A107038 - OEIS

%I #27 Aug 29 2024 12:14:33

%S 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,

%T 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,

%U 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

%N First differences of indices of squarefree Fibonacci numbers.

%C First differences of A037918.

%H Amiram Eldar, <a href="/A107038/b107038.txt">Table of n, a(n) for n = 0..1078</a> (terms 0..763 from Muniru A Asiru)

%p 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

%t Range[200] // Select[#, SquareFreeQ[Fibonacci[#]]&]& // Differences (* _Jean-François Alcover_, Aug 29 2024 *)

%o (GAP) P1:=List(List(List([1..180], n->Fibonacci(n)),Factors),Collected);;

%o 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

%o (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

%Y Cf. A000045, A037918.

%K nonn

%O 0,5

%A _Paul Barry_, May 09 2005

%E More terms from _Emeric Deutsch_, May 30 2005