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

1,1

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

Table of n, a(n) for n=1..56.

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

Prog

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

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]).

Sequence in context: A117717 A359252 A176060 * A127305 A363753 A333519

Adjacent sequences: A168169 A168170 A168171 * A168173 A168174 A168175

Keyword

nonn

Author

M. F. Hasler, Nov 28 2009

Status

approved