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

Author

David W. Wilson

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000045, A045468, A003631, A064739.

Programs

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 *)

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