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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, 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 (list; graph; refs; listen; history; text; internal format)
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 7-th 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-Fran├žois 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: A059998 A339731 A234475 * A329907 A329958 A309969

Adjacent sequences:  A339079 A339080 A339081 * A339083 A339084 A339085

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Nov 24 2020

STATUS

approved

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Last modified May 9 19:04 EDT 2021. Contains 343745 sequences. (Running on oeis4.)