A366304 Square array A(n, k), n, k >= 0, read and filled by upwards antidiagonals the greedy way with distinct nonnegative integers such that the binary expansions of any two distinct terms in the same row or column have no common 1's.

0, 1, 2, 4, 8, 5, 10, 16, 18, 24, 32, 33, 40, 36, 64, 80, 68, 128, 3, 256, 160, 384, 512, 768, 320, 640, 576, 1024, 1536, 2048, 3072, 1152, 20, 1280, 2176, 2304, 4096, 4224, 4160, 8192, 9, 6144, 8256, 5120, 4608, 10240, 8448, 16384, 16896, 34, 8194, 32768, 49152, 24576, 40960

Offset

0,3

Comments

This sequence is a variant of A366031, with one less constraint.

All the powers of 2 appear in the sequence, in ascending order.

For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.

Will every nonnegative integer appear in the sequence?

Links

Table of n, a(n) for n=0..54.

Rémy Sigrist, Colored representation of the array for n, k <= 666 (grayish pixels correspond to powers of 2)

Rémy Sigrist, PARI program

Example

Array A(n, k) begins:
  n\k |     0      1       2       3        4        5        6        7
  ----+-----------------------------------------------------------------
    0 |     0      2       5      24       64      160     1024     2304
    1 |     1      8      18      36      256      576     2176     5120
    2 |     4     16      40       3      640     1280     8256    49152
    3 |    10     33     128     320       20     6144    32768     8704
    4 |    32     68     768    1152        9     8194     4112   327680
    5 |    80    512    3072    8192       34       12      257   131200
    6 |   384   2048    4160   16896     9216       17        6   524296
    7 |  1536   4224   16384   34816   196608   786432  1048584        7
    8 |  4096   8448   98304  393216    18432  5242880      544  2097168
    9 | 10240  17408  262144   69632  1081344  2228224  4718592       96

Prog

(PARI) See Links section.

Crossrefs

Cf. A336350, A366031.

Sequence in context: A036117 A307357 A116624 * A361191 A248573 A372129

Adjacent sequences: A366301 A366302 A366303 * A366305 A366306 A366307

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Oct 06 2023

Status

approved