

A299237


a(n) = the index m satisfying t(m) = reversal of t(n), where t(n) is the nth {2,3}power tower; see Comments.


3



1, 2, 3, 5, 4, 6, 7, 9, 8, 10, 11, 15, 13, 19, 12, 16, 21, 31, 14, 20, 17, 23, 22, 32, 25, 33, 27, 39, 43, 63, 18, 24, 26, 34, 35, 47, 51, 67, 28, 40, 44, 64, 29, 41, 45, 65, 36, 48, 52, 68, 37, 49, 53, 69, 55, 79, 87, 127, 71, 95, 103, 135, 30, 42, 46, 66
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OFFSET

1,2


COMMENTS

Suppose that S is a set of real numbers. An Spowertower, 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(k1)); (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 selfinverse 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(15) = (2,3,3) = reversal of t(12); therefore a(12) = 15.


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;
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_] := Reverse[t[n]]
Flatten[Table[Select[Range[2000], t[#] == r[n] &], {n, 1, 1500}]]; (* A299237 *)


CROSSREFS

Cf. A299229, A299239 (fixed points of the permutation; palindromes).
Sequence in context: A131141 A130981 A074145 * A257676 A257677 A105363
Adjacent sequences: A299234 A299235 A299236 * A299238 A299239 A299240


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 07 2018


STATUS

approved



