A338919 -id:A338919 - cp's OEIS frontend

A338872 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, Sum_{ i = 1..n, j = 1..k } T(i, j) is divisible by n * k.

1, 3, 5, 2, 7, 6, 10, 12, 8, 4, 9, 16, 19, 14, 24, 11, 15, 31, 27, 18, 20, 13, 17, 21, 43, 30, 22, 38, 23, 33, 41, 47, 40, 48, 26, 46, 36, 63, 35, 39, 88, 70, 44, 62, 45, 32, 66, 55, 71, 52, 60, 28, 42, 29, 51, 25, 86, 90, 67, 98, 56, 54, 34, 73, 91, 57

Offset: 1

Rémy Sigrist, Nov 13 2020

This sequence is a 2-dimensional variant of A019444.

			Array T(n, k) begins:
  n\k|   1   2   3    4    5    6    7    8    9   10
  ---+-----------------------------------------------
    1|   1   5   6    4   24   20   38   46   45   51
    2|   3   7   8   14   18   22   26   62   29   91
    3|   2  12  19   27   30   48   44   42   73   53
    4|  10  16  31   43   40   70   28   34   61   37
    5|   9  15  21   47   88   60   54  106   77  133
    6|  11  17  41   39   52   56   50  118  129  157
    7|  13  33  35   71   98  116  173  117  181  213
    8|  23  63  55   67   82  136  155  187  141  161
    9|  36  66  90   84   99  111  179  143  146  256
   10|  32  86  74  124  109  121  203  235   78  188

Rémy Sigrist, Table of n, a(n) for n = 1..5050
Rémy Sigrist, PARI program for A338872

See A338918 and A338919 for similar sequences.

Cf. A019444.

PARI
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A338918 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, T(n, k) is divisible by n * k.

Original entry on oeis.org

1, 2, 4, 3, 8, 6, 12, 18, 24, 16, 5, 32, 9, 40, 10, 30, 20, 36, 48, 50, 42, 7, 60, 15, 64, 45, 72, 14, 56, 28, 54, 80, 100, 90, 70, 88, 27, 96, 21, 120, 25, 144, 63, 112, 81, 110, 108, 168, 84, 150, 180, 140, 192, 126, 130, 11, 160, 135, 128, 35, 216, 105, 224, 162, 200, 22

Offset: 1

Rémy Sigrist, Nov 15 2020

All integers appear in this sequence.

			Array T(n, k) begins:
  n\k|    1    2    3    4    5    6    7    8    9   10
  ---+--------------------------------------------------
    1|    1    4    6   16   10   42   14   88   81  130
    2|    2    8   24   40   50   72   70  112  126  200
    3|    3   18    9   48   45   90   63  192  162  270
    4|   12   32   36   64  100  144  140  224  288  360
    5|    5   20   15   80   25  180  105  280  315  300
    6|   30   60   54  120  150  216  336  432  486  540
    7|    7   28   21   84   35  294   49  448  441  490
    8|   56   96  168  128  240  384  392  256  576  640
    9|   27  108  135  252  225  378  189  504  243  900
   10|  110  160  210  320  250  420  350  400  810  500

Rémy Sigrist, Table of n, a(n) for n = 1..5050
Rémy Sigrist, PARI program for A338918
Index entries for sequences that are permutations of the natural numbers

See A338872 and A338919 for similar sequences.

PARI
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See Links section.
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T(p, 1) = p for any prime number p.

A361927 Square array A(n, k) of distinct positive integers, n, k > 0, read and filled by upwards antidiagonals in the greedy way such that A(n, k) is a multiple of A(n, 1) and of A(1, k).

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 12, 10, 8, 9, 21, 20, 16, 11, 13, 18, 35, 24, 22, 14, 15, 39, 45, 56, 44, 28, 17, 19, 30, 65, 72, 77, 84, 34, 23, 25, 57, 60, 104, 99, 42, 68, 46, 26, 27, 75, 95, 120, 143, 126, 119, 92, 52, 29, 31, 54, 50, 152, 165, 182, 153, 161, 156, 58, 32

Offset: 1

Rémy Sigrist, Mar 30 2023

This sequence is a variant of A361926.

As a flat sequence, this is a permutation of the positive integers with inverse A361941.

			Array A(n, k) begins:
  n\k |  1   2    3    4    5    6    7    8    9   10
  ----+-----------------------------------------------
    1 |  1   3    5    8   11   14   17   23   26   29
    2 |  2   6   10   16   22   28   34   46   52   58
    3 |  4  12   20   24   44   84   68   92  156  116
    4 |  7  21   35   56   77   42  119  161  364  203
    5 |  9  18   45   72   99  126  153  207  234  261
    6 | 13  39   65  104  143  182  221  299   78  377
    7 | 15  30   60  120  165  210  255  345  390  435
    8 | 19  57   95  152  209  266  323  437  494  551
    9 | 25  75   50  200  275  350  425  575  650  725
   10 | 27  54  135  216  297  378  459  621  702  783

Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A338919, A361926, A361941 (inverse).

PARI
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See Links section.
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cp's OEIS Frontend

A338872 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, Sum_{ i = 1..n, j = 1..k } T(i, j) is divisible by n * k.

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A338918 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, T(n, k) is divisible by n * k.

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A361927 Square array A(n, k) of distinct positive integers, n, k > 0, read and filled by upwards antidiagonals in the greedy way such that A(n, k) is a multiple of A(n, 1) and of A(1, k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI