MikaStars39/nano-eval huggingface dataset:
For the theoretical stress concentration factor α and the effective stress concentration factor Kσ, there are the following four conclusions. Which of these options is correct?

Options:
A. α has no relationship with material composition, Kσ is related to stress levels
B. α and Kσ have a relationship with geometric factors but not material properties
C. α has no relationship with the material properties, Kσ is related to material properties
D. α depends on the material properties, Kσ depends on stress concentration
E. α is proportional to loading conditions, Kσ is inversely related to material properties
F. α and Kσ are both related to material properties
G. α is related to dimensional properties, Kσ is related to stress concentration
H. α has a relationship with thermal properties, Kσ is related to material properties
I. α and Kσ have no relationship with material properties
J. α is related to material properties, Kσ has no relationship with material properties
Answer: C
Set the inner diameter of the hollow circular shaft to $d$, the outer diameter to $D$, with $d/D = a$, what are the expressions for its polar moment of inertia $I_p$ and torsional section modulus $W_p$?

Options:
A. $I_p = \frac{1}{32} \pi D^4 (a^4 - 1)$,$W_p = \frac{1}{16} \pi D^3 (a^4 - 1)$
B. $I_p = \frac{1}{64} \pi (D^4 - d^3)$,$W_p = \frac{1}{32} \pi (D^3 - d^2)$
C. $I_p = \frac{1}{32} \pi D^4 (1 - a^3)$,$W_p = \frac{1}{64} \pi D^3 (1 - a^4)$
D. $I_p = \frac{1}{64} \pi D^4 (1 - a^3)$,$W_p = \frac{1}{32} \pi D^3 (1 - a^4)$
E. $I_p = \frac{1}{64} \pi D^4 (1 - a^4)$,$W_p = \frac{1}{32} \pi D^3 (1 - a^3)$
F. $I_p = \frac{1}{64} \pi (D^4 - d^4)$,$W_p = \frac{1}{32} \pi (D^3 - d^3)$
G. $I_p = \frac{1}{32} \pi D^4 (1 - a^4)$,$W_p = \frac{1}{16} \pi D^3 (1 - a^3)$
H. $I_p = \frac{1}{32} \pi D^4 (1 - 2a^4)$,$W_p = \frac{1}{16} \pi D^3 (1 - 2a^4)$
I. $I_p = \frac{1}{32} \pi D^4 (1 - a^4)$,$W_p = \frac{1}{16} \pi D^3 (1 - a^4)$
J. $I_p = \frac{1}{32} \pi (D^4 - d^4)$,$W_p = \frac{1}{16} \pi (D^3 - d^3)$
Answer: I
Which of the following reactions represents a sulfonation reaction?

Options:
A. $\text{C} + \text{O}_2 = \text{CO}_2$
B. $\text{ZnS} + \text{H}_2\text{O} = \text{ZnO} + \text{H}_2\text{S}$
C. $\text{ZnS} + \text{O}_2 = \text{ZnO} + \text{SO}_2$
D. $\text{FeS} + \text{Cu}_2\text{O} = \text{FeO} + \text{Cu}_2\text{S}$
E. $\text{Cu}_2\text{S} + \text{O}_2 = \text{Cu}_2\text{O} + \text{SO}_2$
F. $\text{H}_2\text{S} + \text{O}_2 = \text{SO}_2 + \text{H}_2\text{O}$
G. $\text{CuS} + \text{Fe}_2\text{O}_3 = \text{CuO} + \text{Fe}_2\text{S}_3$
H. $\text{Fe}_3\text{O}_4 + \text{FeS} + \text{SiO}_2 = \text{FeO}\cdot\text{SiO}_2 + \text{SO}_2$
I. $\text{CuS} + \text{H}_2\text{O} = \text{CuO} + \text{H}_2\text{S}$
Answer: D
Regarding DDZ-III type transmitters, the correct statement is ( )

Options:
A. On-site transmission signal ranges 3~~15mA
B. Current transmission, current reception
C. Remote transmission signal ranges 3~~15mA
D. Each unit is powered individually by 220V
E. Output transmission, current reception
F. On-site transmission signal is 4~~20mA
G. Each unit functions independently at 110V
H. On-site transmission signal 0~~10mA
I. On-site transmission signal is 5~~25mA
Answer: F
When $\mathrm{y i-y i^{*} > 0}$ in the system, ( ).

Options:
A. Absorption process occurs
B. Neutralization process commences
C. Distillation process occurs
D. Extraction process starts
E. No net transfer of substance
F. Condensation process initiates
G. Sedimentation process begins
H. Evaporation process happens
I. Crystallization process occurs
Answer: A
In liquid-phase bimolecular adsorption, U-shaped adsorption refers to the adsorption process where the adsorbent ( ).

Options:
A. The curve always preferentially adsorbs one component
B. The solvent is adsorbed first, followed by the solute
C. Equal presence of both components on the adsorbent
D. Adsorption levels fluctuate based on external conditions
E. Adsorption initially favors the solvent over time
F. The solute is adsorbed first, followed by the solvent
G. One phase's molecules dominate the adsorption curve
H. The solute and solvent have similar adsorption amounts
I. The adsorbent equally splits between solute and solvent
J. The adsorption rate remains constant throughout the process
Answer: A
In a photonic crystal, assuming the refractive index contrast of the material is 2 and the lattice constant is 500 nm, calculate the width of the photonic band gap.

Options:
A. 45 nm
B. 50 nm
C. 30 nm
D. 5 nm
E. 10 nm
F. 20 nm
G. 35 nm
H. 15 nm
I. 40 nm
J. 25 nm
Answer: F
In a fiber optic communication system, if the signal passes through an optical amplifier with a gain of 3 dB and the input power to the amplifier is -20 dBm, calculate the output power of the amplifier (dBm).

Options:
A. -17 dBm
B. -15 dBm
C. -18 dBm
D. -16 dBm
E. -22 dBm
F. -14 dBm
G. -23 dBm
H. -7 dBm
I. -10 dBm
J. -13 dBm
Answer: J
A fiber optic communication system employs 16-QAM modulation, where each symbol carries 4 bits of information. If the signal's carrier frequency is 80 GHz, find the maximum data rate of the system under ideal conditions (in Gbps).

Options:
A. 160
B. 400
C. 280
D. 320
E. 560
F. 80
G. 480
H. 640
I. 240
J. 200
Answer: D
Consider a fiber optic communication system where the signal passes through a dispersion-compensating fiber. The dispersion slope of the dispersion-compensating fiber is 0.05 ps/nm²/km, the spectral width of the signal is 40 nm, and the transmission distance is 100 km. Calculate the second-order dispersion introduced by the dispersion-compensating fiber (in ps²).

