A060383 a(1) = a(2) = 1; for n >2, a(n) = smallest prime factor of n-th Fibonacci number.

1, 1, 2, 3, 5, 2, 13, 3, 2, 5, 89, 2, 233, 13, 2, 3, 1597, 2, 37, 3, 2, 89, 28657, 2, 5, 233, 2, 3, 514229, 2, 557, 3, 2, 1597, 5, 2, 73, 37, 2, 3, 2789, 2, 433494437, 3, 2, 139, 2971215073, 2, 13, 5, 2, 3, 953, 2, 5, 3, 2, 59, 353, 2, 4513, 557, 2, 3, 5, 2, 269, 3, 2, 5

Offset: 1

Author

Labos Elemer, Apr 03 2001

Keywords

• nonn

Examples

			For n=82: F(82) = 2789*59369*370248451, so a(82)=2789.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..1452 (terms 1..1000 from Alois P. Heinz, derived from Kelly's data, terms 1001..1408 from Amiram Eldar)
• Blair Kelly, Fibonacci and Lucas Factorizations

Crossrefs

Cf. A000045, A022307, A001605, A060319, A060320, A051694, A139044.

Programs

Magma

[1,1] cat [Minimum(PrimeDivisors(Fibonacci(n))): n in [3..70]]; // Vincenzo Librandi, Dec 25 2016

Mathematica

f[n_] := (FactorInteger@ Fibonacci@ n)[[1,1]]; Array[f, 70] (* Robert G. Wilson v, Jul 07 2007 *)

PARI

a(n) = if ((f=fibonacci(n))==1, 1, factor(f)[1,1]); \\ Michel Marcus, Nov 15 2014

Formula

a(n) = A020639(A000045(n)). - Michel Marcus, Nov 15 2014

Extensions

Better definition from Omar E. Pol, Apr 25 2008