbers whose binary expansion is palindromic. For example, a number like 9 (which is 1001 in binary) reads the same forwards and backwards in binary form. Given the input x_list (a series of values): [49, 50, 51, 52, 53, 54, 55, 56, 57, 58], determine the corresponding output sequence y_list.

Options:
A. [560, 584, 632, 644, 692, 716, 764, 770, 818, 842]
B. [559, 583, 631, 643, 691, 715, 763, 769, 817, 841]
C. [562, 586, 634, 646, 694, 718, 766, 772, 820, 844]
D. [557, 581, 629, 641, 689, 713, 761, 767, 815, 839]
E. [563, 587, 635, 647, 695, 719, 767, 773, 821, 845]
F. [566, 590, 638, 650, 698, 722, 770, 776, 824, 848]
G. [561, 585, 633, 645, 693, 717, 765, 771, 819, 843]
H. [564, 588, 636, 648, 696, 720, 768, 774, 822, 846]
I. [565, 589, 637, 649, 697, 721, 769, 775, 823, 847]
J. [558, 582, 630, 642, 690, 714, 762, 768, 816, 840]
Answer: G
We now define an algorithm: The definition of a(n) is the trajectory of 1 under the morphism 1 -> {1, 2, 1}, 2 -> {2, 2, 2}, starting with a(0) = 1. 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, 2, 2, 2, 1, 2, 2, 2, 1, 2]
B. [2, 2, 1, 2, 2, 1, 2, 2, 1, 2]
C. [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
D. [1, 2, 2, 1, 1, 2, 2, 1, 1, 2]
E. [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
F. [2, 2, 1, 1, 2, 2, 1, 1, 2, 2]
G. [1, 1, 2, 2, 1, 1, 2, 2, 1, 1]
H. [2, 1, 1, 2, 2, 1, 1, 2, 2, 1]
I. [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]
J. [2, 1, 2, 1, 2, 1, 2, 1, 2, 1]
Answer: C
We now define an algorithm: The definition of a(n) is: Has simplest possible tree complexity of all transcendental sequences. Tree complexity of a sequence refers to the minimal size of a binary tree capable of generating the sequence using a fixed set of production rules. The tree's size is determined by the total number of nodes and edges. 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, 0, 0, 1, 1, 0, 1, 0, 0, 1]
B. [0, 0, 1, 0, 1, 0, 1, 0, 1, 0]
C. [0, 1, 1, 0, 1, 0, 0, 1, 0, 1]
D. [0, 1, 0, 1, 0, 1, 0, 0, 0, 1]
E. [1, 1, 0, 0, 1, 1, 0, 0, 1, 0]
F. [0, 0, 1, 1, 0, 1, 0, 1, 0, 1]
G. [1, 0, 1, 0, 1, 0, 1, 1, 1, 0]
H. [0, 1, 0, 1, 1, 0, 1, 0, 1, 0]
I. [1, 0, 1, 0, 0, 1, 0, 1, 0, 0]
J. [1, 1, 0, 1, 0, 1, 0, 1, 0, 0]
Answer: D
We now define an algorithm: The definition of a(n) is as follows: For a binary reflected Gray code, the (Hamming/Euclidean) distance between two subsequent points x and y is 1, in coordinate k. If y has a 1 in coordinate k and x has a 0, then (x,y) is indicated by k; if it is the other way around, (x,y) is indicated by -k. Gray codes are binary sequences used in error correction and digital communications. The sequence exhibits a fractal character such that G(d+1) = G(d) d+1 R(G(d)), where R(G(d)) alters d to -d and leaves all other numbers invariant. Generate the sequence based on this recursive definition. 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. [-2, 4, 1, 3, -2, -3, 1, -1, -3, 5]
B. [1, -3, 1, -2, 2, 4, 1, 3, -2, 5]
C. [-1, 4, 1, 2, -1, -3, 1, -2, -1, 5]
D. [2, -5, 1, 3, -1, 2, -1, 3, -2, 4]
E. [-1, 5, 2, -3, 1, -3, -1, 2, -1, 4]
F. [-1, 3, 2, 1, -2, 4, -1, -2, 1, 5]
G. [-1, 3, 2, 1, -1, -4, 2, -1, -3, 4]
H. [2, -4, 1, 3, -1, 3, 2, -1, -3, 4]
I. [1, -3, 3, -1, 1, -4, 2, 1, -2, 4]
J. [1, -4, 2, -3, 1, 3, -2, 1, 3, -5]
