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A299241 Ranks of {2,3}-power towers in which #2's = #3's; see Comments. 4
4, 5, 18, 20, 22, 23, 25, 31, 62, 74, 76, 77, 82, 84, 85, 90, 92, 93, 96, 97, 99, 104, 105, 107, 128, 129, 131, 135, 238, 246, 250, 252, 253, 294, 298, 300, 301, 306, 308, 309, 312, 313, 315, 326, 330, 332, 333, 338, 340, 341, 344, 345, 347, 358, 362, 364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

This sequence together with A299240 and A299242 partition the positive integers.

LINKS

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

EXAMPLE

The first six terms are the ranks of these towers: t(4) = (2,3), t(5) = (3,2), t(18) = (3,3,2,2), t(20) = (3,2,2,3), t(22) = (3,2,3,2), t(23) = (2,3,2,3).

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[1000], Count[t[#], 2] > Count[t[#], 3] &];   (* A299240 *)

Select[Range[1000], Count[t[#], 2] == Count[t[#], 3] &];  (* A299241 *)

Select[Range[1000], Count[t[#], 2] < Count[t[#], 3] &];   (* A299242 *)

CROSSREFS

Cf. A299229, A299240, A299241.

Sequence in context: A066879 A276091 A258410 * A134750 A051949 A275961

Adjacent sequences:  A299238 A299239 A299240 * A299242 A299243 A299244

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 07 2018

STATUS

approved

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Last modified May 16 18:13 EDT 2021. Contains 343949 sequences. (Running on oeis4.)