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 2, 5, 7, 8, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124 (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..10000 FORMULA a(n) = 2n for all n except 2, 3, and 5. 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], First[t[#]] == 2 &]; (* A299231 *) Select[Range[200], First[t[#]] == 3 &]; (* A299232 *) CROSSREFS Cf. A299229, A299231 (complement). Sequence in context: A214518 A242401 A050941 * A153083 A140592 A153086 Adjacent sequences:  A299229 A299230 A299231 * A299233 A299234 A299235 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 06 2018 STATUS approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)