A187966 Numbers n for which Fibonacci(n) mod n equals some nonzero Fibonacci(k) and k divides n.

2, 3, 4, 6, 10, 11, 14, 19, 20, 22, 29, 31, 38, 41, 54, 55, 56, 58, 59, 61, 62, 71, 76, 79, 80, 82, 89, 93, 95, 101, 109, 110, 118, 121, 122, 123, 124, 131, 139, 142, 145, 149, 151, 152, 153, 155, 158, 165, 174, 178, 179, 181, 190, 191, 196, 199, 202, 205, 209, 211, 213

Offset

1,1

Comments

If Fibonacci(n) (mod n) = 1, then we assume that k=1 (even though Fibonacci(2) also equals 1). Subsequence of A182625.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..2000

Example

14 is in this sequence because fib(14)=377 is congruent to 13 (mod 14), 13=fib(7), and 7 divides 14.

Mathematica

nn = 13; f = Table[Fibonacci[n], {n, nn}]; okQ[n_] := Module[{pos = Position[f, Mod[Fibonacci[n], n]]}, pos != {} && Mod[n, pos[[1, 1]]] == 0]; Select[Range[f[[-1]]], okQ] (* T. D. Noe, Apr 04 2011 *)

Prog

(PARI) ok(n)={my(m=fibonacci(n)%n); fordiv(n, k, my(t=fibonacci(k)); if(t>=m, return(t==m))); 0} \\ Andrew Howroyd, Feb 25 2018

Crossrefs

Cf. A182625.

Sequence in context: A005457 A005453 A180242 * A280584 A225649 A225651

Adjacent sequences: A187963 A187964 A187965 * A187967 A187968 A187969

Keyword

nonn

Author

Carmine Suriano, Mar 30 2011

Status

approved