A299327 - OEIS

A299327

Rectangular array by antidiagonals: row n gives the ranks of {2,3}-power towers in which the maximal runlength is n; see Comments.

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

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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))); (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 22 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};