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A288939
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Nonprime numbers k such that k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.
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2
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1, 6, 14, 26, 38, 40, 46, 56, 60, 66, 68, 72, 80, 87, 93, 95, 115, 122, 126, 128, 146, 156, 158, 160, 180, 186, 192, 203, 206, 208, 220, 221, 235, 237, 238, 264, 266, 280, 282, 290, 294, 300, 303, 320, 341, 350, 363, 381, 395, 399, 404, 405, 417, 418, 436, 438, 447, 450
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OFFSET
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1,2
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COMMENTS
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The corresponding prime numbers k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 = 1111111_k are in A194194; all these Brazilian primes belong to A085104 and A285017.
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LINKS
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EXAMPLE
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6 is in the sequence because 6^6 + 6^5 + 6^4 + 6^3 + 6^2 + 6 + 1 = 1111111_6 = 55987 which is prime.
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MAPLE
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for n from 1 to 200 do s(n):= 1+n+n^2+n^3+n^4+n^5+n^6;
if not isprime(n) and isprime(s(n)) then print(n, s(n)) else fi; od:
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MATHEMATICA
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Select[Range@ 450, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 6]]] &] (* Michael De Vlieger, Jun 19 2017 *)
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PROG
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(PARI) isok(n) = !isprime(n) && isprime(1+n+n^2+n^3+n^4+n^5+n^6); \\ Michel Marcus, Jun 19 2017
(Python)
from sympy import isprime
A288939_list = [n for n in range(10**3) if not isprime(n) and isprime(n*(n*(n*(n*(n*(n + 1) + 1) + 1) + 1) + 1) + 1)] # Chai Wah Wu, Jul 13 2017
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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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