Options:
A. 500
B. 3000
C. 100
D. 200
E. 250
F. 20
G. 50
H. 2000
I. 2
J. 150
Answer: H
In photonic integrated circuit design, what is the most important parameter to consider for achieving mode coupling in a photonic crystal waveguide?

Options:
A. intensity of light in the waveguide
B. width of the waveguide
C. polarization of the light in the waveguide
D. refractive index of the waveguide
E. electrical conductivity of the waveguide
F. temperature around the waveguide
G. bend radius of the waveguide
H. color of the waveguide exterior
I. length of the waveguide
J. thickness of the waveguide material
Answer: D
In photonics, the linewidth of a fiber ring cavity is mainly determined by:

Options:
A. cavity dispersion
B. cavity reflectivity
C. cavity width
D. cavity material
E. cavity color
F. cavity temperature
G. cavity length
H. cavity density
I. cavity texture
J. cavity loss
Answer: A
When a steady current passes through a conductor, its current and application are proportional to the voltage at both ends of the conductor, and the proportionality constant is called the () of the object.

Options:
A. Kinetic Energy
B. Power Stability
C. Resistance Force
D. Circuit Flexibility
E. Voltage Gradient
F. Current Density
G. Thermal Conductivity
H. Electrical Conductivity
I. Electrical Resistance
J. Magnetic Resistance
Answer: H
A type of music and dance from the Shun tribe, which was recorded in Han Feizi's "Five Pests," states that Shun, during his leadership, conquered the Miao people using which of the following dances?

Options:
A. Bird Dance
B. Water Spirit Dance
C. Dry Feather Dance
D. Feather Dance
E. Wind Dance
F. Leafy Dance
G. Stone Dance
H. Cloud Dance
I. Fire Dance
J. War Dance
Answer: C
In cold chain logistics, within what range is the temperature most commonly maintained?

Options:
A. -5°C to 0°C
B. 5°C to 9°C
C. -30°C to -20°C
D. 8°C to 12°C
E. 10°C to 14°C
F. -15°C to -5°C
G. -25°C to -15°C
H. 2°C to 6°C
I. -20°C to -10°C
J. 0°C to 4°C
Answer: J
What is a "whole tone scale"?

Options:
A. a scale using a mix of whole and half steps
B. a scale that includes seven natural tones
C. a scale consisting of only diminished intervals
D. a scale that repeats every five notes
E. a scale that excludes minor seconds entirely
F. a scale that combines major and minor tones
G. a scale that contains all twelve semitones
H. a scale built from consecutive major thirds
I. a scale made up of only perfect fifths
J. a scale that avoids any sharp or flat notes
Answer: G
A 23-year-old female experiences nausea and vomiting after consuming dried fish fillets and beer. A few hours later, she complains of numbness in the lips, weakness in the limbs, followed by difficulty breathing and coma. The most likely diagnosis is __.

Options:
A. Scombroid fish intoxication
B. Insecticide fish contamination
C. Botulism
D. Cyanobacteria fish hazard
E. Acute alcohol poisoning
F. Histamine fish poisoning
G. Marine biotoxin exposure
H. Pufferfish (fugu) poisoning
I. Anaphylactic shock
J. Heavy metal fish toxicity
Answer: H
The solubility characteristics of humic acid salts are generally ( ).

Options:
A. Soluble in water
B. Soluble in alkali
C. Soluble in alcohol
D. Soluble in ether
E. Insoluble in acid
F. Alcohol, oil, and ether are all soluble.
G. Soluble in oil
H. Water, acid, and alkali are all soluble.
I. Insoluble in water
J. Soluble in acid
Answer: B
What material is suitable for large volume concrete engineering?

Options:
A. Polymer cement mortar
B. Super sulfate cement
C. Fly ash blend
D. Slag cement
E. Ordinary Portland cement
F. High alumina cement
G. Gypsum plaster
H. Portland cement
I. Epoxy resin mixture
J. Magnesium oxychloride
Answer: D
The most effective method for treating external fish diseases is ().

Options:
A. Electromagnetic radiation method
B. Hypothermic treatment method
C. Physical control method
D. Oral administration method
E. Injection method
F. Whole pond sprinkling method
G. Isolation tank method
H. Ultrasonic wave treatment method
I. Genetic modification method
J. Vaccination routine method
Answer: F
For long-distance oil and gas pipelines, what is the most important maintenance task?

Options:
A. Environmental monitoring
B. Antifreeze
C. Emergency drills
D. Endpoint security
E. Leak Prevention
F. Anticorrosion
G. Engine maintenance
H. Fire Prevention
I. Electrical grounding
J. Equipment inspection
Answer: F
Labyrinthine fistula complicating otitis media is most commonly located in the ()

Options:
A. Superior semicircular canal
B. Vestibule
C. Lateral semicircular canal
D. Posterior semicircular canal
E. Eustachian tube
F. External auditory canal
G. Round window
H. Cochlea
I. Tympanic membrane
J. Oval window
Answer: C
In patients with otogenic brain abscess, once brain herniation occurs, which of the following is incorrect?

Options:
A. Apply cold compresses to the forehead to reduce fever
B. Emergency puncture and drainage of the brain abscess
C. Administer anticoagulants to prevent blood clots
D. Urgently consult neurosurgery for collaborative rescue
E. Do not use dehydrating agents to prevent electrolyte imbalance
F. Lower head of the bed to reduce pressure
G. Increase fluid intake to maintain hydration levels
H. Perform tracheotomy or intubation if necessary
I. Provide oxygen and artificial respiration
J. Use high doses of antibiotics immediately
Answer: E
Which of the following treatment methods for patulous eustachian tube is incorrect?

Options:
A. Balloon sinus dilation procedure
B. Using earwax removal drops
C. Applying silver nitrate to the eustachian tube orifice
D. Chewing gum frequently
E. Loud noise-based therapies
F. Soft palate closure
G. Tensor veli palatini muscle release surgery
H. Salicylic acid powder insufflation for eustachian tube dilation
I. Steam inhalation therapy
J. High-altitude training exercises
Answer: D
In what year was the Daily Chronicle founded by whom?

Options:
A. Winston Churchill in 1940.
B. Genghis Khan in 1227.
C. Marco Polo in 1298.
D. Alexander the Great in 332 B.C.
E. Queen Elizabeth I in 1601.
F. Albert Einstein in 1921.
G. Leonardo da Vinci in 1503.
H. Thomas Jefferson in 1776.
I. Napoleon Bonaparte in 1803.
J. Julius Caesar in 59 B.C.
Answer: J
How does the refractive index distribution affect optical waveguides?

Options:
A. Acoustic noise in the transmission path
B. Scattering of light within the guide
C. Propagation speed of sound waves
D. Chromatic dispersion in the medium
E. Directionality of the optical signal
F. Absorption of the optical signal
G. Refraction corrections in optical fibers
H. Diffraction efficiency of the material
I. Polarization state of the optical wave
Answer: E
In optical communication, the relationship between transmission distance and signal attenuation is ().