Answer: C
We now define an algorithm: The definition of a(n) is Dyck language interpreted as binary numbers in ascending order, where Dyck language consists of balanced strings of parentheses that can be translated into binary numbers by interpreting '(' as '1' and ')' as '0'. 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. [11010110, 11100101, 11101100, 11110011, 11111010, 1010110010, 1010110110, 1010111010, 1011000010, 1011000110]
B. [11011010, 11100110, 11101010, 11111000, 11110010, 1010111010, 1010111100, 1011000010, 1011000100, 1011001000]
C. [11011100, 11100011, 11100101, 11101100, 11101000, 1010101011, 1010101101, 1010110101, 1010110111, 1010111010]
D. [11011011, 11101101, 11111011, 11111101, 1010000000, 1010101111, 1011000010, 1011000111, 1011010100, 1011100100]
E. [11011000, 11100010, 11100100, 11101000, 11110000, 1010101010, 1010101100, 1010110010, 1010110100, 1010111000]
F. [11011001, 11101010, 11110000, 11111100, 1010101010, 1010101110, 1010110100, 1011000000, 1011000010, 1011001100]
G. [11011101, 11101110, 11110000, 11110010, 11110110, 1011001010, 1011001100, 1011010000, 1011010100, 1011011000]
H. [11010100, 11100001, 11100011, 11101001, 11110001, 1010101000, 1010101110, 1010110000, 1010110110, 1010111100]
I. [11011110, 11101000, 11101011, 11110000, 11110100, 1010111110, 1011000000, 1011000110, 1011001000, 1011001100]
J. [11010111, 11100111, 11110101, 11111001, 1010101010, 1010110011, 1010111101, 1011000101, 1011001010, 1011010100]
Answer: E
We now define an algorithm: The definition of a(n) is the nth term of the Rudin-Shapiro or Golay-Rudin-Shapiro sequence, which can be obtained from the coefficients of the Shapiro polynomials, describing specific properties in signal processing and combinatorial design. 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. [1, -1, -1, 1, 1, -1, 1, 1, -1, -1]
B. [1, 1, 1, -1, -1, -1, 1, 1, -1, -1]
C. [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
D. [1, 1, -1, 1, -1, 1, -1, 1, 1, -1]
E. [1, 1, -1, -1, 1, 1, -1, -1, 1, 1]
F. [-1, -1, 1, 1, -1, -1, 1, -1, 1, 1]
G. [1, -1, 1, 1, -1, -1, 1, -1, -1, 1]
H. [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]
I. [1, 1, 1, 1, -1, -1, -1, 1, -1, 1]
J. [-1, 1, 1, -1, 1, 1, -1, -1, 1, -1]
Answer: I
We now define an algorithm: The definition of a(n) is the continued fraction representation of the cube root of 2. Given the input x_list (a series of values): [73, 74, 75, 76, 77, 78, 79, 80, 81, 82], determine the corresponding output sequence y_list.

Options:
A. [4, 3, 6, 12, 1, 1, 4, 15, 1, 3]
B. [5, 3, 4, 13, 2, 1, 4, 16, 2, 5]
C. [3, 5, 4, 11, 2, 2, 6, 16, 1, 4]
D. [5, 4, 3, 12, 1, 2, 5, 13, 2, 4]
E. [4, 4, 5, 11, 2, 1, 6, 15, 1, 5]
F. [3, 4, 5, 13, 1, 1, 6, 14, 1, 3]
G. [4, 5, 3, 12, 1, 2, 5, 14, 2, 4]
H. [3, 5, 6, 11, 2, 2, 6, 14, 2, 5]
I. [4, 4, 5, 12, 1, 1, 5, 15, 1, 4]
J. [4, 3, 5, 13, 2, 1, 4, 15, 1, 5]
Answer: I
We now define an algorithm: The definition of a(n) is a Chebyshev transform of the central binomial numbers C(2n, n), which are the coefficients in the binomial expansion of $(1 + x)^{(2n)}$. 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. [720000000, 2609600000, 9483300000, 34509000000, 125730000000, 458580000000, 1674300000000, 6118500000000, 22379000000000, 81913500000000]
