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 A379414 #9 Jan 20 2025 17:11:59
%S A379414 3,7,11,15,19,23,28,31,35,40,44,47,52,56,59,64,68,72,76,80,84,88,92,
%T A379414 96,100,105,108,112,117,120,124,129,133,136,141,145,149,153,157,161,
%U A379414 165,169,173,177,181,185,189,194,197,201,206,210,213,218,222,225,230
%N A379414 a(n) = n + floor(n*s/r) + floor(n*t/r), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).
%C A379414 This sequence and A379415 and A379416 partition the positive integers; see A184812 for a proof.
%C A379414 For each k in A000027, write "a" if k=A379414(n) for some n, "b" if k=A379415(n) for some n, and "c" if k=A379416(n) for some n. Concatenating these letters for k = 1,2,3,... spells the following infinite word:
%C A379414 cbacbcabccabcbacbcacbcabcbcacbacbcabccbacbcabcacbcbacbcacbacbcbacbcacbcabcbaccbacbcabccabcbacbcacbcabcbcacbacbcabccbacbacbcabccbacbcabcacbcba
%F A379414 a(n) = n + floor(n*r) + floor(n*r^2), where r = 3^(1/4).
%t A379414 r = 3^(1/4); s = 3^(1/2); t = 3^(3/4);
%t A379414 Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}] (* A379411 *)
%t A379414 Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}] (* A379412 *)
%t A379414 Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}] (* A379413 *)
%Y A379414 Cf. A184812, A379415, A379416.
%Y A379414 Cf. also A011002, A002194, A011022.
%K A379414 nonn
%O A379414 1,1
%A A379414 _Clark Kimberling_, Jan 18 2025