Options:
A. linearly decreasing
B. exponentially increasing
C. not correlated
D. directly proportional
E. sinusoidally varying
F. negatively proportional
G. logarithmically mapped
H. frequency dependent
I. randomly changing
J. inversely proportional
Answer: D
What is the most effective time for moderate-intensity exercise?

Options:
A. 55 minutes
B. 30 minutes
C. 15 minutes
D. 25 minutes
E. 40 minutes
F. 70 minutes
G. 75 minutes
H. 35 minutes
I. 50 minutes
J. 65 minutes
Answer: B
Which dust removal method should be used for dust particles with a diameter of more than $75\mu m$ in dust-laden gas? Which method should be used for dust particles above 5μm and below 1μm?

Options:
A. Wet scrubber; ionizer; bag filter
B. Bag filter; electrostatic precipitator; venturi scrubber
C. Advanced filters; ionizer; HEPA filter
D. Electrostatic precipitator; wet scrubber; HEPA filter
E. HEPA filter; wet scrubber; gravity settling chamber
F. HEPA filter; wet scrubber; cyclonic scrubber
G. Dust removal chamber; cyclone separator; bag filter
H. Pre-filter; venturi scrubber; HEPA filter
Answer: G
What method should be used to make the centrifuge have a larger separation factor and ensure that the drum has sufficient mechanical strength?

Options:
A. Medium speed, small diameter
B. High speed, small diameter
C. High speed, large weight
D. Low speed, large diameter
E. High speed, low temperature
F. Low speed, small diameter
G. Low speed, high temperature
H. Medium speed, large thickness
I. Medium speed, average weight
Answer: B
Industrial gas dust removal is often carried out after cooling. What is the reason?

Options:
A. Raising temperature hastens gas diffusion
B. Lowering vapor pressure improves gas separation
C. Reducing viscosity can increase sedimentation rate
D. Draining water vapor reduces dew formation
E. Supplementing heat can aid in combustion
F. Moistening particles can lessen dust sticking
G. Improving the smell can decrease odor contamination
H. Steaming gases can speed up heat transfer
I. Aeration process can be made more efficient
J. Facilitating reactions can enhance chemical bonding
Answer: C
How does the viscosity μ of a fluid usually change with temperature t?

Options:
A. As t increases for liquids, μ stays the same, gases vary
B. As t increases for liquids, μ stays constant, unlike gases
C. As t increases for gases, μ decreases, while liquids remain constant
D. As t increases for liquids, μ increases, and the same for gases
E. As t increases for liquids, μ decreases, and gases do too
F. As t increases for gases, μ decreases, and vice versa for liquids
G. As t increases for gases, μ remains constant, unlike liquids
H. As t increases for gases, μ remains unchanged, opposite for liquids
I. As t increases for liquids, μ decreases, and vice versa for gases
Answer: I
What can the characteristics of a traveling wave be summarized as?

Options:
A. Diffraction Patterns Formed by Waves Passing Through Slits
B. Waves That Only Exist at Specific Frequencies
C. Amplitude Modulation of Waves Near Absorptive Boundaries
D. Specific Type of Transmitted Wave Propagating Parallel to the Stratigraphic Interface
E. Interaction of Converging Waves in Nonlinear Mediums
F. Propagation models under the condition of identical speeds in upper and lower strata
G. Polarization Effects Observed at Critical Angles of Incidence
H. The phenomenon when the angle between the incident wave and the normal reaches a specific value
I. Refraction Phenomena Due to Density Differences in Layers
J. Excitation When Incident Waves Align with Magnetic Fields
Answer: D
What is the lift of an aircraft with a wing effective lift area of 400 square centimeters, a lift coefficient of 1.5, and a speed of 100 meters per second?

Options:
A. 720 Newtons
B. 600 Newtons
C. 690 Newtons
D. 680 Newtons
E. 610 Newtons
F. 750 Newtons
G. 800 Newtons
H. 700 Newtons
I. 550 Newtons
J. 650 Newtons
Answer: B
What is the most suitable drainage method for heavy clay when choosing agricultural drainage measures?

Options:
A. Contour bunding techniques
B. Water storage tanks
C. Natural swale formations
D. Open channel ditches
E. Surface runoff systems
F. Ridge and furrow method
G. Elevated planter beds
H. Underground drainage
I. Embedded drain pipes
J. Gravel-filled trenches
Answer: H
Where does the phrase 'I casually pass the time while holding a fan adorned with peach blossoms' come from?

Options:
A. Whispering Silent Songs
B. Inscription on a Painting
C. Dancing under Moonlight
D. Guarding the Tower
E. Leaving the Courtyard
F. Wandering the Wilderness
G. Smiling at the Past
H. Embracing the Echoes
I. Lingering Charm
J. Lost in Rose Gardens
Answer: B
A landowner contracted to sell a plot of land to a buyer for \$50,000.
After agreeing to the sale, the landowner discovered a mineral deposit on the land, driving the worth of the land up to \$500,000. The contract did not indicate that either party would bear the risk of a mistake as to the value of the land or the absence or presence of any mineral deposits on the land.
The landowner now refuses to sell the land as agreed, and the buyer has sued for specific performance of the contract.
Which of the following facts, if true, would be most helpful to the landowner in resisting the sale?

Options:
A. Prior to the parties' contract, the buyer had conducted a survey and found that the land was free of any valuable minerals.
B. Prior to the parties' contract, the landowner had received professional advice indicating that the land would only be useful for agriculture.
C. Unbeknownst to the landowner at the time of contract, the buyer's agent had evaluated the land for speculative investment purposes only.
D. Prior to the parties' contract, the buyer had misrepresented the status of the bank loan that the buyer intended to use to pay for the land.
E. Prior to the parties' contract, the landowner had done extensive excavation work on the land and had never before found any indication of a mineral deposit.
F. Prior to the parties' contract, the landowner had inherited the land from a relative who had kept no records of its mineral composition.
G. Unbeknownst to the buyer at the time of contract, the landowner had recently received an offer to buy the land for a similar price.
H. Unbeknownst to the buyer at the time of contract, the land had been part of a contentious legal dispute with a neighboring property owner.
I. Unbeknownst to the landowner at the time of contract, the buyer had recently discovered a mineral deposit of the same kind, just across the boundary line on adjacent land.
J. Unbeknownst to the buyer at the time of contract, the landowner was suffering severe financial difficulties.
Answer: I
Infrared radiation is a method of sterilization by ___

Options:
A. Biological process
B. Ultrasonic treatment
C. Mechanical method
D. Electromagnetic waves
E. Chemical method
F. Moist heat
G. Nuclear reaction
H. Radiowave emission
I. Photochemical effect
Answer: C
Direct methods are not suitable for measuring the following surface contaminations:

Options:
A. Background radiation level is high.
B. Surface temperature is unpredictably volatile.
C. Ion exchange resins are depleting fast.
D. Electric field interference is significant.
E. Loose Surface Contamination
F. Dry powders are difficult to assess.
G. Fixed Surface Contamination
H. Non-ionizing radiation levels are rising.
I. Contaminated soil is unevenly distributed.
J. Portable instruments are not calibrated.
Answer: A
The dry arcing distance of a 110kV rod-shaped insulator is 1m. According to national standards, calculate the margins it has during impulse and power frequency dry tests. If, during a rain test, the air gap and distance on the wet surface are 40cm and 70cm respectively, what is the margin during the rain test?

