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A299238
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a(n) = the index m satisfying t(m) = 5 - t(n), where t(n) is the n-th {2,3}-power tower; see Comments.
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2
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2, 1, 7, 5, 4, 16, 3, 15, 12, 11, 10, 9, 34, 33, 8, 6, 32, 31, 26, 25, 24, 23, 22, 21, 20, 19, 70, 69, 68, 67, 18, 17, 14, 13, 66, 65, 64, 63, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 142, 141, 140, 139, 138, 137, 136, 135, 38, 37, 36
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OFFSET
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1,1
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COMMENTS
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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 is a self-inverse permutation of the positive integers.
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LINKS
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EXAMPLE
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t(12) = (3,3,2) and t(9) = (2,2,3) = 5 - (3,3,2), so that a(12) = 9. (Note: 5 - (x(1),x(2),...,x(k)) means (5-x(1), 5-x(2),...,5-x(k)).
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MATHEMATICA
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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[#] == 5 - t[n] &], {n, 1, 150}]] (* A299238 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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