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

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, 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, 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

Offset: 1

Author

John W. Layman, Dec 11 2008

Keywords

• nonn

Comments

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.

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A001651 (a(n)=2).

Programs

Maple

f:= proc(n) local m,k;
m:= combinat:-fibonacci(n);
for k from 2 do if m mod k <> 0 then return k fi od:
end proc:
map(f, [$1..100]); # Robert Israel, Mar 06 2020

Mathematica

a[n_] := Module[{f = Fibonacci[n], d}, For[d = 2, True, d++, If[!Divisible[f, d], Return[d]]]];
Array[a, 100] (* Jean-François Alcover, Jul 24 2020 *)

PARI

a(n) = my(f = fibonacci(n)); my(d = 2); while((f%d) == 0, d++); d; \\ Michel Marcus, Jul 10 2014

Sage

def A152727(n) :
    d = 2
    f = fibonacci(n)
    while ((f % d) == 0) :
        d = d + 1
    return(d)
[A152727(n) for n in (1..105)] # Jani Melik, Jul 10 2014