B. [719150000, 2609580000, 9483260000, 34508800000, 125727300000, 458573550000, 1674270500000, 6118473000000, 22378379000000, 81913223500000]
C. [719180000, 2609577000, 9483269000, 34508680000, 125726500000, 458573500000, 1674265000000, 6118475000000, 22378380000000, 81913220000000]
D. [719000000, 2609605000, 9483290000, 34508750000, 125728000000, 458573000000, 1674278000000, 6118440000000, 22378360000000, 81913250000000]
E. [718000000, 2609560000, 9483250000, 34508600000, 125726000000, 458572000000, 1674260000000, 6118460000000, 22378300000000, 81913000000000]
F. [718500000, 2609570000, 9483280000, 34508820000, 125727000000, 458573000000, 1674270000000, 6118470000000, 22378450000000, 81913200000000]
G. [719170800, 2609577700, 9483269007, 34508808780, 125727351180, 458573578970, 1674270763580, 6118472289880, 22378379004140, 81913223571700]
H. [715000000, 2609500000, 9483200000, 34508000000, 125720000000, 458570000000, 1674200000000, 6118400000000, 22378000000000, 81912000000000]
I. [719170850, 2609577701, 9483269008, 34508808789, 125727351186, 458573578977, 1674270763584, 6118472289889, 22378379004146, 81913223571701]
J. [720170000, 2609580000, 9483270000, 34508850000, 125727500000, 458574000000, 1674275000000, 6118475000000, 22378400000000, 81913250000000]
Answer: I
We now define an algorithm: The definition of a(n) is Tetranacci numbers arising in connection with current algebras sp(2)_n, where a Tetranacci sequence is a generalized Fibonacci sequence where each term is the sum of the previous four terms. The initial terms are provided for the specific sequence in this context. 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. [18484483, 35629981, 68678991, 132383006, 255176443, 491868403, 948106825, 1827534659, 3522686312, 6790196181]
B. [18484479, 35629977, 68678987, 132383002, 255176439, 491868399, 948106821, 1827534655, 3522686308, 6790196177]
C. [18484485, 35629983, 68678993, 132383008, 255176445, 491868405, 948106827, 1827534661, 3522686314, 6790196183]
D. [18484477, 35629975, 68678985, 132383000, 255176437, 491868397, 948106819, 1827534653, 3522686306, 6790196175]
E. [18484481, 35629979, 68678989, 132383004, 255176441, 491868401, 948106823, 1827534657, 3522686310, 6790196179]
F. [18484484, 35629982, 68678992, 132383007, 255176444, 491868404, 948106826, 1827534660, 3522686313, 6790196182]
G. [18484482, 35629980, 68678990, 132383005, 255176442, 491868402, 948106824, 1827534658, 3522686311, 6790196180]
H. [18484486, 35629984, 68678994, 132383009, 255176446, 491868406, 948106828, 1827534662, 3522686315, 6790196184]
I. [18484480, 35629978, 68678988, 132383003, 255176440, 491868400, 948106822, 1827534656, 3522686309, 6790196178]
J. [18484478, 35629976, 68678986, 132383001, 255176438, 491868398, 948106820, 1827534654, 3522686307, 6790196176]
Answer: D
We now define an algorithm: The definition of a(n) is the expansion of (phi(-q^3) * psi(q))^3 / (phi(-q) * psi(q^3)) in powers of q, where phi(q) and psi(q) are Ramanujan's theta functions. Ramanujan's theta functions are defined as follows: \n\nphi(q) = sum(q^(n^2), n, -∞, ∞) \npsi(q) = sum(q^(n(n+1)/2), n, -∞, ∞). Given the input x_list (a series of values): [44, 45, 46, 47, 48, 49, 50, 51, 52, 53], determine the corresponding output sequence y_list.

