A358359 a(n) = number of occurrences of n in A128440; i.e., as a number [k*r^m], where r = golden ratio = (1+sqrt(5))/2, k and m are positive integers, and [ ] = floor.

1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 3, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1

Offset: 1

Author

Clark Kimberling, Nov 11 2022

Keywords

• nonn

Comments

Conjecture: every positive integers occurs infinitely many times.

Crossrefs

Cf. A128440.

Programs

Mathematica

r = (1 + Sqrt[5])/2; f[n_] := Fibonacci[n]; nr = 300; nc = 200;
t[n_, k_] := k*f[n - 1] + Floor[k*r*f[n]];  (* A128440 *)
u = Sort[Flatten[Table[t[k, n], {k, 1, nr}, {n, 1, nc}]]];
Table[Count[u, n], {n, 1, nr}]