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

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-1)); (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

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

Example

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).

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}]]

Crossrefs

Cf. A299229, A299237.

Sequence in context: A073439 A188084 A242750 * A335033 A107998 A276884

Adjacent sequences: A299236 A299237 A299238 * A299240 A299241 A299242

Keyword

nonn,easy

Author

Clark Kimberling, Feb 07 2018

Status

approved