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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 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 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 September 10 09:32 EDT 2024. Contains 375786 sequences. (Running on oeis4.)