A363932 - OEIS

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.

%I #5 Jul 02 2023 09:10:11

%S 1,2,12,3,31,123,11,13,113,1231,32,21,211,132,12311,111,112,121,1112,

%T 321,123113,212,122,22,1221,1121,2111,1231132,213,131,1311,311,221,

%U 2122,11121,12311321,114,14,4,41,3114,13114,2213,11212,123113211,15,151,1511,5,15111,151111,1141,2131,1212,1231132111

%N 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.

%C Leading zeros are ignored.

%C Will every positive integer appear?

%H Rémy Sigrist, <a href="/A363932/a363932.txt">C++ program</a>

%e Array A(n, k) begins:

%e n\k| 1 2 3 4 5 6 7 8

%e ---+------------------------------------------------------------

%e 1| 1 2 3 11 32 111 212 213

%e 2| 12 31 13 21 112 122 131 14

%e 3| 123 113 211 121 22 1311 4 1511

%e 4| 1231 132 1112 1221 311 41 5 11113

%e 5| 12311 321 1121 221 3114 15111 1312 1122

%e 6| 123113 2111 2122 13114 151111 312 11221 13111

%e 7| 1231132 11121 2213 1141 51 11131 21122 113111

%e 8| 12311321 11212 2131 141 511 11312 112211 311111

%e .

%e Array A(n, k), with digits vertically aligned, begins:

%e +-+-+-+---+---+-----+-----+-----+-----+---+-------+-------+---------+

%e |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|

%e +-+-+-+-+-+-+-+-+---+-+---+-+---+-+---+---+-+-----+-+-----+-+-------+

%e |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|

%e +---+-+-+---+---+-+---+-+---+-----+-+-+-----+-+-----+-+-----+-+-----+

%e |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|

%e +-----+-+---+-+---+---+-+---+-+-----+-+-+-+---+-----+-+-------+

%e |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|

%e +-------+-+---+-+-----+-+-----+-----+-+-+-+-----+---+---+-----+-+

%e |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|

%e +---------+-+---+---+---+---+-+-------+---------+-+-----+-------+-+

%e |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|

%e +-----------+-+-----+---+---+---+-----+-+---+-----+---+-+-------+-+

%e |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|

%e +-------------+-+-------+-+-----+-+-----+---+-+-------+-+-------+---+

%e |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|

%e +---------------+---------+-------+-----+-----+---------+-----------+

%o (C++) See Links section.

%Y Cf. A329127, A363931.

%K nonn,base,tabl

%O 1,2

%A _Rémy Sigrist_, Jun 28 2023