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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

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

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).

Sequence in context: A146327 A344939 A278742 * A285622 A081706 A359251

Adjacent sequences: A250171 A250172 A250173 * A250175 A250176 A250177

Keyword

nonn

Author

Eric Chen, Dec 24 2014

Status

approved