Options:
A. $$
215\%,~3 8 5. \ 6 4\%,~3 8 5. \ 6 4\%
$$
B. $$
225\%,~3 9 2. \ 6 9\%,~3 9 2. \ 6 9\%
$$
C. $$
221\%,~3 9 0. \ 6 7\%,~3 9 0. \ 6 7\%
$$
D. $$
218\%,~3 9 0. \ 6 2\%,~3 9 0. \ 6 2\%
$$
E. $$
231\%,~3 9 5. \ 7 3\%,~3 9 5. \ 7 3\%
$$
F. $$
240\%,~4 0 0. \ 8 0\%,~4 0 0. \ 8 0\%
$$
G. $$
230\%,~3 9 8. \ 7 6\%,~3 9 8. \ 7 6\%
$$
H. $$
212\%,~3 8 0. \ 5 9\%,~3 8 0. \ 5 9\%
$$
I. $$
237\%,~3 9 9. \ 7 5\%,~3 9 9. \ 7 5\%
$$
J. $$
220\%,~3 9 1. \ 6 8\%,~3 9 1. \ 6 8\%
$$
Answer: C
We now define an algorithm: The definition of a(n) is natural numbers in square maze arrangement, read by antidiagonals, where each number represents the step count required to reach a specific position in a square matrix. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_list.

Options:
A. [39, 59, 65, 97, 99, 120, 118, 82, 76, 52]
B. [42, 62, 68, 100, 102, 123, 121, 85, 79, 55]
C. [44, 64, 70, 102, 104, 125, 123, 87, 81, 57]
D. [36, 56, 62, 94, 96, 117, 115, 79, 73, 49]
E. [41, 61, 67, 99, 101, 122, 120, 84, 78, 54]
F. [43, 63, 69, 101, 103, 124, 122, 86, 80, 56]
G. [37, 57, 63, 95, 97, 118, 116, 80, 74, 50]
H. [38, 58, 64, 96, 98, 119, 117, 81, 75, 51]
I. [40, 60, 66, 98, 100, 121, 119, 83, 77, 53]
J. [45, 65, 71, 103, 105, 126, 124, 88, 82, 58]
Answer: E
We now define an algorithm: The definition of a(n) is: Triangular array that counts rooted polyominoes, where a rooted polyomino is a polyomino with one designated cell that serves as its root, arranged in triangle form. 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. [15, 5, 17305, 15030, 11465, 7592, 4303, 2066, 827, 262]
B. [11, 4, 17320, 15120, 11515, 7575, 4300, 2068, 826, 268]
C. [10, 1, 17303, 15115, 11505, 7590, 4302, 2067, 825, 265]
D. [14, 3, 17250, 15025, 11475, 7595, 4305, 2070, 828, 264]
E. [12, 2, 17203, 15015, 11455, 7490, 4301, 2065, 822, 266]
F. [13, 2, 17325, 15100, 11525, 7585, 4299, 2074, 829, 261]
G. [18, 2, 17310, 15095, 11425, 7580, 4295, 2063, 824, 267]
H. [16, 1, 17330, 15125, 11555, 7600, 4310, 2075, 830, 263]
I. [17, 3, 17255, 15065, 11490, 7588, 4306, 2064, 823, 269]
J. [19, 4, 17280, 15130, 11535, 7597, 4304, 2069, 821, 270]
Answer: C
We now define an algorithm: The definition of a(n) is the number of 1-punctured staircase polygons (lattice polygons that resemble a staircase) with a hole of perimeter 4, enumerated by their perimeter. 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. [160645504, 699030226, 3014470024, 12901501696, 54863119744, 232022899306, 976598630968, 4093581923320, 17096805375360, 71176501409756]
B. [160645509, 699030236, 3014470070, 12901501720, 54863119790, 232022899356, 976598631018, 4093581923420, 17096805375385, 71176501409800]
C. [160645505, 699030228, 3014470030, 12901501700, 54863119750, 232022899316, 976598630978, 4093581923340, 17096805375365, 71176501409760]
D. [160645510, 699030238, 3014470080, 12901501725, 54863119800, 232022899366, 976598631028, 4093581923440, 17096805375390, 71176501409810]
E. [160645507, 699030232, 3014470050, 12901501710, 54863119770, 232022899336, 976598630998, 4093581923380, 17096805375375, 71176501409780]
F. [160645508, 699030234, 3014470060, 12901501715, 54863119780, 232022899346, 976598631008, 4093581923400, 17096805375380, 71176501409790]
G. [160645506, 699030230, 3014470040, 12901501705, 54863119760, 232022899326, 976598630988, 4093581923360, 17096805375370, 71176501409770]
H. [160645512, 699030242, 3014470100, 12901501735, 54863119820, 232022899386, 976598631048, 4093581923480, 17096805375400, 71176501409830]
I. [160645513, 699030244, 3014470110, 12901501740, 54863119830, 232022899396, 976598631058, 4093581923500, 17096805375405, 71176501409840]
J. [160645511, 699030240, 3014470090, 12901501730, 54863119810, 232022899376, 976598631038, 4093581923460, 17096805375395, 71176501409820]
Answer: A
We now define an algorithm: The definition of a(n) is: At step number k ≥ 1, the 2^(k-1) open intervals that are erased from [0,1] in the Cantor middle-third set construction are I(k,n) = (a(n)/3^k, (1+a(n))/3^k), where n = 1..2^(k-1). 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. [1537, 1543, 1627, 1633, 1645, 1651, 1681, 1687, 1699, 1705]
B. [1529, 1535, 1619, 1625, 1637, 1643, 1673, 1679, 1691, 1697]
C. [1538, 1544, 1628, 1634, 1646, 1652, 1682, 1688, 1700, 1706]
D. [1532, 1538, 1622, 1628, 1640, 1646, 1676, 1682, 1694, 1700]
E. [1534, 1540, 1624, 1630, 1642, 1648, 1678, 1684, 1696, 1702]
F. [1536, 1542, 1626, 1632, 1644, 1650, 1680, 1686, 1698, 1704]
G. [1531, 1537, 1621, 1627, 1639, 1645, 1675, 1681, 1693, 1699]
H. [1530, 1536, 1620, 1626, 1638, 1644, 1674, 1680, 1692, 1698]
I. [1533, 1539, 1623, 1629, 1641, 1647, 1677, 1683, 1695, 1701]
J. [1535, 1541, 1625, 1631, 1643, 1649, 1679, 1685, 1697, 1703]
Answer: G
We now define an algorithm: The definition of a(n) is the coordination sequence of the snub-632 tiling with respect to a hexavalent node, representing the number of nodes at distance n from a given node. 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. [213, 419, 417, 224, 339, 434, 219, 355, 463, 243]
B. [205, 313, 422, 217, 329, 445, 227, 349, 467, 239]
C. [212, 318, 416, 223, 338, 436, 221, 354, 465, 242]
D. [206, 310, 423, 218, 334, 440, 226, 350, 470, 238]
E. [208, 314, 419, 219, 335, 437, 225, 351, 466, 237]
F. [203, 311, 421, 215, 331, 443, 229, 347, 469, 241]
G. [209, 316, 415, 214, 332, 435, 224, 352, 464, 236]
H. [211, 317, 415, 222, 337, 433, 223, 353, 462, 235]
I. [204, 312, 420, 216, 330, 444, 228, 348, 468, 240]
J. [207, 420, 418, 225, 340, 431, 220, 356, 461, 244]
Answer: I
We now define an algorithm: The definition of a(n) is the number of possible queen moves on an n X n chessboard, considering all positions where a queen can move horizontally, vertically, or diagonally across the board. Given the input x_list (a series of values): [27, 28, 29, 30, 31, 32, 33, 34, 35, 36], determine the corresponding output sequence y_list.

