A260317 - OEIS (original) (raw)

1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 16, 19, 21, 24, 26, 29, 32, 34, 37, 40, 42, 45, 50, 53, 55, 58, 63, 66, 68, 71, 76, 79, 84, 87, 89, 92, 97, 100, 105, 108, 110, 113, 118, 121, 126, 131, 134, 139, 142, 144, 147, 152, 155, 160, 165, 168, 173, 176, 178, 181

COMMENTS

It appears that the difference sequence consists entirely of Fibonacci numbers (A000045); see A260311.

In fact, the difference sequence consists only of the numbers 1,2,3,5. Proved with the Walnut theorem-prover. - Jeffrey Shallit, Oct 12 2022

MATHEMATICA

r = GoldenRatio; z = 1060;

u[n_] := u[n] = Floor[n*r]; v[n_] := v[n] = Floor[n*r^2];

s[m_, n_] := v[m] + v[n];

t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}]; (* A259601 *)

w = Flatten[Table[Count[Flatten[t], n], {n, 1, z}]];

p0 = Flatten[Position[w, 0]] (* A260317 *)

d = Differences[p0] (* A260311 *)