A338762 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, 5, 5, 13, 13, 5, 13, 89, 89, 233, 233, 89, 233, 1597, 1597, 5, 1597, 1597, 13, 28657, 28657, 13, 28657, 28657, 5, 514229, 514229, 2, 514229, 514229, 89, 13, 89, 89, 13, 233, 233, 0, 233, 433494437, 433494437, 5, 433494437, 2971215073, 2971215073, 13, 2971215073

Offset

1,1

Comments

a(n) = 0 for n = 39, 60, 69, 72, ... .

a(5385) has 1126 decimal digits. - Chai Wah Wu, Nov 19 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..5384 (n = 1..1000 from Alois P. Heinz)

Example

a(6) = 13 because F(6)^2 + 1 = 8^2 + 1 = 65 = 5*13 and 13 is the greatest prime Fibonacci divisor.

Maple

a:= proc(n) local F, m, t; F, m, t:=
      [1, 2], 0, (<<0|1>, <1|1>>^n)[2, 1]^2+1;
      while F[2]<=t do if isprime(F[2]) and irem(t, F[2])=0
        then m:=F[2] fi; F:= [F[2], F[1]+F[2]]
      od; m
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Nov 07 2020

Prog

(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
a(n) = my(f=factor(fibonacci(n)^2+1)[, 1]~, v=select(x->isfib(x), f)); if (#v, vecmax(v), 0); \\ Michel Marcus, Nov 07 2020

Crossrefs

Cf. A000045, A005478, A245306.

Sequence in context: A056504 A122205 A368923 * A364486 A178115 A094967

Adjacent sequences: A338759 A338760 A338761 * A338763 A338764 A338765

Keyword

nonn

Author

Michel Lagneau, Nov 07 2020

Status

approved