Options:
A. [62700, 70050, 77950, 86410, 95470, 105140, 115440, 126400, 138030, 150350]
B. [62900, 70300, 78300, 86700, 95700, 106500, 116800, 128100, 140040, 152360]
C. [62721, 70123, 78002, 86519, 95578, 105333, 115566, 126543, 138069, 150485]
D. [62500, 69900, 77800, 86200, 95200, 104800, 114800, 125600, 137000, 149000]
E. [64000, 71500, 79700, 88300, 97500, 107000, 117000, 128000, 140000, 153000]
F. [63000, 70500, 78500, 87000, 96000, 106000, 116500, 127500, 139000, 151000]
G. [62712, 70056, 77952, 86420, 95480, 105152, 115456, 126412, 138040, 150360]
H. [62800, 70200, 78200, 86600, 95600, 106200, 116400, 127600, 139400, 151600]
I. [62000, 69500, 77500, 86000, 95000, 104500, 114500, 125000, 136000, 148000]
J. [62300, 69700, 77700, 86100, 95000, 104500, 114500, 125400, 137040, 149360]
Answer: G
We now define an algorithm: The definition of a(n) is the number of n-bead necklaces with 2 colors when turning over is not allowed; also the number of output sequences from a simple n-stage cycling shift register; also the number of binary irreducible polynomials whose degree divides n. 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. [2581433, 4971073, 9587585, 18512797, 35792573, 69273673, 134219801, 260301181, 505294133, 981706837]
B. [2581425, 4971065, 9587577, 18512789, 35792565, 69273665, 134219793, 260301173, 505294125, 981706829]
C. [2581428, 4971068, 9587580, 18512792, 35792568, 69273668, 134219796, 260301176, 505294128, 981706832]
D. [2581426, 4971066, 9587578, 18512790, 35792566, 69273666, 134219794, 260301174, 505294126, 981706830]
E. [2581434, 4971074, 9587586, 18512798, 35792574, 69273674, 134219802, 260301182, 505294134, 981706838]
F. [2581431, 4971071, 9587583, 18512795, 35792571, 69273671, 134219799, 260301179, 505294131, 981706835]
G. [2581430, 4971070, 9587582, 18512794, 35792570, 69273670, 134219798, 260301178, 505294130, 981706834]
H. [2581432, 4971072, 9587584, 18512796, 35792572, 69273672, 134219800, 260301180, 505294132, 981706836]
I. [2581427, 4971067, 9587579, 18512791, 35792567, 69273667, 134219795, 260301175, 505294127, 981706831]
J. [2581429, 4971069, 9587581, 18512793, 35792569, 69273669, 134219797, 260301177, 505294129, 981706833]
Answer: C
We now define an algorithm: The definition of a(n) is: Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals. Delannoy numbers D(i,j) count the number of paths from (0,0) to (i,j) in a grid where only three types of steps are allowed: right (R), up (U), and diagonally up-right (D). 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. [142, 22, 6, 6, 24, 178, 830, 2238, 3650, 3650]
B. [149, 15, 7, 7, 25, 185, 837, 2245, 3657, 3657]
C. [150, 14, 9, 9, 27, 186, 838, 2246, 3658, 3658]
D. [148, 16, 5, 5, 23, 184, 836, 2244, 3656, 3656]
E. [145, 19, 1, 1, 21, 181, 833, 2241, 3653, 3653]
F. [144, 18, 0, 0, 20, 180, 832, 2240, 3652, 3652]
G. [143, 21, 4, 4, 18, 179, 831, 2239, 3651, 3651]
H. [147, 17, 3, 3, 19, 183, 835, 2243, 3655, 3655]
I. [146, 20, 2, 2, 22, 182, 834, 2242, 3654, 3654]
J. [141, 23, 8, 8, 26, 177, 829, 2237, 3649, 3649]
Answer: E
We now define an algorithm: The definition of a(n) is one half of the number of permutations of [n] such that the differences have exactly 4 runs with the same signs. "Runs" here refers to consecutive elements with differences having the same sign. 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. [514178624, 2079532132, 8385437900, 33726903710, 135691291200, 544217772580, 2183315942550, 8742985786232, 35023081823100, 140313634667076]
B. [515183724, 2082553132, 8395437930, 33776903714, 135691891272, 544517772984, 2183315948550, 8748985781230, 35043081823140, 140313684667076]
C. [515183725, 2082553134, 8395437931, 33776903716, 135691891274, 544517772985, 2183315948551, 8748985781231, 35043081823141, 140313684667077]
D. [516183724, 2082653132, 8395437932, 33776913714, 135691891372, 544517773984, 2183315949650, 8748985781240, 35043081823150, 140313684667176]
E. [513183724, 2081553132, 8395437930, 33775903714, 135691891272, 544507772984, 2183315848550, 8748985781230, 35043081823140, 140313684637076]
F. [515183723, 2082553130, 8395437928, 33776903712, 135691891270, 544517772982, 2183315948548, 8748985781228, 35043081823138, 140313684667074]
G. [515183724, 2082553030, 8395437730, 33776902710, 135691881270, 544517762980, 2183315947350, 8748985781130, 35043081823130, 140313684667070]
H. [515183724, 2082553135, 8395437929, 33776903713, 135691891271, 544517772983, 2183315948549, 8748985781229, 35043081823139, 140313684667075]
I. [414152620, 1662042516, 6716350344, 27021522970, 108086611670, 432346446684, 1729385782020, 6917543184982, 27670116135990, 110680464529692]
J. [515183720, 2082553131, 8395437939, 33776903715, 135691891279, 544517772981, 2183315948559, 8748985781239, 35043081823149, 140313684667079]
Answer: B
We now define an algorithm: The definition of a(n) is the Boustrophedon transform of the sequence 1, 2, 2, 2, 2, ... 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. [192935698, 1719682167, 16412215306, 167273350543, 1809239623978, 20732358920387, 250773962654186, 3192953258362243, 42686640718276258, 597853508941260207]
B. [192835798, 1718681167, 16412215306, 167273350543, 1809239623978, 20732358920387, 250773962654186, 3192953258362243, 42686640718276258, 597853508941260207]
C. [192835698, 1718682167, 16412205306, 167173350543, 1809239622978, 20732358910387, 250773962554186, 3192953259262243, 42686640718266258, 597853508941160207]
D. [193835698, 1728682167, 16512205306, 168173350543, 1819239622978, 20832358910387, 251773962554186, 3202953259262243, 42786640718266258, 598853508941160207]
E. [192835698, 1718682167, 16402205306, 167073350543, 1808239622978, 20722358910387, 250673962554186, 3191953259262243, 42676640718266258, 597753508941160207]
F. [194835698, 1728681167, 16412205306, 168173350543, 1819239622978, 20832358910387, 251773962554186, 3202953259262243, 42786640718266258, 598853508941160207]
G. [194835698, 1728682167, 16412205306, 168173350543, 1819239622978, 20832358910387, 251773962554186, 3202953259262243, 42786640718266258, 598853508941160207]
H. [192735698, 1717682167, 16412215306, 167273350543, 1809239623978, 20732358920387, 250773962654186, 3192953258362243, 42686640718276258, 597853508941260207]
I. [192735698, 1717682167, 16402205306, 167073350543, 1808239622978, 20722358910387, 250673962554186, 3191953259262243, 42676640718266258, 597753508941160207]
Answer: C
We now define an algorithm: The definition of a(n) is the sequence where a(n) represents the number of male offspring in a hypothetical population modelled by two interrelated recurrences, tracking the growth of both male and female populations over time. Given the input x_list (a series of values): [64, 65, 66, 67, 68, 69, 70, 71, 72, 73], determine the corresponding output sequence y_list.

