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 A379408 #10 Jan 18 2025 09:25:06
%S A379408 3,6,9,13,16,19,22,27,30,33,36,40,43,46,50,54,57,60,64,67,70,73,77,81,
%T A379408 84,88,91,94,97,101,104,108,111,115,118,121,125,128,131,135,139,142,
%U A379408 145,148,152,155,159,163,166,169,172,176,179,182,186,190,193,196
%N A379408 a(n) = n + floor(n*s/r) + floor(n*t/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).
%C A379408 This sequence and A379409 and A379410 partition the positive integers. For each k in A000027, write "a" if k=A379408(n) for some n, "b" if k=A379409(n) for some n, and "c" if k=A379410(n) for some n. Concatenating these letters for k = 1,2,3,... spells the following infinite word:
%C A379408 cbacbacbacbcabcabcabcacbcbacbacbacbacbcabcabcacbcabcbacbacbacbcabcabcacbacbcabcbacbacbcabcabcacbacbcabcabcb...
%F A379408 a(n) = n + floor(n*r) + floor(n*r^2), where r = u^(1/4), u = golden ratio.
%t A379408 u = (1 + 5^(1/2))/2;
%t A379408 r = u^(1/4); s = u^(1/2); t = u^(3/4);
%t A379408 Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}] (* A379408 *)
%t A379408 Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}] (* A379409 *)
%t A379408 Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}] (* A379410 *)
%Y A379408 Cf. A000027, A001622, A379409, A379410.
%K A379408 nonn
%O A379408 1,1
%A A379408 _Clark Kimberling_, Jan 15 2025