A049996 - OEIS

%I #13 May 28 2019 19:31:41

%S 1,1,1,3,1,3,3,4,3,1,5,4,3,6,5,1,3,7,6,3,4,8,7,3,1,5,9,8,4,3,6,10,9,5,

%T 1,3,7,11,10,6,3,4,8,12,11,7,3,1,5,9,13,12,8,4,3,6,10,14,13,9,5,1,3,7,

%U 11,15,14,10,6,3,4,8,12,16,15,11,7,3,1,5,9,13,17

%N a(n) is the index k such that F(k)=d(n), where d=A049874 (difference sequence of ordered products of Fibonacci numbers).

%H Michel Marcus, <a href="/A049996/b049996.txt">Table of n, a(n) for n = 1..1010</a>

%t Block[{nn = 123, s, t}, s = Differences@ Take[#, nn] &@ Union@ Flatten[Table[Fibonacci[i]*Fibonacci[j], {i, 0, nn}, {j, i + 1, nn}]]; t = Fibonacci@ Range@ nn; Array[First@ FirstPosition[t, s[[#]] ] &, Length@ s]] (* _Michael De Vlieger_, May 27 2019 *)

%o (PARI) ifib(n) = if (n==1, 1, log(n*sqrt(5) + 1/2)\log((1+sqrt(5))/2));

%o lista(nn) = {my(out = List([0])); for (i=0, nn, for (j=i+1, nn, listput(out, fibonacci(i)*fibonacci(j)););); my(v = Vec(vecsort(select(x->(x < fibonacci(nn+1)), out), , 8))); my(w = vector(#v-1, k, v[k+1] - v[k])); vector(#w, k, ifib(w[k]));} \\ _Michel Marcus_, May 27 2019

%Y Cf. A049862, A049874.

%K nonn

%O 1,4

%A _Clark Kimberling_

%E More terms from _Michel Marcus_, May 27 2019