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A168172 Least prime p == -1 (mod n) that divides Fibonacci((p+1)/n), or 0 if no such prime exists. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A212501 A117717 A176060 * A270294 A005584 A072416

Adjacent sequences:  A168169 A168170 A168171 * A168173 A168174 A168175

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 28 2009

STATUS

approved

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Last modified March 26 12:27 EDT 2019. Contains 321497 sequences. (Running on oeis4.)