A363931 Square array of distinct positive integers A(n, k), n, k > 0, read and filled the greedy way by antidiagonals upwards such that the concatenations of the terms of two distinct rows are always equal.

1, 11, 12, 112, 2, 3, 1123, 31, 311, 111, 11231, 1111, 1112, 1121, 121, 112311, 11121, 21, 13, 32, 321, 1123111, 11213, 3211, 32111, 211, 1113, 113, 11231111, 1213, 2111, 131, 312, 1312, 122, 1221, 112311112, 213, 21113, 3122, 22, 212, 2121, 1211, 2112

Offset

1,2

Comments

Leading zeros are ignored.

Will every positive integer appear?

Links

Table of n, a(n) for n=1..45.

Rémy Sigrist, C++ program

Example

Array A(n, k) begins:
  n\k|       1      2      3      4       5       6       7
  ---+-----------------------------------------------------
    1|       1     12      3    111     121     321     113
    2|      11      2    311   1121      32    1113     122
    3|     112     31   1112     13     211    1312    2121
    4|    1123   1111     21  32111     312     212   11211
    5|   11231  11121   3211    131      22  121121  111112
    6|  112311  11213   2111   3122   12112  111111     222
    7| 1123111   1213  21113  12212  112111  111222    3131
.
Array A(n, k), with digits vertically aligned, begins:
    +-+---+-+-----+-----+-----+-----+-------+-------+---------+
    |1|1 2|3|1 1 1|1 2 1|3 2 1|1 1 3|1 2 2 1|2 1 1 2|1 1 1 1 1|
    +-+-+-+-+---+-+-----+---+-+-----+-----+-+-----+-+-------+-+-----+
    |1 1|2|3 1 1|1 1 2 1|3 2|1 1 1 3|1 2 2|1 2 1 1|2 1 1 1 1|1 1 2 2|
    +---+-+---+-+-----+-+-+-+---+---+---+-+-----+-+-------+-+-------+
    |1 1 2|3 1|1 1 1 2|1 3|2 1 1|1 3 1 2|2 1 2 1|1 2 1 1 1|1 1 1 2 2|
    +-----+-+-+-----+-+-+-+-----+-+-----+-----+-+-------+-+-------+-+
    |1 1 2 3|1 1 1 1|2 1|3 2 1 1 1|3 1 2|2 1 2|1 1 2 1 1|1 1 1 1 2|
    +-------+-+-----+---+-------+-+---+-+-+---+-------+-+---------+
    |1 1 2 3 1|1 1 1 2 1|3 2 1 1|1 3 1|2 2|1 2 1 1 2 1|1 1 1 1 1 2|
    +---------+-+-------+-+-----+-+---+---+---------+-+---------+-+
    |1 1 2 3 1 1|1 1 2 1 3|2 1 1 1|3 1 2 2|1 2 1 1 2|1 1 1 1 1 1|
    +-----------+-+-------+-------+-+-----+---+-----+-----+-----+-----+
    |1 1 2 3 1 1 1|1 2 1 3|2 1 1 1 3|1 2 2 1 2|1 1 2 1 1 1|1 1 1 2 2 2|
    +-------------+-------+---------+---------+-----------+-----------+

Prog

(C++) See Links section.

Crossrefs

Cf. A329127, A363932.

Sequence in context: A110382 A095764 A342944 * A296447 A110380 A164854

Adjacent sequences: A363928 A363929 A363930 * A363932 A363933 A363934

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jun 28 2023

Status

approved