This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379409 #8 Jan 18 2025 09:25:37
%S A379409 2,5,8,11,14,17,20,24,26,29,32,35,38,41,44,48,51,53,56,59,62,65,68,72,
%T A379409 75,78,80,83,86,89,92,96,99,102,105,107,110,113,116,120,123,126,129,
%U A379409 132,134,137,141,144,147,150,153,156,158,161,165,168,171,174,177
%N A379409 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).
%C A379409 This sequence and A379408 and A379410 partition the positive integers.
%F A379409 a(n) = n + floor(n/r) + floor(n*r), where r = u^(1/4), u = golden ratio.
%t A379409 u = (1 + 5^(1/2))/2;
%t A379409 r = u^(1/4); s = u^(1/2); t = u^(3/4);
%t A379409 Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}] (* A379408 *)
%t A379409 Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}] (* A379409 *)
%t A379409 Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}] (* A379410 *)
%Y A379409 Cf. A001622, A379408, A379410.
%K A379409 nonn
%O A379409 1,1
%A A379409 _Clark Kimberling_, Jan 15 2025