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 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. 3
 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, 57, 112, 111, 26, 22, 30, 39, 59, 113, 224, 223, 32, 23, 36, 43, 71, 115, 225, 448, 447, 33, 25, 37, 58, 79, 119, 227, 449, 896, 895, 50, 31, 40, 60, 87, 143, 231 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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-1)); (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. LINKS EXAMPLE Northwest corner:    1     4     5    11    12    15    3     8     9    10    18    20    6    14    17    19    21    30   13    28    29    35    39    43   27    56    57    59    71    79   55   112   113   115   119   143 MATHEMATICA t = {2}; t = {3}; t = {2, 2}; t = {2, 3}; t = {3, 2}; t = {2, 2, 2}; t = {3, 3}; t = {3, 2, 2}; t = {2, 2, 3}; t = {2, 3, 2}; t = {3, 2, 3}; t = {3, 3, 2}; z = 400; g[k_] := If[EvenQ[k], {2}, {3}]; f = 6; While[f < 13, n = f; While[n < z, p = 1;    While[p < 18, m = 2 n + 1; v = t[n]; k = 0;    While[k < 2^p, t[m + k] = Join[g[k], t[n + Floor[k/2]]]; k = k + 1];    p = p + 1; n = m]]; f = f + 1] r[n_] := Select[Range, Count[t[#], 2] == n &] TableForm[Table[r[n], {n, 1, 15}]]  (* A299323, array *) w[n_, k_] := r[n][[k]]; Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A299323, sequence *) CROSSREFS Cf. A299229, A299324. Sequence in context: A306835 A033546 A236360 * A010475 A256367 A242910 Adjacent sequences:  A299320 A299321 A299322 * A299324 A299325 A299326 KEYWORD nonn,easy,tabl AUTHOR Clark Kimberling, Feb 08 2018 STATUS approved

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Last modified October 1 11:02 EDT 2022. Contains 357147 sequences. (Running on oeis4.)