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A152727 Smallest positive non-divisor of the n-th Fibonacci number (A000045).

%I A152727 #24 Jul 24 2020 15:59:42
%S A152727 2,2,3,2,2,3,2,2,3,2,2,5,2,2,3,2,2,3,2,2,3,2,2,5,2,2,3,2,2,3,2,2,3,2,
%T A152727 2,5,2,2,3,2,2,3,2,2,3,2,2,5,2,2,3,2,2,3,2,2,3,2,2,7,2,2,3,2,2,3,2,2,
%U A152727 3,2,2,5,2,2,3,2,2,3,2,2,3,2,2,5,2,2,3,2,2,3,2,2,3,2,2,5,2,2,3,2,2,3,2,2,3
%N A152727 Smallest positive non-divisor of the n-th Fibonacci number (A000045).
%C A152727 Other values are a(840)=17 and a(12600)=37. Not all terms are prime; for example, the smallest non-divisor of F(2520) is 25.
%C A152727 It appears that the indices k for which a(n) is not prime are divisible by 2520 and that the sequence k/2520 is A047201. - _Michel Marcus_, Jul 10 2014
%H A152727 Robert Israel, <a href="/A152727/b152727.txt">Table of n, a(n) for n = 1..10000</a>
%p A152727 f:= proc(n) local m,k;
%p A152727 m:= combinat:-fibonacci(n);
%p A152727 for k from 2 do if m mod k <> 0 then return k fi od:
%p A152727 end proc:
%p A152727 map(f, [$1..100]); # _Robert Israel_, Mar 06 2020
%t A152727 a[n_] := Module[{f = Fibonacci[n], d}, For[d = 2, True, d++, If[!Divisible[f, d], Return[d]]]];
%t A152727 Array[a, 100] (* _Jean-François Alcover_, Jul 24 2020 *)
%o A152727 (PARI) a(n) = my(f = fibonacci(n)); my(d = 2); while((f%d) == 0, d++); d; \\ _Michel Marcus_, Jul 10 2014
%o A152727 (Sage)
%o A152727 def A152727(n) :
%o A152727     d = 2
%o A152727     f = fibonacci(n)
%o A152727     while ((f % d) == 0) :
%o A152727         d = d + 1
%o A152727     return(d)
%o A152727 [A152727(n) for n in (1..105)] # _Jani Melik_, Jul 10 2014
%Y A152727 Cf. A000045, A001651 (a(n)=2).
%K A152727 nonn
%O A152727 1,1
%A A152727 _John W. Layman_, Dec 11 2008