A023173 Numbers k such that Fibonacci(k) == 1 (mod k).

1, 2, 11, 19, 22, 29, 31, 38, 41, 58, 59, 61, 62, 71, 79, 82, 89, 101, 109, 118, 122, 131, 139, 142, 149, 151, 158, 178, 179, 181, 191, 199, 202, 211, 218, 229, 239, 241, 251, 262, 269, 271, 278, 281, 298, 302, 311, 323, 331, 349, 358, 359, 362, 379, 382, 389, 398, 401

Offset

1,2

Comments

Sequence contains 1, A064739(k) for all k>=0, 2*A064739(k) for k>1. - Benoit Cloitre, Apr 06 2002

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

lst={}; Do[If[Mod[Fibonacci[n], n]==1, AppendTo[lst, n]], {n, 1, 7!}]; Take[Union[lst], 5! ] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Select[Range[500], Mod[Fibonacci[#]-1, #]==0&] (* Harvey P. Dale, Sep 22 2021 *)

Prog

(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
is(n)=fibmod(n, n)==1 \\ Charles R Greathouse IV, Oct 06 2016

Crossrefs

Cf. A000045, A045468, A003631, A064739.

Sequence in context: A352932 A066144 A102343 * A018443 A163058 A161504

Adjacent sequences: A023170 A023171 A023172 * A023174 A023175 A023176

Keyword

nonn,easy

Author

David W. Wilson

Status

approved