A168172 Least prime p == -1 (mod n) that divides Fibonacci((p+1)/n), or 0 if no such prime exists.

2, 13, 47, 0, 0, 113, 307, 0, 233, 0, 967, 0, 2417, 797, 0, 0, 1087, 233, 5737, 0, 5417, 5653, 1103, 0, 0, 2417, 4373, 0, 6263, 0, 25357, 0, 3167, 42533, 0, 0, 4513, 5737, 2417, 0, 61417, 5417, 32507, 0, 0, 36017, 1597, 0, 97607, 0, 27947, 0, 42293, 4373, 0, 0

Offset: 1

Author

M. F. Hasler, Nov 28 2009

Keywords

• nonn

Comments

Max Alekseyev has proved (cf. link) that a(n)=0 if n is a multiple of 4 or 5; for all other n, a prime a(n) with the required property seems to exist.

Links

• Max Alekseyev, Re: Primes p = nk-1 dividing Fibonacci( k ), SeqFan mailing list, Nov. 2009.

Crossrefs

Cf. A168171 (least p | F[(p-1)/n]), A122487 (p | F[(p+1)/2]), A047652 (p | F[(p-1)/3]), A001583 (Artiads: p | F[(p-1)/5]), A125252 (p | F[(p+1)/7]), A125253 (p | F[(p-1)/7]).

Programs

PARI

A168172(n) = n%4 && n%5 && forstep(p=n-1,1e9,n, isprime(p) || next; fibonacci((p+1)/n)%p || return(p))