54 lines
1.5 KiB
Python
54 lines
1.5 KiB
Python
'''
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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
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There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
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What 12-digit number do you form by concatenating the three terms in this sequence?
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'''
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import math
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import numpy as np
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from itertools import permutations
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def sieve(n):
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assert n > 1
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ns = [True] * n
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for i in range(2, math.ceil(np.sqrt(n))):
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if ns[i]:
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j = pow(i, 2)
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while j < n:
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ns[j] = False
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j = j + i
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return [i for i,val in enumerate(ns) if val][2:]
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def digitToList(n):
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return [int(c) for c in str(n)]
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def listToDigit(l):
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res = 0
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for i in l:
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res = 10 * res + i
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return res
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def main():
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print("Hello this is Patrick")
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primeSet = set(sieve(10000)) - set(sieve(1000))
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primeList = list(primeSet)
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for p in primeList:
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perms = list(set(map(listToDigit, list(permutations(digitToList(p))))))
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for perm in perms:
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if p != perm and perm in primeSet:
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if max(p, perm) + abs(p - perm) in primeSet and max(p, perm) + abs(p - perm) in perms:
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print(min(p, perm), max(p, perm), max(p, perm) + abs(p - perm))
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if __name__ == "__main__":
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main() |