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 A078345 Numbers n such that F(n) mod n divides F(F(n) mod n) where F(k) denotes the k-th Fibonacci number. 1

%I

%S 1,2,5,8,10,11,12,13,19,20,21,22,24,25,26,29,31,32,36,37,38,41,44,48,

%T 49,50,55,58,59,60,61,62,65,71,72,73,79,80,82,84,89,95,96,97,101,104,

%U 108,109,118,120,122,125,131,132,139,140,142,144,145,149,151,155,156

%N Numbers n such that F(n) mod n divides F(F(n) mod n) where F(k) denotes the k-th Fibonacci number.

%H Robert Israel, <a href="/A078345/b078345.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: a(n) is asymptotic to c*n*log(n) with c>0.7

%e F(44) = 701408733; 701408733 mod 44 = 25, F(25)=75025 and 25 divides 75025, hence 44 is in the sequence.

%p fmod:= proc(n,m) local M,t; uses LinearAlgebra:-Modular;

%p if m <= 1 then return 0 fi;

%p if m < 2^25 then t:= float[8] else t:= integer fi;

%p M:= Mod(m,<<1,1>|<1,0>>,t);

%p round(MatrixPower(m,M,n)[1,2])

%p end proc:

%p filter:= proc(n) local s;

%p s:= fmod(n,n);

%p fmod(s,s) = 0

%p end proc:

%p select(filter, [\$1..200]); # _Robert Israel_, May 10 2016

%Y Cf. A000045, A002708, A023172.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Nov 22 2002

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Last modified May 7 00:22 EDT 2021. Contains 343609 sequences. (Running on oeis4.)