A260317 Numbers not of the form v(m) + v(n), where v = A001950 (upper Wythoff numbers) and 1 <= m <= n - 1, for n >= 2.

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

Offset: 1

Author

Clark Kimberling, Jul 22 2015

Keywords

• nonn
• easy

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

Links

• Wieb Bosma, Rene Bruin, Robbert Fokkink, Jonathan Grube, Anniek Reuijl, and Thian Tromp, Using Walnut to solve problems from the OEIS, arXiv:2503.04122 [math.NT], 2025. See pp. 2-3.

Crossrefs

Cf. A000045, A259556, A259600, A259601, A260311.

Programs

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 *)

Formula

n <= a(n) < 5n, see Shallit comment. - Charles R Greathouse IV, Nov 22 2024