Options:
A. [39, 39, 40, 41, 41, 42, 42, 43, 44, 44]
B. [43, 43, 44, 45, 45, 46, 46, 47, 48, 48]
C. [36, 36, 37, 38, 38, 39, 39, 40, 41, 41]
D. [44, 44, 45, 46, 46, 47, 47, 48, 49, 49]
E. [35, 35, 36, 37, 37, 38, 38, 39, 40, 40]
F. [40, 40, 41, 42, 42, 43, 43, 44, 45, 45]
G. [42, 42, 43, 44, 44, 45, 45, 46, 47, 47]
H. [37, 37, 38, 39, 39, 40, 40, 41, 42, 42]
I. [41, 41, 42, 43, 43, 44, 44, 45, 46, 46]
J. [38, 38, 39, 40, 40, 41, 41, 42, 43, 43]
Answer: F
We now define an algorithm: The definition of a(n) is a Motzkin triangle: a(n,k), where n is greater than or equal to 2 and k is between 2 and n inclusive. The value a(n,k) represents the number of complete, strictly subdiagonal staircase functions. Given the input x_list (a series of values): [74, 75, 76, 77, 78, 79, 80, 81, 82, 83], determine the corresponding output sequence y_list.

Options:
A. [9, 90, 397, 1425, 3625, 5799, 3, 3, 3, 3]
B. [2, 68, 393, 1418, 3618, 5803, 7, 7, 7, 7]
C. [1, 69, 389, 1413, 3613, 5796, 8, 8, 8, 8]
D. [5, 65, 385, 1415, 3605, 5795, 1, 1, 1, 1]
E. [8, 80, 395, 1410, 3615, 5805, 2, 2, 2, 2]
F. [6, 70, 392, 1422, 3610, 5798, 0, 0, 0, 0]
G. [3, 60, 390, 1430, 3630, 5797, 4, 4, 4, 4]
H. [4, 67, 388, 1405, 3608, 5801, 5, 5, 5, 5]
I. [10, 72, 391, 1420, 3611, 5802, 6, 6, 6, 6]
J. [7, 75, 400, 1400, 3620, 5800, 1, 1, 1, 1]
Answer: F
We now define an algorithm: The definition of a(n) is the smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire that make use of the n-th hole, where players distribute stones across holes on a board according to specific game rules common to Mancala variants. 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. [624, 648, 671, 718, 733, 779, 801, 842, 870, 916]
B. [621, 649, 672, 719, 732, 783, 805, 839, 871, 920]
C. [624, 647, 670, 718, 734, 781, 803, 841, 870, 918]
D. [623, 649, 674, 719, 735, 781, 803, 841, 871, 919]
E. [622, 648, 673, 717, 735, 782, 805, 843, 872, 920]
F. [622, 648, 672, 718, 732, 780, 802, 840, 870, 918]
G. [620, 646, 670, 719, 732, 781, 804, 841, 873, 919]
H. [621, 647, 671, 717, 731, 779, 801, 839, 869, 917]
I. [623, 647, 671, 719, 734, 780, 805, 840, 872, 919]
J. [622, 649, 673, 716, 732, 782, 802, 841, 871, 922]
Answer: F
We now define an algorithm: The definition of a(n) is: Binary counter with odd/even bit positions swapped; base-4 counter with 1's replaced by 2's and vice versa. 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. [60, 63, 62, 64, 128, 131, 130, 132, 136, 139]
B. [64, 62, 61, 60, 132, 130, 129, 128, 140, 138]
C. [62, 63, 61, 60, 130, 131, 129, 128, 138, 139]
D. [60, 62, 61, 63, 128, 130, 129, 131, 136, 138]
E. [63, 60, 62, 61, 131, 128, 130, 129, 139, 136]
F. [64, 61, 60, 63, 132, 129, 128, 131, 140, 137]
G. [60, 61, 64, 63, 128, 129, 132, 131, 136, 137]
H. [61, 63, 62, 64, 129, 131, 130, 132, 137, 139]
I. [62, 60, 63, 61, 130, 128, 131, 129, 138, 136]
J. [63, 61, 60, 62, 131, 129, 128, 130, 139, 137]
Answer: D
We now define an algorithm: The definition of a(n) is Łukasiewicz words for the rooted plane binary trees (interpretation d in Stanley's exercise 19) with the last leaf implicit, i.e., these words are given without the last trailing zero, except for the null tree which is encoded as 0. 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. [22020020, 22023220, 22020210, 22022100, 22202012, 22221000, 22220012, 22202100, 2022020200, 2021222200]
B. [22022200, 22120020, 22020220, 22020202, 22202021, 22202100, 22202011, 22221111, 2022222020, 2020222010]
C. [22102200, 22010020, 22020120, 22012000, 22221020, 22201210, 22202100, 22212000, 2020202101, 2020222200]
D. [22011022, 22020220, 22002202, 22021200, 22220210, 22201202, 22220012, 22223000, 2020102022, 2021220200]
E. [22011200, 22022020, 22021020, 22020212, 22201200, 22202202, 22221002, 22201000, 2020202220, 2021222000]
F. [22012200, 22010220, 22021200, 22011200, 22210220, 22201200, 22210200, 22210220, 2020112020, 2021202100]
G. [22002200, 22020020, 22020200, 22022000, 22200020, 22200200, 22202000, 22220000, 2020202020, 2020202200]
H. [22201200, 22020210, 22022202, 22022222, 22202220, 22220200, 22200022, 22222000, 2022012022, 2020222100]
