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A152727 Smallest positive non-divisor of the n-th Fibonacci number (A000045). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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-Fran├žois Alcover, Jul 24 2020 *)

PROG

(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

CROSSREFS

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

Sequence in context: A261865 A003589 A082204 * A087159 A218800 A062502

Adjacent sequences:  A152724 A152725 A152726 * A152728 A152729 A152730

KEYWORD

nonn

AUTHOR

John W. Layman, Dec 11 2008

STATUS

approved

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Last modified October 21 22:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)