A250174 Numbers n such that Phi_14(n) is prime, where Phi is the cyclotomic polynomial.

2, 3, 10, 11, 14, 15, 16, 17, 18, 21, 24, 25, 29, 37, 43, 44, 46, 49, 52, 54, 61, 66, 72, 73, 78, 84, 86, 87, 99, 101, 106, 114, 115, 128, 133, 135, 136, 143, 145, 148, 164, 169, 170, 173, 200, 219, 224, 226, 228, 231, 234, 240, 248, 255, 262, 275, 281, 282, 298, 301

Offset: 1

Author

Eric Chen, Dec 24 2014

Keywords

• nonn

Comments

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

Examples

			2 is in the sequence because 2^6-2^5+2^4-2^3+2^2-2+1 = 43 which is prime.
		

Links

• Serge Batalov, Table of n, a(n) for n = 1..1595

Crossrefs

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).

Programs

Mathematica

a250174[n_] := Select[Range[n], PrimeQ@Cyclotomic[14, #] &]; a250174[256]

PARI

isok(n) = isprime(polcyclo(14, n)); \\ Michel Marcus, Mar 13 2015