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

1,2

Links

Table of n, a(n) for n=1..91.

Index entries for sequences that are permutations of the natural numbers.

Example

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

Crossrefs

Cf. A375375 (3rd row), A375376 (the inverse permutation to each row).

Sequence in context: A167289 A200329 A023122 * A375376 A200272 A167286

Adjacent sequences: A375374 A375375 A375376 * A375378 A375379 A375380

Keyword

nonn,tabl

Author

Pontus von Brömssen, Aug 14 2024

Status

approved