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 A299323 #13 Aug 07 2024 14:24:08 %S A299323 1,4,3,5,8,6,11,9,14,13,12,10,17,28,27,15,18,19,29,56,55,24,20,21,35, %T A299323 57,112,111,26,22,30,39,59,113,224,223,32,23,36,43,71,115,225,448,447, %U A299323 33,25,37,58,79,119,227,449,896,895,50,31,40,60,87,143,231 %N A299323 Rectangular array by antidiagonals: row n gives the ranks of {2,3}-power towers in which the number of 2's is n; see Comments. %C A299323 Suppose that S is a set of real numbers. An S-power-tower, t, is a number t = x(1)^x(2)^...^x(k), where k >= 1 and x(i) is in S for i = 1..k. We represent t by (x(1), x(2), ..., x(k)), which for k > 1 is defined as (x(1), (x(2), ..., x(k))); (2,3,2) means 2^9. The number k is the *height* of t. If every element of S exceeds 1 and all the power towers are ranked in increasing order, the position of each in the resulting sequence is its *rank*. See A299229 for a guide to related sequences. %e A299323 Northwest corner: %e A299323 1 4 5 11 12 15 %e A299323 3 8 9 10 18 20 %e A299323 6 14 17 19 21 30 %e A299323 13 28 29 35 39 43 %e A299323 27 56 57 59 71 79 %e A299323 55 112 113 115 119 143 %t A299323 t[1] = {2}; t[2] = {3}; t[3] = {2, 2}; t[4] = {2, 3}; t[5] = {3, 2}; %t A299323 t[6] = {2, 2, 2}; t[7] = {3, 3}; %t A299323 t[8] = {3, 2, 2}; t[9] = {2, 2, 3}; t[10] = {2, 3, 2}; %t A299323 t[11] = {3, 2, 3}; t[12] = {3, 3, 2}; %t A299323 z = 400; g[k_] := If[EvenQ[k], {2}, {3}]; %t A299323 f = 6; While[f < 13, n = f; While[n < z, p = 1; %t A299323 While[p < 18, m = 2 n + 1; v = t[n]; k = 0; %t A299323 While[k < 2^p, t[m + k] = Join[g[k], t[n + Floor[k/2]]]; k = k + 1]; %t A299323 p = p + 1; n = m]]; f = f + 1] %t A299323 r[n_] := Select[Range[5000], Count[t[#], 2] == n &] %t A299323 TableForm[Table[r[n], {n, 1, 15}]] (* this array *) %t A299323 w[n_, k_] := r[n][[k]]; %t A299323 Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* this sequence *) %Y A299323 Cf. A299229, A299324. %K A299323 nonn,easy,tabl %O A299323 1,2 %A A299323 _Clark Kimberling_, Feb 08 2018