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
Keywords
Links
- Michel Marcus, Table of n, a(n) for n = 1..1010
Programs
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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