A107038 First differences of indices of squarefree Fibonacci numbers.

1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1

Offset: 0

Author

Paul Barry, May 09 2005

Keywords

• nonn

Comments

First differences of A037918.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1078 (terms 0..763 from Muniru A Asiru)

Crossrefs

Cf. A000045, A037918.

Programs

GAP

P1:=List(List(List([1..180], n->Fibonacci(n)),Factors),Collected);;
P2:=Positions(List(List([1..Length(P1)],i->List([1..Length(P1[i])],j->P1[i][j][2])),Set),[1]);; a:=List([1..Length(P2)-1],j->P2[j+1]-P2[j]); # Muniru A Asiru, Jul 06 2018

Maple

with(numtheory): with(combinat): a:=proc(n) if mobius(fibonacci(n))<>0 then n else fi end:A:=[seq(a(n),n=1..180)]:seq(A[j]-A[j-1],j=2..nops(A)); # Emeric Deutsch, May 30 2005

Mathematica

Range[200] // Select[#, SquareFreeQ[Fibonacci[#]]&]& // Differences (* Jean-François Alcover, Aug 29 2024 *)

PARI

lista(nn) = {my(v = select(x->issquarefree(x), vector(nn, k, fibonacci(k)), 1)); vector(#v-1, k, v[k+1] - v[k]);} \\ Michel Marcus, Jul 09 2018

Extensions

More terms from Emeric Deutsch, May 30 2005