A023173 - OEIS

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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

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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]