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A335568 a(n) is the number m such that F(m) is the greatest prime Fibonacci divisor of F(n)^2 + 1 where F(n) is the n-th Fibonacci number, or 0 if no such prime factor exists. 3
3, 3, 5, 5, 7, 7, 5, 7, 11, 11, 13, 13, 11, 13, 17, 17, 5, 17, 17, 7, 23, 23, 7, 23, 23, 5, 29, 29, 3, 29, 29, 11, 7, 11, 11, 7, 13, 13, 0, 13, 43, 43, 5, 43, 47, 47, 7, 47, 47, 17, 7, 17, 17, 11, 3, 11, 11, 3, 3, 0, 7, 7, 13, 13, 7, 13, 23, 23, 0, 23, 23, 0, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Fibonacci index of the terms in A338762.

All terms are prime or 0. - Alois P. Heinz, Nov 21 2020

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..20000

FORMULA

A000045(a(n)) = A338762(n).

EXAMPLE

a(10) = 11 because F(10)^2 + 1 = 55^2 + 1 = 3026 = 2*17*89 and 89 = F(11) is the greatest prime Fibonacci divisor of 3026.

MAPLE

a:= proc(n) local i, F, m, t; F, m, t:=

      [1, 2], 0, (<<0|1>, <1|1>>^n)[2, 1]^2+1;

      for i from 3 while F[2]<=t do if isprime(F[2]) and

        irem(t, F[2])=0 then m:=i fi; F:= [F[2], F[1]+F[2]]

      od; m

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Nov 21 2020

MATHEMATICA

a[n_] := Module[{i, F = {1, 2}, m = 0, t}, t = MatrixPower[{{0, 1}, {1, 1}}, n][[2, 1]]^2 + 1; For[i = 3, F[[2]] <= t, i++, If[PrimeQ[F[[2]]] && Mod[t, F[[2]]] == 0, m = i]; F = {F[[2]], F[[1]] + F[[2]]}]; m];

Array[a, 100] (* Jean-Fran├žois Alcover, Dec 01 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000040, A000045, A005478, A245306, A338762, A338794 (indices of the 0's).

Sequence in context: A233808 A141424 A069902 * A085779 A078936 A293702

Adjacent sequences:  A335565 A335566 A335567 * A335569 A335570 A335571

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Nov 20 2020

STATUS

approved

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Last modified July 24 02:31 EDT 2021. Contains 346270 sequences. (Running on oeis4.)