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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
1, 2, 5, 8, 10, 11, 12, 13, 19, 20, 21, 22, 24, 25, 26, 29, 31, 32, 36, 37, 38, 41, 44, 48, 49, 50, 55, 58, 59, 60, 61, 62, 65, 71, 72, 73, 79, 80, 82, 84, 89, 95, 96, 97, 101, 104, 108, 109, 118, 120, 122, 125, 131, 132, 139, 140, 142, 144, 145, 149, 151, 155, 156 (list; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A000045, A002708, A023172.

Sequence in context: A083724 A072476 A167541 * A161817 A080228 A153052

Adjacent sequences:  A078342 A078343 A078344 * A078346 A078347 A078348

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Nov 22 2002

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)