Options:
A. [344, 466, 316, 244, 139, 281, 408, 418, 410, 266]
B. [353, 457, 307, 235, 148, 290, 397, 409, 401, 275]
C. [350, 460, 310, 238, 145, 287, 400, 412, 404, 272]
D. [347, 463, 313, 241, 142, 284, 404, 415, 407, 269]
E. [349, 461, 311, 239, 144, 286, 402, 413, 405, 271]
F. [348, 462, 312, 240, 143, 285, 403, 414, 406, 270]
G. [351, 459, 309, 237, 146, 288, 399, 411, 403, 273]
H. [345, 465, 315, 243, 140, 282, 407, 417, 409, 267]
I. [352, 458, 308, 236, 147, 289, 398, 410, 402, 274]
J. [346, 464, 314, 242, 141, 283, 406, 416, 408, 268]
Answer: F
We now define an algorithm: The definition of a(n) is numerators in the Taylor series for the inverse hyperbolic cosine function (arccosh(x)) subtracted by the natural logarithm of 2 times x (log(2*x)). 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. [856261275, 2418157975, 7892326442, 22427411535, 463012370465, 814589420475, 2687300306927, 14801325804718, 71989816618513, 121683714103008]
B. [756261275, 4418157975, 6892326443, 42427411435, 163012370465, 814589420475, 3687300306925, 15801325804719, 71989816618513, 221683714103007]
C. [756261276, 3418157975, 8892326441, 22427411335, 363012370465, 914589420475, 2687300306926, 14801325804719, 71989816618513, 221683714103007]
D. [756261276, 3418157976, 4892326440, 12427411435, 563012370465, 214589420475, 1687300306925, 5801325804718, 51989816618513, 121683714103006]
E. [756261275, 4418157975, 6892326441, 22427411435, 263012370465, 514589420475, 2687300306925, 15801325804719, 61989816618513, 121683714103007]
F. [956261276, 3418157975, 5892326440, 32427411436, 263012370464, 514589420475, 1687300306924, 5801325804719, 81989816618512, 101683714103007]
G. [756261275, 5418157976, 9892326441, 32427411435, 263012370465, 714589420475, 3687300306925, 4801325804719, 81989816618513, 121683714103009]
H. [656261275, 5418157975, 5892326441, 42427411435, 363012370465, 614589420475, 1687300306925, 5801325804719, 71989816618513, 131683714103007]
I. [856261275, 3418157975, 7892326441, 32427411435, 163012370465, 414589420475, 3687300306925, 25801325804719, 51989816618513, 101683714103007]
J. [956261275, 4418157975, 1892326441, 52427411435, 463012370465, 614589420475, 3687300306926, 25801325804720, 71989816618513, 121683714103005]
Answer: E
We now define an algorithm: The definition of a(n) is: M-sequences $m_0, m_1, m_2, m_3$ with $m_1 < n$, where M-sequences are generated from an iterative process of polynomial interpolation using specific conditions. Each term $m_i$ is derived from evaluating the resulting polynomial at predetermined integer points. Given the input x_list (a series of values): [23, 24, 25, 26, 27, 28, 29, 30, 31, 32], determine the corresponding output sequence y_list.

Options:
A. [882488, 1135535, 1446406, 1825227, 2283400, 2833706, 3490412, 4269382, 5188192, 6266249]
B. [882000, 1135400, 1446300, 1825100, 2283200, 2833500, 3490100, 4269000, 5187800, 6265900]
C. [882310, 1135450, 1446320, 1825150, 2283300, 2833610, 3490290, 4269200, 5187900, 6266000]
D. [882500, 1135500, 1446500, 1825300, 2283500, 2833700, 3490500, 4269400, 5188000, 6266100]
E. [884321, 1136723, 1447890, 1827008, 2285300, 2835600, 3492468, 4272000, 5190801, 6269982]
F. [882800, 1135690, 1446710, 1825510, 2283700, 2833900, 3490710, 4269610, 5188200, 6266300]
G. [882588, 1135588, 1446588, 1825388, 2283488, 2833688, 3490488, 4269288, 5188088, 6266088]
H. [881231, 1134600, 1446200, 1824800, 2283000, 2833300, 3489900, 4268900, 5187700, 6265600]
I. [883000, 1135600, 1446600, 1825400, 2283600, 2833800, 3490600, 4269500, 5188100, 6266200]
J. [882999, 1135599, 1446599, 1825399, 2283499, 2833699, 3490499, 4269299, 5188099, 6266099]
Answer: A
We now define an algorithm: The definition of a(n) is numbers n such that the polynomial $x^n + x^{(n-1)} + x^{(n-2)} + ... + x + 1$ is irreducible over the finite field GF(5), which contains exactly 5 elements. Given the input x_list (a series of values): [46, 47, 48, 49, 50, 51, 52, 53, 54, 55], determine the corresponding output sequence y_list.

