A086391 Numbers k such that F(k^2+1) == 1 (mod k) where F(k) denotes the k-th Fibonacci number.

2, 3, 4, 7, 9, 10, 11, 12, 13, 17, 19, 20, 23, 24, 27, 28, 29, 31, 36, 37, 41, 43, 47, 48, 50, 53, 59, 60, 61, 63, 67, 71, 72, 73, 76, 79, 83, 84, 89, 96, 97, 99, 100, 101, 103, 107, 108, 109, 110, 113, 120, 127, 131, 137, 139, 140, 144, 149, 151, 157, 161, 163, 167, 168

Offset

1,1

Comments

Except p=5, all prime numbers p are in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Mathematica

Select[Range[200], Mod[Fibonacci[#^2 + 1], #] == 1 &] (* Amiram Eldar, May 13 2022 *)

Prog

(PARI) isok(n) = ((fibonacci(n^2+1) % n) == 1); \\ Michel Marcus, Dec 06 2013

Crossrefs

Cf. A000045, A002522.

Sequence in context: A172024 A285500 A119345 * A120127 A047548 A095378

Adjacent sequences: A086388 A086389 A086390 * A086392 A086393 A086394

Keyword

nonn

Author

Benoit Cloitre, Sep 06 2003

Status

approved