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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.

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.

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%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