A049996 a(n) is the index k such that F(k)=d(n), where d=A049874 (difference sequence of ordered products of Fibonacci numbers).

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Michel Marcus, Table of n, a(n) for n = 1..1010

Crossrefs

Cf. A049862, A049874.

Programs

Mathematica

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 *)

PARI

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

Extensions

More terms from Michel Marcus, May 27 2019