A088875 Cyclotomic(n,-n) is prime.

1, 3, 4, 5, 6, 9, 12, 14, 17, 82, 86, 157, 158, 180, 210, 236, 245, 368, 462, 842, 1034, 3512, 3977, 8636

Offset: 1

Author

T. D. Noe, Oct 20 2003

Keywords

• hard
• nonn

Comments

This is a generalization of A056826. See A088817 for another generalization. Note that (n^n+1)/(n+1) = cyclotomic(n,-n) when n is prime. Also note that, for odd n>1, cyclotomic(n,-n) = cyclotomic(2n,n) and for n a multiple of 4, cyclotomic(n,-n) = cyclotomic(n,n).

Some of the larger entries may only correspond to probable primes.

Links

• Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

Crossrefs

Cf. A056826 ((n^n+1)/(n+1) is prime), A070519 (cyclotomic(n, n) is prime), A088817 (cyclotomic(2n, n) is prime).

Programs

Mathematica

Do[p=Prime[n]; If[PrimeQ[Cyclotomic[n, -n]], Print[p]], {n, 100}]