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%I #32 Apr 02 2015 04:08:49
%S 2,3,10,11,14,15,16,17,18,21,24,25,29,37,43,44,46,49,52,54,61,66,72,
%T 73,78,84,86,87,99,101,106,114,115,128,133,135,136,143,145,148,164,
%U 169,170,173,200,219,224,226,228,231,234,240,248,255,262,275,281,282,298,301
%N Numbers n such that Phi_14(n) is prime, where Phi is the cyclotomic polynomial.
%C n = 9069 * 2^64163 + 1 is an example of a rather large member of this sequence. The generated 115914 decimal digit prime is proved by the N-1 method (because n is prime and n*(n-1) is fully factored and this provides for an exactly 33.33...% factorization for Phi_14(n) - 1). - _Serge Batalov_, Mar 13 2015
%H Serge Batalov, <a href="/A250174/b250174.txt">Table of n, a(n) for n = 1..1595</a>
%e 2 is in the sequence because 2^6-2^5+2^4-2^3+2^2-2+1 = 43 which is prime.
%t a250174[n_] := Select[Range[n], PrimeQ@Cyclotomic[14, #] &]; a250174[256]
%o (PARI) isok(n) = isprime(polcyclo(14, n)); \\ _Michel Marcus_, Mar 13 2015
%Y See A250177 for cross-references, A100330 (Phi_7(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 primes; these two sequences can also be considered an extension of each other into negative n values), A250177 (Phi_21(n) primes).
%K nonn
%O 1,1
%A _Eric Chen_, Dec 24 2014