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, 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

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-François 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