A336350 Square spiral of distinct nonnegative integers constructed by greedy algorithm, such that two terms on the same row or on the same column have no common one bit in their binary representations.

0, 1, 2, 4, 8, 6, 16, 3, 12, 32, 24, 64, 5, 48, 72, 128, 256, 17, 96, 512, 10, 33, 144, 320, 1024, 516, 192, 1280, 2048, 4096, 9, 130, 1536, 288, 2112, 4100, 8192, 514, 160, 6144, 16384, 32768, 13, 1152, 768, 10240, 20480, 65536, 18, 32800, 12288, 2304, 640

Offset

0,3

Comments

We can always extend the sequence with a power of 2 greater than any previous term, so the sequence is well defined.

For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10200

Rémy Sigrist, Colored representation of the spiral for -250 <= x <= 250 and -250 <= y <= 250 (where the hue is function of a(n) and black pixels indicate powers of 2)

Rémy Sigrist, PARI program for A336350

Example

The spiral begins:
         264------80--262144---81920----5120---32896----2560----8224-------7
           |                                                               |
       49152    8192----4100----2112-----288----1536-----130-------9   65552
           |       |                                               |       |
        3072     514     256-----128------72------48-------5    4096  131072
           |       |       |                               |       |       |
        4608     160      17       8-------4-------2      64    2048   17408
           |       |       |       |               |       |       |       |
       73728    6144      96       6       0-------1      24    1280     640
           |       |       |       |                       |       |       |
      393216   16384     512      16-------3------12------32     192    2304
           |       |       |                                       |       |
      524288   32768      10------33-----144-----320----1024-----516   12288
           |       |                                                       |
     1048576      13----1152-----768---10240---20480---65536------18---32800
           |
          19---65792---18432----9216---33280--655360--266240-2097152-1048584

Prog

(PARI) See Links section.

Crossrefs

See A336349 for a similar sequence.

Sequence in context: A269382 A253886 A253885 * A140692 A048640 A242353

Adjacent sequences: A336347 A336348 A336349 * A336351 A336352 A336353

Keyword

nonn,look,base

Author

Rémy Sigrist, Jul 19 2020

Status

approved