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

Author

Carmine Suriano, Mar 30 2011

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A182625.

Programs

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 *)

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