Options:
A. [475, 485, 495, 505, 515, 525, 535, 545, 555, 565]
B. [580, 590, 600, 615, 625, 635, 645, 655, 665, 675]
C. [580, 590, 600, 610, 620, 630, 640, 650, 660, 670]
D. [576, 586, 592, 606, 612, 616, 646, 652, 672, 676]
E. [583, 593, 603, 613, 623, 633, 643, 653, 663, 673]
F. [576, 586, 597, 607, 617, 627, 637, 647, 657, 667]
G. [578, 588, 598, 614, 622, 632, 642, 650, 662, 674]
H. [576, 587, 598, 609, 620, 631, 642, 653, 664, 675]
I. [478, 489, 511, 523, 533, 543, 553, 563, 575, 585]
J. [589, 597, 603, 611, 619, 627, 635, 643, 651, 659]
Answer: D
We now define an algorithm: The definition of a(n) is the unique attractor for the transformation that first applies the "RIGHT" shift operation followed by the "MÖBIUS" transform. Given the input x_list (a series of values): [49, 50, 51, 52, 53, 54, 55, 56, 57, 58], determine the corresponding output sequence y_list.

Options:
A. [-148, -137, -176, -179, -205, -215, -258, -244, -282, -296]
B. [-141, -135, -169, -182, -210, -209, -254, -250, -277, -297]
C. [-147, -139, -173, -176, -209, -207, -251, -252, -278, -289]
D. [-143, -137, -171, -181, -207, -211, -252, -247, -279, -293]
E. [-149, -136, -177, -184, -204, -216, -259, -253, -274, -288]
F. [-142, -139, -168, -179, -209, -210, -253, -249, -278, -294]
G. [-140, -138, -170, -180, -212, -208, -256, -246, -280, -295]
H. [-145, -136, -175, -177, -208, -212, -250, -248, -276, -290]
I. [-146, -138, -174, -183, -206, -214, -257, -251, -275, -292]
J. [-144, -134, -172, -178, -211, -213, -255, -245, -281, -291]
Answer: F
We now define an algorithm: The definition of a(n) is the coefficients in the harmonic expansion (or factorial expansion) of the Euler-Mascheroni constant γ. 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. [11, 33, 34, 49, 43, 50, 16, 13, 40, 49]
B. [19, 34, 31, 44, 45, 52, 14, 15, 37, 45]
C. [13, 30, 35, 48, 40, 51, 17, 12, 41, 46]
D. [22, 31, 30, 47, 41, 48, 18, 11, 38, 47]
E. [10, 35, 29, 46, 46, 53, 13, 17, 36, 44]
F. [12, 32, 32, 48, 42, 49, 15, 14, 39, 48]
G. [14, 37, 28, 49, 44, 46, 20, 18, 38, 43]
H. [16, 29, 27, 45, 38, 54, 11, 10, 34, 42]
I. [15, 36, 33, 50, 39, 47, 19, 16, 42, 50]
J. [21, 38, 36, 43, 47, 45, 12, 19, 35, 51]
Answer: F
We now define an algorithm: The definition of a(n) is the Odious numbers: numbers with an odd number of 1's in their binary expansion. Given the input x_list (a series of values): [56, 57, 58, 59, 60, 61, 62, 63, 64, 65], determine the corresponding output sequence y_list.

Options:
A. [109, 111, 113, 116, 118, 120, 123, 126, 129, 131]
B. [111, 113, 116, 118, 120, 122, 125, 128, 131, 133]
C. [111, 114, 116, 118, 120, 123, 125, 128, 130, 132]
D. [110, 113, 116, 119, 120, 123, 126, 129, 131, 134]
E. [112, 115, 117, 119, 121, 124, 126, 129, 131, 133]
F. [109, 111, 115, 117, 119, 121, 123, 125, 127, 129]
G. [109, 112, 115, 118, 121, 123, 126, 128, 131, 135]
H. [113, 115, 118, 120, 123, 125, 127, 130, 134, 136]
I. [108, 110, 113, 115, 119, 122, 124, 127, 130, 133]
J. [110, 112, 115, 117, 118, 121, 122, 124, 127, 128]
Answer: J
We now define an algorithm: The definition of a(n) is the characteristic function of the lucky numbers, where a(n) = 1 if n is a lucky number and a(n) = 0 otherwise. Lucky numbers are a sequence of numbers generated by a specific sieving process similar to the Sieve of Eratosthenes used to generate prime numbers. 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. [1, 0, 1, 0, 0, 1, 0, 0, 1, 0]
B. [1, 0, 0, 0, 1, 0, 0, 0, 0, 1]
C. [0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
D. [0, 1, 1, 0, 0, 0, 0, 0, 1, 0]
E. [0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
F. [1, 0, 0, 1, 0, 1, 0, 0, 0, 0]
G. [0, 1, 0, 0, 1, 0, 0, 1, 0, 0]
H. [0, 1, 0, 0, 0, 0, 1, 0, 1, 0]
I. [0, 0, 1, 0, 0, 1, 0, 1, 0, 0]
J. [0, 0, 0, 0, 1, 0, 0, 1, 0, 0]
Answer: C
We now define an algorithm: The definition of a(n) is a fractal sequence derived from Fibonacci numbers or the Wythoff array. Given the input x_list (a series of values): [76, 77, 78, 79, 80, 81, 82, 83, 84, 85], determine the corresponding output sequence y_list.

