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

%I A060383 #30 Feb 17 2023 01:59:16
%S A060383 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,
%T A060383 2,3,514229,2,557,3,2,1597,5,2,73,37,2,3,2789,2,433494437,3,2,139,
%U A060383 2971215073,2,13,5,2,3,953,2,5,3,2,59,353,2,4513,557,2,3,5,2,269,3,2,5
%N A060383 a(1) = a(2) = 1; for n >2, a(n) = smallest prime factor of n-th Fibonacci number.
%H A060383 Tyler Busby, <a href="/A060383/b060383.txt">Table of n, a(n) for n = 1..1452</a> (terms 1..1000 from Alois P. Heinz, derived from Kelly's data, terms 1001..1408 from Amiram Eldar)
%H A060383 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%F A060383 a(n) = A020639(A000045(n)). - _Michel Marcus_, Nov 15 2014
%e A060383 For n=82: F(82) = 2789*59369*370248451, so a(82)=2789.
%t A060383 f[n_] := (FactorInteger@ Fibonacci@ n)[[1,1]]; Array[f, 70] (* _Robert G. Wilson v_, Jul 07 2007 *)
%o A060383 (PARI) a(n) = if ((f=fibonacci(n))==1, 1, factor(f)[1,1]); \\ _Michel Marcus_, Nov 15 2014
%o A060383 (Magma) [1,1] cat [Minimum(PrimeDivisors(Fibonacci(n))): n in [3..70]]; // _Vincenzo Librandi_, Dec 25 2016
%Y A060383 Cf. A000045, A022307, A001605, A060319, A060320, A051694, A139044.
%K A060383 nonn
%O A060383 1,3
%A A060383 _Labos Elemer_, Apr 03 2001
%E A060383 Better definition from _Omar E. Pol_, Apr 25 2008