A348356 Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348330(m) = k.

1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 16, 18, 14, 11, 12, 32, 36, 28, 22, 13, 15, 64, 72, 56, 44, 26, 17, 19, 128, 144, 112, 88, 52, 33, 20, 21, 256, 288, 224, 176, 104, 66, 40, 23, 24, 512, 576, 448, 352, 208, 132, 80, 45, 25, 27, 1024, 1152, 896, 704, 416, 264, 160, 90, 50, 29, 30, 2048, 2304, 1792, 1408, 832, 528, 320, 180, 100, 57, 31, 34

Offset: 1

Author

Rémy Sigrist, Oct 14 2021

Keywords

• nonn
• tabl

Comments

When interpreted as a flat array, we have a permutation of the positive integers.

Examples

			Array T(n, k) begins:
  n\k|    1     2     3     4     5     6     7     8     9    10
  ---+-----------------------------------------------------------
    1|    1     3     6    10    12    15    19    21    24    27
    2|    2     5     7    11    13    17    20    23    25    29
    3|    4     9    14    22    26    33    40    45    50    57
    4|    8    18    28    44    52    66    80    90   100   114
    5|   16    36    56    88   104   132   160   180   200   228
    6|   32    72   112   176   208   264   320   360   400   456
    7|   64   144   224   352   416   528   640   720   800   912
    8|  128   288   448   704   832  1056  1280  1440  1600  1824
    9|  256   576   896  1408  1664  2112  2560  2880  3200  3648
   10|  512  1152  1792  2816  3328  4224  5120  5760  6400  7296
		

Links

• Rémy Sigrist, PARI program for A348356
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000079, A348330, A348357.

Programs

PARI

See Links section.

Formula

Sum_{i = 1..n-1} T(i, k) < T(n, k).

T(n, 1) = 2^(n-1).