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

1,3

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = if ((f=fibonacci(n))==1, 1, factor(f)[1, 1]); \\ Michel Marcus, Nov 15 2014
(Magma) [1, 1] cat [Minimum(PrimeDivisors(Fibonacci(n))): n in [3..70]]; // Vincenzo Librandi, Dec 25 2016

Crossrefs

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

Sequence in context: A137458 A079369 A102867 * A139044 A060442 A060385

Adjacent sequences: A060380 A060381 A060382 * A060384 A060385 A060386

Keyword

nonn

Author

Labos Elemer, Apr 03 2001

Extensions

Better definition from Omar E. Pol, Apr 25 2008

Status

approved