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
Examples
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|
+---------------+---------+-------+-----+-----+---------+-----------+
Links
- Rémy Sigrist, C++ program
Comments