A299238 - OEIS

A299238

a(n) = the index m satisfying t(m) = 5 - t(n), where t(n) is the n-th {2,3}-power tower; see Comments.

2, 1, 7, 5, 4, 16, 3, 15, 12, 11, 10, 9, 34, 33, 8, 6, 32, 31, 26, 25, 24, 23, 22, 21, 20, 19, 70, 69, 68, 67, 18, 17, 14, 13, 66, 65, 64, 63, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 142, 141, 140, 139, 138, 137, 136, 135, 38, 37, 36

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OFFSET

1,1

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.

This sequence is a self-inverse permutation of the positive integers.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

t(12) = (3,3,2) and t(9) = (2,2,3) = 5 - (3,3,2), so that a(12) = 9. (Note: 5 - (x(1), x(2), ..., x(k)) means (5-x(1), 5-x(2), ..., 5-x(k))).

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 = 190; g[k_] := If[EvenQ[k], {2}, {3}]; f = 6;

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

While[p < 12, m = 2 n + 1; v = t[n]; k = 0;