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

Author

Rémy Sigrist, Jul 19 2020

Keywords

• nonn
• look
• base

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.

Examples

			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
		

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

Crossrefs

See A336349 for a similar sequence.

Programs

PARI

See Links section.