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%I #15 Oct 13 2022 10:58:32
%S 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,
%T 55,58,63,66,68,71,76,79,84,87,89,92,97,100,105,108,110,113,118,121,
%U 126,131,134,139,142,144,147,152,155,160,165,168,173,176,178,181
%N Numbers not of the form v(m) + v(n), where v = A001950 (upper Wythoff numbers) and 1 <= m <= n - 1, for n >= 2.
%C It appears that the difference sequence consists entirely of Fibonacci numbers (A000045); see A260311.
%C 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
%t r = GoldenRatio; z = 1060;
%t u[n_] := u[n] = Floor[n*r]; v[n_] := v[n] = Floor[n*r^2];
%t s[m_, n_] := v[m] + v[n];
%t t = Table[s[m, n], {n, 2, z}, {m, 1, n - 1}]; (* A259601 *)
%t w = Flatten[Table[Count[Flatten[t], n], {n, 1, z}]];
%t p0 = Flatten[Position[w, 0]] (* A260317 *)
%t d = Differences[p0] (* A260311 *)
%Y Cf. A000045, A259556, A259600, A259601, A260311.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 22 2015
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