A107038 - OEIS

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

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OFFSET

0,5

COMMENTS

First differences of A037918.

LINKS

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A000045, A037918.

Sequence in context: A055457 A277873 A032542 * A236833 A328511 A371245

Adjacent sequences: A107035 A107036 A107037 * A107039 A107040 A107041

KEYWORD

nonn

AUTHOR

Paul Barry, May 09 2005

EXTENSIONS

More terms from Emeric Deutsch, May 30 2005

STATUS

approved