47 lines
1.1 KiB
Python
47 lines
1.1 KiB
Python
#!/usr/bin/env python3
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# Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
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#
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# 2^2=4, 2^3=8, 2^4=16, 2^5=32
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# 3^2=9, 3^3=27, 3^4=81, 3^5=243
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# 4^2=16, 4^3=64, 4^4=256, 4^5=1024
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# 5^2=25, 5^3=125, 5^4=625, 5^5=3125
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#
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# If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
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#
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# 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
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#
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# How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
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from numpy import zeros
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from projecteuler import timing
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@timing
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def p029() -> None:
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_powers = zeros(9801)
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# Generate all the powers
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for i in range(2, 101):
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a = i
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for j in range(2, 101):
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_powers[(i-2)*99+j-2] = a ** j
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# Sort the values and count the different values.
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powers = list(_powers)
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powers.sort()
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count = 1
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for i in range(1, 9801):
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if powers[i] != powers[i-1]:
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count = count + 1
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print('Project Euler, Problem 29')
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print(f'Answer: {count}')
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if __name__ == '__main__':
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p029()
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