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A299234 Ranks of {2,3}-power towers that end with 3; see Comments. 3
2, 4, 7, 9, 11, 15, 16, 19, 20, 23, 24, 31, 32, 33, 34, 39, 40, 41, 42, 47, 48, 49, 50, 63, 64, 65, 66, 67, 68, 69, 70, 79, 80, 81, 82, 83, 84, 85, 86, 95, 96, 97, 98, 99, 100, 101, 102, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Suppose that S is a set of real numbers.  As 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

t(80) = (3,2,2,2,2,3), so that 80 is in the sequence.

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]

Select[Range[200], Last[t[#]] == 2 &]; (* A299233 *)

Select[Range[200], Last[t[#]] == 3 &]; (* A299234 *)

CROSSREFS

Cf. A299229, A299233 (complement).

Sequence in context: A182761 A329830 A081841 * A213273 A027904 A193600

Adjacent sequences:  A299231 A299232 A299233 * A299235 A299236 A299237

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 06 2018

STATUS

approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)