Options:
A. [2, 30, 19, 12, 31, 8, 32, 20, 5, 33]
B. [4, 28, 19, 12, 33, 10, 30, 23, 5, 32]
C. [3, 31, 18, 13, 30, 9, 33, 21, 6, 34]
D. [5, 30, 17, 14, 34, 8, 29, 20, 6, 33]
E. [2, 31, 16, 10, 35, 9, 28, 21, 7, 30]
F. [2, 29, 20, 11, 32, 7, 31, 22, 4, 35]
G. [6, 30, 19, 14, 37, 10, 25, 24, 9, 33]
H. [3, 29, 22, 15, 36, 7, 26, 23, 4, 31]
I. [2, 33, 18, 12, 38, 11, 34, 25, 5, 32]
J. [1, 32, 21, 13, 31, 11, 27, 22, 8, 34]
Answer: A
We now define an algorithm: The definition of a(n) is scaled Chebyshev U-polynomials evaluated at sqrt(3)/2; expansion of 1/(1 - 3*x + 3*x^2). Given the input x_list (a series of values): [26, 27, 28, 29, 30, 31, 32, 33, 34, 35], determine the corresponding output sequence y_list.

Options:
A. [3188643, 4782965, 4782965, -3, -14348910, -43046725, -86093445, -129140170, -129140170, -3]
B. [3188645, 4782968, 4782968, -1, -14348906, -43046720, -86093441, -129140162, -129140162, -1]
C. [3188647, 4782970, 4782970, 1, -14348908, -43046722, -86093443, -129140164, -129140164, 1]
D. [3188648, 4782972, 4782972, 2, -14348904, -43046718, -86093438, -129140158, -129140158, 2]
E. [3188651, 4782976, 4782976, 6, -14348903, -43046717, -86093437, -129140157, -129140157, 6]
F. [3188649, 4782973, 4782973, 3, -14348909, -43046723, -86093444, -129140165, -129140165, 3]
G. [3188642, 4782964, 4782964, -4, -14348911, -43046726, -86093446, -129140171, -129140171, -4]
H. [3188650, 4782975, 4782975, 5, -14348902, -43046715, -86093435, -129140150, -129140150, 5]
I. [3188644, 4782967, 4782967, -2, -14348905, -43046719, -86093439, -129140159, -129140159, -2]
J. [3188646, 4782969, 4782969, 0, -14348907, -43046721, -86093442, -129140163, -129140163, 0]
Answer: J
We now define an algorithm: The definition of a(n) is: Triangle in which first row is 0, n-th row (n>1) lists the exponents of distinct prime factors ("ordered prime signature") in the prime factorization of n. For example, the prime factorization of 12 is 2^2 * 3^1, so it contributes the row [2, 1]. 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. [1, 1, 1, 1, 1, 1, 1, 3, 2, 1]
B. [1, 1, 2, 1, 1, 3, 1, 1, 1, 2]
C. [1, 1, 2, 1, 3, 1, 1, 2, 1, 1]
D. [1, 1, 3, 1, 1, 1, 2, 1, 1, 2]
E. [1, 2, 1, 1, 3, 1, 1, 1, 2, 1]
F. [3, 1, 1, 2, 1, 1, 1, 1, 1, 3]
G. [2, 1, 1, 1, 1, 2, 1, 1, 3, 1]
H. [1, 2, 1, 1, 1, 1, 2, 3, 1, 1]
I. [2, 1, 1, 1, 1, 1, 1, 1, 3, 2]
J. [1, 1, 1, 2, 1, 1, 3, 1, 1, 2]
Answer: A