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A299239 Ranks of palindromic {2,3}-power towers; see Comments. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A107998 A276884 A053438

Adjacent sequences:  A299236 A299237 A299238 * A299240 A299241 A299242

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 07 2018

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)