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
Keywords
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
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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
Comments