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A299233
Ranks of {2,3}-power towers that end with 2; see Comments.
3
1, 3, 5, 6, 8, 10, 12, 13, 14, 17, 18, 21, 22, 25, 26, 27, 28, 29, 30, 35, 36, 37, 38, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 71, 72, 73, 74, 75, 76, 77, 78, 87, 88, 89, 90, 91, 92, 93, 94, 103, 104, 105, 106, 107, 108, 109, 110, 111
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))); (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
EXAMPLE
t(76) = (3,2,3,3,2,2), so that 76 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, A299234 (complement).
Sequence in context: A068125 A139437 A233746 * A320997 A083042 A082977
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 06 2018
STATUS
approved