OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Conjecture: a(n) is asymptotic to c*n*log(n) with c>0.7
EXAMPLE
F(44) = 701408733; 701408733 mod 44 = 25, F(25)=75025 and 25 divides 75025, hence 44 is in the sequence.
MAPLE
fmod:= proc(n, m) local M, t; uses LinearAlgebra:-Modular;
if m <= 1 then return 0 fi;
if m < 2^25 then t:= float[8] else t:= integer fi;
M:= Mod(m, <<1, 1>|<1, 0>>, t);
round(MatrixPower(m, M, n)[1, 2])
end proc:
filter:= proc(n) local s;
s:= fmod(n, n);
fmod(s, s) = 0
end proc:
select(filter, [$1..200]); # Robert Israel, May 10 2016
MATHEMATICA
Unprotect[Divisible];
Divisible[0, 0] = True;
okQ[n_] := Module[{F = Fibonacci, m}, m = Mod[F[n], n]; Divisible[F[m], m]];
Select[Range[75000], okQ] (* Jean-François Alcover, Jul 09 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Nov 22 2002
STATUS
approved