|
| |
|
|
A299323
|
|
Rectangular array by antidiagonals: row n gives the ranks of {2,3}-power towers in which the number of 2's is n; see Comments.
|
|
3
|
|
|
|
1, 4, 3, 5, 8, 6, 11, 9, 14, 13, 12, 10, 17, 28, 27, 15, 18, 19, 29, 56, 55, 24, 20, 21, 35, 57, 112, 111, 26, 22, 30, 39, 59, 113, 224, 223, 32, 23, 36, 43, 71, 115, 225, 448, 447, 33, 25, 37, 58, 79, 119, 227, 449, 896, 895, 50, 31, 40, 60, 87, 143, 231
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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-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
|
|
|
|
EXAMPLE
|
Northwest corner:
1 4 5 11 12 15
3 8 9 10 18 20
6 14 17 19 21 30
13 28 29 35 39 43
27 56 57 59 71 79
55 112 113 115 119 143
|
|
|
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 = 400; g[k_] := If[EvenQ[k], {2}, {3}];
f = 6; While[f < 13, n = f; While[n < z, p = 1;
While[p < 18, 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]
r[n_] := Select[Range[5000], Count[t[#], 2] == n &]
TableForm[Table[r[n], {n, 1, 15}]] (* A299323, array *)
w[n_, k_] := r[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A299323, sequence *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
