A339082 a(n) is the number m such that F(prime(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.

2, 2, 3, 3, 4, 4, 3, 4, 5, 5, 6, 6, 5, 6, 7, 7, 3, 7, 7, 4, 9, 9, 4, 9, 9, 3, 10, 10, 2, 10, 10, 5, 4, 5, 5, 4, 6, 6, 0, 6, 14, 14, 3, 14, 15, 15, 4, 15, 15, 7, 4, 7, 7, 5, 2, 5, 5, 2, 2, 0, 4, 4, 6, 6, 4, 6, 9, 9, 0, 9, 9, 0, 3, 3, 5, 5, 3, 5, 5, 2, 23, 23, 7

Offset

1,1

Comments

If a(n) > 0, then prime(a(n)) = A335568(n).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..30000

Formula

If A335568(n) = 0, then a(n) = 0, otherwise a(n) = A000720(A335568(n)).

Example

a(15) = 7 because F(15)^2 + 1 = 610^2 + 1 = 372101 = 233*1597, 1597 = F(17) is the greatest prime Fibonacci divisor of 372101 and 17 is the 7th prime.

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; numtheory[pi](m)
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 25 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]]}]; PrimePi[m]];
Array[a, 100] (* Jean-François Alcover, Dec 01 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A000045, A005478, A245306, A335568, A338762, A338794 (indices of the 0's).

Sequence in context: A361384 A339731 A234475 * A329907 A329958 A309969

Adjacent sequences: A339079 A339080 A339081 * A339083 A339084 A339085

Keyword

nonn

Author

Chai Wah Wu, Nov 24 2020

Status

approved