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A299327 Rectangular array by antidiagonals: row n gives the ranks of {2,3}-power towers in which the maximal runlength is n; see Comments. 2
1, 2, 3, 4, 7, 6, 5, 8, 14, 13, 10, 9, 16, 28, 27, 11, 12, 19, 34, 56, 55, 22, 15, 26, 39, 70, 112, 111, 23, 17, 29, 54, 79, 142, 224, 223, 45, 18, 30, 57, 110, 159, 286, 448, 447, 48, 20, 33, 58, 113, 222, 319, 574, 896, 895, 92, 21, 38, 69, 114, 225, 446 (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

Table of n, a(n) for n=1..62.

EXAMPLE

Northwest corner:

   1   2   4   5   10   11   23   23   45   48

   3   7   8   9   12   15   17   18   20   21

   6  14  16  19   26   29   30   33   38   40

  13  28  34  39   54   57   58   69   78   80

  27  56  70  79  110  113  114  141  158  160

MATHEMATICA

t[1] = {2}; t[2] = {3}; t[3] = {2, 2}; t[4] = {2, 3}; t[5] = {3, 2};

t[6] = {2, 2, 2}; t[7] = {3, 3};

t[8] = {3, 2, 2}; t[9] = {2, 2, 3}; t[10] = {2, 3, 2};

t[11] = {3, 2, 3}; t[12] = {3, 3, 2};

z = 500; g[k_] := If[EvenQ[k], {2}, {3}];

f = 6; While[f < 13, n = f; While[n < z, p = 1;

While[p < 15, 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[30000], Max[Map[Length, Split[t[#]]]] == n & , 12];

TableForm[Table[r[n], {n, 1, 12}]]  (* A299327, array *)

w[n_, k_] := r[n][[k]];

Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A299327, sequence *)

CROSSREFS

Cf. A299229.

Sequence in context: A106453 A122199 A270196 * A231551 A122198 A122155

Adjacent sequences:  A299324 A299325 A299326 * A299328 A299329 A299330

KEYWORD

nonn,easy,tabl

AUTHOR

Clark Kimberling, Feb 08 2018

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)