

A250174


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


21



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 N1 method (because n is prime and n*(n1) is fully factored and this provides for an exactly 33.33...% factorization for Phi_14(n)  1).  Serge Batalov, Mar 13 2015


LINKS



EXAMPLE

2 is in the sequence because 2^62^5+2^42^3+2^22+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 crossreferences, 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).


KEYWORD

nonn


AUTHOR



STATUS

approved