I. [22012220, 22020021, 22022200, 22011100, 22200012, 22220120, 22221120, 22222100, 2020212020, 2022012200]
J. [22120200, 22022020, 22021010, 22021010, 22202220, 22221222, 22200120, 22220200, 2021112020, 2022112200]
Answer: G
We now define an algorithm: The definition of a(n) is the Ternary Thue-Morse sequence: closed under the substitutions a -> abc, b -> ac, and c -> b, starting with a = 0, b = 1, and c = 2. 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. [2, 0, 1, 0, 2, 1, 2, 0, 2, 1]
B. [2, 2, 0, 2, 1, 0, 1, 0, 1, 2]
C. [0, 2, 1, 2, 0, 1, 0, 1, 2, 1]
D. [1, 0, 1, 0, 2, 2, 0, 2, 1, 2]
E. [1, 2, 0, 2, 1, 0, 1, 2, 2, 0]
F. [1, 0, 2, 0, 1, 2, 0, 2, 1, 0]
G. [0, 1, 0, 1, 2, 0, 2, 1, 2, 1]
H. [1, 2, 0, 2, 1, 2, 0, 1, 0, 2]
I. [2, 1, 0, 1, 2, 0, 1, 2, 0, 1]
J. [0, 1, 2, 1, 0, 2, 1, 0, 2, 0]
Answer: A
We now define an algorithm: The definition of a(n) is the number of binary vectors of length n that do not have a segment of consecutive 1's that is exactly of length 1. 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. [635624, 1028457, 1664083, 2692536, 4356617, 7049158, 11405777, 18454932, 29860703, 48315631]
B. [635628, 1028464, 1664085, 2692545, 4356623, 7049160, 11405780, 18454935, 29860711, 48315639]
C. [635620, 1028453, 1664076, 2692535, 4356615, 7049151, 11405770, 18454928, 29860702, 48315630]
D. [635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634]
E. [635629, 1028465, 1664077, 2692546, 4356624, 7049162, 11405771, 18454936, 29860708, 48315640]
F. [635623, 1028459, 1664081, 2692539, 4356619, 7049157, 11405775, 18454931, 29860705, 48315635]
G. [635627, 1028463, 1664078, 2692532, 4356622, 7049159, 11405779, 18454925, 29860709, 48315638]
H. [635626, 1028462, 1664084, 2692534, 4356621, 7049150, 11405778, 18454933, 29860707, 48315637]
I. [635621, 1028460, 1664079, 2692537, 4356614, 7049155, 11405776, 18454934, 29860701, 48315636]
Answer: D
We now define an algorithm: The definition of a(n) is: Number of aperiodic necklaces (Lyndon words) with 9 black beads and n white beads. In combinatorial mathematics, an aperiodic necklace is a sequence that is invariant under cyclic permutations and does not repeat periodically. 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. [2017357, 2615086, 3362261, 4289781, 5433715, 6835973, 8544966, 10616464, 13114466, 16112058]
B. [2017360, 2615095, 3362268, 4289795, 5433725, 6835985, 8544975, 10616475, 13114475, 16112075]
C. [2017355, 2615084, 3362259, 4289779, 5433713, 6835971, 8544964, 10616462, 13114464, 16112056]
D. [2017358, 2615087, 3362262, 4289782, 5433716, 6835974, 8544967, 10616465, 13114467, 16112059]
E. [2017365, 2615090, 3362265, 4289790, 5433720, 6835980, 8544970, 10616470, 13114470, 16112070]
F. [2017350, 2615080, 3362250, 4289770, 5433710, 6835960, 8544950, 10616460, 13114460, 16112050]
G. [2017370, 2615100, 3362270, 4289800, 5433730, 6835990, 8544980, 10616480, 13114480, 16112080]
H. [2017359, 2615088, 3362263, 4289783, 5433717, 6835975, 8544968, 10616466, 13114468, 16112060]
I. [2017356, 2615085, 3362260, 4289780, 5433714, 6835972, 8544965, 10616463, 13114465, 16112057]
J. [2017362, 2615098, 3362269, 4289798, 5433728, 6835988, 8544978, 10616478, 13114478, 16112078]
Answer: I
We now define an algorithm: The definition of a(n) is the sequence obtained by enumerating the table T(n,k) by antidiagonals. The order of the list progresses through a symmetrical movement from the center to the edges along the diagonal. 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. [59, 60, 58, 61, 63, 65, 67, 68, 76, 75]
B. [57, 55, 56, 59, 61, 63, 65, 67, 76, 72]
C. [65, 63, 62, 66, 68, 70, 72, 71, 75, 79]
D. [66, 64, 63, 67, 69, 71, 73, 74, 70, 77]
E. [58, 56, 57, 62, 64, 66, 65, 68, 74, 77]
F. [63, 61, 60, 64, 66, 68, 70, 72, 73, 80]
G. [61, 59, 58, 62, 64, 66, 68, 70, 78, 74]
H. [60, 58, 57, 61, 63, 65, 67, 69, 79, 76]
I. [59, 57, 56, 58, 60, 62, 64, 66, 77, 75]
J. [64, 62, 61, 65, 67, 69, 71, 73, 72, 78]
Answer: I
We now define an algorithm: The definition of a(n) is the continued fraction expansion of w = 2 * cos(Pi/7). Given the input x_list (a series of values): [85, 86, 87, 88, 89, 90, 91, 92, 93, 94], determine the corresponding output sequence y_list.

