A363932 Square array of distinct positive integers A(n, k), n, k > 0, read and filled the greedy way by antidiagonals downwards such that the concatenations of the terms of two distinct rows are always equal.

1, 2, 12, 3, 31, 123, 11, 13, 113, 1231, 32, 21, 211, 132, 12311, 111, 112, 121, 1112, 321, 123113, 212, 122, 22, 1221, 1121, 2111, 1231132, 213, 131, 1311, 311, 221, 2122, 11121, 12311321, 114, 14, 4, 41, 3114, 13114, 2213, 11212, 123113211, 15, 151, 1511, 5, 15111, 151111, 1141, 2131, 1212, 1231132111

Offset

1,2

Comments

Leading zeros are ignored.

Will every positive integer appear?

Links

Table of n, a(n) for n=1..55.

Rémy Sigrist, C++ program

Example

Array A(n, k) begins:
  n\k|        1      2     3      4       5      6       7       8
  ---+------------------------------------------------------------
    1|        1      2     3     11      32    111     212     213
    2|       12     31    13     21     112    122     131      14
    3|      123    113   211    121      22   1311       4    1511
    4|     1231    132  1112   1221     311     41       5   11113
    5|    12311    321  1121    221    3114  15111    1312    1122
    6|   123113   2111  2122  13114  151111    312   11221   13111
    7|  1231132  11121  2213   1141      51  11131   21122  113111
    8| 12311321  11212  2131    141     511  11312  112211  311111
.
Array A(n, k), with digits vertically aligned, begins:
    +-+-+-+---+---+-----+-----+-----+-----+---+-------+-------+---------+
    |1|2|3|1 1|3 2|1 1 1|2 1 2|2 1 3|1 1 4|1 5|1 1 1 1|3 1 2 1|1 2 2 1 1|
    +-+-+-+-+-+-+-+-+---+-+---+-+---+-+---+---+-+-----+-+-----+-+-------+
    |1 2|3 1|1 3|2 1|1 1 2|1 2 2|1 3 1|1 4|1 5 1|1 1 1 3|1 2 1 1|2 2 1 1|
    +---+-+-+---+---+-+---+-+---+-----+-+-+-----+-+-----+-+-----+-+-----+
    |1 2 3|1 1 3|2 1 1|1 2 1|2 2|1 3 1 1|4|1 5 1 1|1 1 3 1|2 1 1 2|
    +-----+-+---+-+---+---+-+---+-+-----+-+-+-+---+-----+-+-------+
    |1 2 3 1|1 3 2|1 1 1 2|1 2 2 1|3 1 1|4 1|5|1 1 1 1 3|1 2 1 1 2|
    +-------+-+---+-+-----+-+-----+-----+-+-+-+-----+---+---+-----+-+
    |1 2 3 1 1|3 2 1|1 1 2 1|2 2 1|3 1 1 4|1 5 1 1 1|1 3 1 2|1 1 2 2|
    +---------+-+---+---+---+---+-+-------+---------+-+-----+-------+-+
    |1 2 3 1 1 3|2 1 1 1|2 1 2 2|1 3 1 1 4|1 5 1 1 1 1|3 1 2|1 1 2 2 1|
    +-----------+-+-----+---+---+---+-----+-+---+-----+---+-+-------+-+
    |1 2 3 1 1 3 2|1 1 1 2 1|2 2 1 3|1 1 4 1|5 1|1 1 1 3 1|2 1 1 2 2|
    +-------------+-+-------+-+-----+-+-----+---+-+-------+-+-------+---+
    |1 2 3 1 1 3 2 1|1 1 2 1 2|2 1 3 1|1 4 1|5 1 1|1 1 3 1 2|1 1 2 2 1 1|
    +---------------+---------+-------+-----+-----+---------+-----------+

Prog

(C++) See Links section.

Crossrefs

Cf. A329127, A363931.

Sequence in context: A365703 A275841 A224841 * A317206 A164869 A347408

Adjacent sequences: A363929 A363930 A363931 * A363933 A363934 A363935

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Jun 28 2023

Status

approved