login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(0)=1. a(n) = number of earlier terms of the sequence that divide the n-th Fibonacci number.
2

%I #19 Sep 21 2024 08:42:56

%S 1,1,2,3,3,2,4,2,4,5,3,2,11,2,2,9,5,2,11,2,9,10,2,2,19,4,2,13,6,2,22,

%T 2,5,15,2,6,27,2,2,18,11,2,23,2,5,25,2,2,34,3,10,22,6,2,28,6,7,23,2,2,

%U 51,2,2,29,7,6,30,2,6,28,11,2,55,2,2,38,6,3,34,2,19,34,2,2,54,6,2,35,9,2

%N a(0)=1. a(n) = number of earlier terms of the sequence that divide the n-th Fibonacci number.

%H Antti Karttunen, <a href="/A130156/b130156.txt">Table of n, a(n) for n = 0..16384</a>

%e The 10th Fibonacci number is 55. Among terms (a(0), a(1),..., a(9)) there are 3 terms (a(0)=1, a(1)=1, a(9)=5) that divide 55, so a(10) = 3.

%p A130156 := proc(nmax) local a,nfib,anew,i,n; a := [1] ; while nops(a) < nmax do n := nops(a) ; nfib := combinat[fibonacci](n) ; anew :=0 ; for i from 1 to nops(a) do if nfib mod op(i,a) = 0 then anew := anew+1 ; fi ; od ; a := [op(a),anew] ; od ; RETURN(a) ; end: A130156(100) ; # _R. J. Mathar_, Jun 07 2007

%o (PARI)

%o up_to = 16384;

%o A130156list(upto_n) = { my(v=vector(1+upto_n),fibo); v[1] = 1; for(n=2,#v,fibo = fibonacci(n-1); v[n] = sum(i=1,n-1,!(fibo%v[i]))); (v); };

%o v130156 = A130156list(up_to);

%o A130156(n) = v130156[1+n]; \\ _Antti Karttunen_, Feb 18 2023

%Y Cf. A000045, A130155.

%K nonn,look

%O 0,3

%A _Leroy Quet_, May 13 2007

%E More terms from _R. J. Mathar_, Jun 07 2007