Options:
A. [13, 2, 3, 14, 2, 1, 27, 2, 123, 8]
B. [10, 1, 4, 11, 2, 1, 24, 3, 120, 5]
C. [9, 1, 2, 10, 3, 1, 22, 1, 119, 3]
D. [12, 1, 1, 13, 4, 1, 26, 3, 122, 7]
E. [8, 2, 5, 9, 3, 1, 19, 1, 116, 3]
F. [8, 1, 1, 9, 4, 1, 20, 2, 115, 2]
G. [5, 1, 2, 6, 6, 1, 18, 2, 114, 2]
H. [11, 2, 2, 12, 1, 1, 25, 2, 121, 6]
I. [7, 2, 3, 8, 4, 1, 23, 2, 117, 4]
J. [6, 1, 3, 7, 5, 1, 21, 1, 118, 4]
Answer: C
We now define an algorithm: The definition of a(n) is a sequence where the generalized Pellian numbers start with 1 and 9, and follow a recurrence relationship specific to these numbers. 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. [5241021418, 22201322980, 94046313330, 398386576270, 1687592618370, 7148757049725, 30282620817255, 128279240318720, 543399582092120, 2301877568687190]
B. [5241021420, 22201322990, 94046313340, 398386576280, 1687592618380, 7148757049730, 30282620817260, 128279240318730, 543399582092130, 2301877568687200]
C. [5241021400, 22201322970, 94046313310, 398386576250, 1687592618360, 7148757049710, 30282620817240, 128279240318710, 543399582092110, 2301877568687170]
D. [5241021417, 22201322981, 94046313329, 398386576269, 1687592618369, 7148757049724, 30282620817254, 128279240318721, 543399582092121, 2301877568687191]
E. [5241021412, 22201322976, 94046313322, 398386576260, 1687592618364, 7148757049720, 30282620817250, 128279240318718, 543399582092118, 2301877568687186]
F. [5241021416, 22201322982, 94046313328, 398386576264, 1687592618367, 7148757049718, 30282620817256, 128279240318715, 543399582092112, 2301877568687180]
G. [5241021411, 22201322975, 94046313319, 398386576259, 1687592618363, 7148757049719, 30282620817248, 128279240318716, 543399582092116, 2301877568687184]
H. [5241021414, 22201322978, 94046313324, 398386576268, 1687592618372, 7148757049726, 30282620817253, 128279240318724, 543399582092126, 2301877568687210]
I. [5241021413, 22201322977, 94046313321, 398386576261, 1687592618365, 7148757049721, 30282620817249, 128279240318717, 543399582092117, 2301877568687185]
J. [5241021415, 22201322979, 94046313325, 398386576263, 1687592618368, 7148757049723, 30282620817251, 128279240318719, 543399582092119, 2301877568687187]
Answer: I
We now define an algorithm: The definition of a(n) is the number of unique binary trees that can be constructed using n nodes, where nodes represent binary variables x and y and the concatenation process follows the given pattern: start with x, xy; then concatenate each word in turn with all preceding words, getting x xy xxy xxxy xyxxy xxxxy xyxxxy xxyxxxy ...; relating to binary trees by degree as x (x,y) (x,(x,y)) (x,(x,(x,y))) ((x,y),(x,(x,y)))... Given the input x_list (a series of values): [27, 28, 29, 30, 31, 32, 33, 34, 35, 36], determine the corresponding output sequence y_list.

Options:
A. [27387932, 48379199, 74875594, 288036832, 317284183, 827469848, 3064465340, 3601670629, 11270463562, 32950838751]
B. [17387931, 38379200, 84875596, 188036830, 417284181, 927469845, 2064465341, 4601670625, 10270463565, 22950838755]
C. [17387929, 38379202, 84875598, 188036828, 417284181, 927469847, 2064465344, 4601670628, 10270463563, 22950838752]
D. [17387934, 38379197, 84875592, 188036834, 417284185, 927469850, 2064465338, 4601670631, 10270463560, 22950838749]
E. [17387933, 38379198, 84875593, 188036833, 417284184, 927469849, 2064465339, 4601670630, 10270463561, 22950838750]
F. [17387931, 38379201, 84875596, 188036831, 417284181, 927469846, 2064465341, 4601670624, 10270463565, 22950838754]
G. [17387931, 38379201, 84875597, 188036831, 417284182, 927469846, 2064465342, 4601670626, 10270463566, 22950838756]
H. [17387932, 38379199, 84875594, 188036832, 417284183, 927469848, 2064465340, 4601670629, 10270463562, 22950838751]
I. [27387931, 48379200, 74875596, 288036830, 317284181, 827469845, 3064465341, 3601670625, 11270463565, 32950838755]
J. [17387930, 38379202, 84875595, 188036829, 417284180, 927469844, 2064465343, 4601670627, 10270463564, 22950838753]
Answer: B
We now define an algorithm: The definition of a(n) is the expansion of the modular form (eta(q^2) / eta(q))^24 in powers of q, where eta(q) is the Dedekind eta function, defined as eta(q) = q^(1/24) * Product_{n>=1} (1 - q^n). 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. [16633756005, 49010118653, 139877936367, 387749049717, 1046413709977, 2754808758141, 7087483527069, 17848133716829, 44056043512485, 106727749011453]
B. [16633756014, 49010118662, 139877936376, 387749049726, 1046413709986, 2754808758150, 7087483527078, 17848133716838, 44056043512494, 106727749011462]
C. [16633756012, 49010118660, 139877936374, 387749049724, 1046413709984, 2754808758148, 7087483527076, 17848133716836, 44056043512492, 106727749011460]
D. [16633756010, 49010118658, 139877936372, 387749049722, 1046413709982, 2754808758146, 7087483527074, 17848133716834, 44056043512490, 106727749011458]
E. [16633756011, 49010118659, 139877936373, 387749049723, 1046413709983, 2754808758147, 7087483527075, 17848133716835, 44056043512491, 106727749011459]
F. [16633756009, 49010118657, 139877936371, 387749049721, 1046413709981, 2754808758145, 7087483527073, 17848133716833, 44056043512489, 106727749011457]
G. [16633756007, 49010118655, 139877936369, 387749049719, 1046413709979, 2754808758143, 7087483527071, 17848133716831, 44056043512487, 106727749011455]
H. [16633756006, 49010118654, 139877936368, 387749049718, 1046413709978, 2754808758142, 7087483527070, 17848133716830, 44056043512486, 106727749011454]
I. [16633756008, 49010118656, 139877936370, 387749049720, 1046413709980, 2754808758144, 7087483527072, 17848133716832, 44056043512488, 106727749011456]
J. [16633756013, 49010118661, 139877936375, 387749049725, 1046413709985, 2754808758149, 7087483527077, 17848133716837, 44056043512493, 106727749011461]
Answer: I