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

1, 2, 3, 6, 7, 10, 11, 13, 16, 20, 25, 27, 34, 35, 40, 45, 48, 53, 55, 66, 70, 75, 80, 89, 100, 109, 111, 119, 130, 142, 147, 155, 160, 168, 177, 185, 196, 204, 213, 221, 223, 247, 258, 266, 278, 286, 291, 315, 320, 344, 353, 377, 388, 412, 421, 445, 447, 463

Offset: 1

Author

Clark Kimberling, Feb 07 2018

Keywords

• nonn
• easy

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.

Examples

			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).
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000 (terms 1..280 from Clark Kimberling)

Crossrefs

Cf. A299229, A299237.

Programs

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]
Flatten[Table[Select[Range[1000], t[#] == Reverse[t[#]] &], {n, 1, 120}]]