A375377 Square array read by antidiagonals: the n-th row is the inverse to the permutation given by the n-th row of A375376.
1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 5, 3, 2, 1, 7, 6, 4, 4, 3, 2, 1, 8, 7, 7, 5, 4, 3, 2, 1, 9, 8, 6, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 7, 5, 4, 3, 3, 1, 11, 10, 10, 8, 6, 6, 6, 4, 2, 2, 1, 12, 11, 12, 9, 8, 7, 7, 5, 5, 3, 2, 1, 13, 12, 9, 10, 9, 8, 5, 6, 6, 4, 4, 2, 1
Offset: 1
Examples
Array begins:
n=1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=2: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=3: 1, 2, 3, 5, 4, 7, 6, 8, 10, 12, 9, 11, 15, 16, 13, ...
n=4: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=5: 1, 2, 3, 4, 5, 7, 6, 8, 9, 12, 10, 13, 15, 17, 11, ...
n=6: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=7: 1, 2, 3, 4, 6, 7, 5, 10, 11, 8, 12, 14, 9, 13, 15, ...
n=8: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=9: 1, 3, 2, 5, 6, 8, 4, 7, 10, 13, 11, 14, 17, 18, 9, ...
n=10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=11: 1, 2, 4, 3, 6, 8, 5, 9, 12, 10, 13, 17, 7, 11, 16, ...
n=12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
n=13: 1, 2, 4, 3, 5, 8, 6, 10, 12, 9, 14, 15, 7, 11, 13, ...
n=14: 1, 2, 3, 4, 5, 7, 6, 9, 10, 8, 11, 12, 13, 14, 15, ...
n=15: 1, 2, 3, 5, 4, 7, 8, 11, 6, 12, 14, 17, 9, 15, 19, ...
For n = 7 = 2^0 + 2^1 + 2^2, the set S (defined in A375376) is {0+2, 1+2, 2+2} = {2, 3, 4}. The first power towers formed by 2's, 3's, and 4's, in colex order, together with their ranks (by magnitude) are:
k | power tower | rank T(7,k)
--+-------------+------------
1 | 2 = 2 | 1
2 | 3 = 3 | 2
3 | 4 = 4 | 3
4 | 2^2 = 4 | 4
5 | 3^2 = 9 | 6
6 | 4^2 = 16 | 7
7 | 2^3 = 8 | 5
8 | 3^3 = 27 | 10
9 | 4^3 = 64 | 11
10 | 2^4 = 16 | 8
11 | 3^4 = 81 | 12
12 | 4^4 = 256 | 14
13 | 2^2^2 = 16 | 9
14 | 3^2^2 = 81 | 13
15 | 4^2^2 = 256 | 15