cp's OEIS Frontend

A299239 Ranks of palindromic {2,3}-power towers; see Comments.

%I A299239 #16 May 23 2025 11:35:28
%S A299239 1,2,3,6,7,10,11,13,16,20,25,27,34,35,40,45,48,53,55,66,70,75,80,89,
%T A299239 100,109,111,119,130,142,147,155,160,168,177,185,196,204,213,221,223,
%U A299239 247,258,266,278,286,291,315,320,344,353,377,388,412,421,445,447,463
%N A299239 Ranks of palindromic {2,3}-power towers; see Comments.
%C A299239 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.
%H A299239 Pontus von Brömssen, <a href="/A299239/b299239.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..280 from Clark Kimberling)
%e A299239 The first six palindromes are t(1) = (2), t(2) = (3), t(3) = (2,2), t(6) = (2,2,2), t(7) = (3,3), t(10) = (2,3,2).
%t A299239 t[1] = {2}; t[2] = {3}; t[3] = {2, 2}; t[4] = {2, 3}; t[5] = {3, 2};
%t A299239 t[6] = {2, 2, 2}; t[7] = {3, 3}; t[8] = {3, 2, 2}; t[9] = {2, 2, 3};
%t A299239 t[10] = {2, 3, 2}; t[11] = {3, 2, 3}; t[12] = {3, 3, 2};
%t A299239 z = 190; g[k_] := If[EvenQ[k], {2}, {3}]; f = 6;
%t A299239 While[f < 13, n = f; While[n < z, p = 1;
%t A299239   While[p < 12, m = 2 n + 1; v = t[n]; k = 0;
%t A299239     While[k < 2^p, t[m + k] = Join[g[k], t[n + Floor[k/2]]]; k = k + 1];
%t A299239    p = p + 1; n = m]]; f = f + 1]
%t A299239 Flatten[Table[Select[Range[1000], t[#] == Reverse[t[#]] &], {n, 1, 120}]]
%Y A299239 Cf. A299229, A299237.
%K A299239 nonn,easy
%O A299239 1,2
%A A299239 _Clark Kimberling_, Feb 07 2018