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A255194
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Numbers n such that prime(n) + {1,2,3,4,5,6} are all products of three primes.
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2
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369, 8788, 16456, 20522, 23335, 53601, 77047, 97930, 100123, 120745, 127847, 139723, 152996, 217177, 230179, 250248, 264618, 304656, 325478, 418592, 452277, 495518, 523028, 574110, 600888, 609574, 615102, 619844, 638584, 716516, 722010, 749479, 789769, 810082, 858158, 901322, 928090, 940735, 999329
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OFFSET
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1,1
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LINKS
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EXAMPLE
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prime(369) + {1,2,3,4,5,6} = {2522,2523,2524,2525,2526,2527} = {2*13*97, 3*29*29, 2*2*631, 5*5*101, 2*3*421, 7*19*19} - all products of 3 primes (A014612).
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MATHEMATICA
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Reap[Do[If[Union[PrimeOmega[Prime[n] + {1, 2, 3, 4, 5, 6}]] == {3},
Sow[n]], {n, 10^6}]][[2, 1]]
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PROG
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(Python)
from sympy import factorint, nextprime
for n in range(1, 10**6):
....if p2 - p > 6:
........for i in range(1, 7):
............fs = factorint(p+i)
............if len(fs) > 3 or sum(list(fs.values())) != 3:
................break
........else:
....p, p2 = p2, nextprime(p2) # Chai Wah Wu, Mar 01 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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