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