A023162 Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.

1, 2, 3, 4, 7, 13, 14, 17, 23, 26, 34, 37, 43, 46, 47, 53, 67, 73, 74, 83, 86, 94, 97, 103, 106, 107, 113, 127, 134, 137, 146, 157, 163, 166, 167, 173, 193, 194, 197, 206, 214, 223, 226, 227, 233, 254, 257, 263, 274, 277, 283, 293, 307, 313, 314, 317, 326, 334

Offset

1,2

Comments

If k is prime then k is in the sequence if and only if k == 2 or 3 (mod 5).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) seems to be asymptotic to c*n*log(n) where c = 1.5... - Benoit Cloitre, Jan 10 2003

Mathematica

Module[{nn = 500, fib}, fib = Thread[{Range[nn], Fibonacci[Range[nn]]}]; Transpose[Select[fib, Mod[Last[#], First[#]] == First[#] - 1 &]][[1]]] (* Harvey P. Dale, May 21 2014 *)
Select[Range[500], Mod[Fibonacci[#], #] == # - 1 &] (* Alonso del Arte, Nov 20 2018 *)

Prog

(PARI) isok(k) = Mod(fibonacci(k), k) == -1; \\ Michel Marcus, Nov 21 2018

Crossrefs

Sequence in context: A207573 A152605 A285222 * A022437 A057983 A200088

Adjacent sequences: A023159 A023160 A023161 * A023163 A023164 A023165

Keyword

nonn

Author

David W. Wilson

Extensions

Name clarified by Alonso del Arte and Michel Marcus, Nov 20 2018

Status

approved