A396725 Fill the square spiral the greedy way with distinct nonnegative integers such that not two points of the form (x, y, z) where 2^z appears in the binary expansion of the value at cell (x, y) are a knight's move apart.

0, 1, 2, 3, 16, 8, 4, 32, 48, 33, 64, 128, 12, 132, 256, 129, 80, 40, 20, 10, 5, 66, 68, 512, 272, 9, 1024, 65, 72, 516, 74, 640, 264, 2048, 320, 11, 336, 41, 1040, 136, 17, 514, 21, 34, 69, 130, 260, 520, 1088, 35, 1280, 160, 1026, 513, 288, 2049, 42, 576

Offset

0,3

Comments

A 3-dimensional variant of A394166 and A396603.

Two points (x, y, z) and (x', y', z') are a knight's move apart iff {abs(x-x'), abs(y-y'), abs(z-z')} = {0, 1, 2}.

For any k >= 0, the first term >= 2^k is a power of 2.

Links

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

Rémy Sigrist, Colored representation of the spiral for |x|, |y| <= 1000

Rémy Sigrist, PARI program

Example

The spiral begins:
      82--131-4112-2176-5376-2065--266--133-4098-2064---18
       |                                                 |
     161 1104--137-4352-2560--304--528-4096--576---42  529
       |    |                                       |    |
    2112  168  336---11--320-2048--264--640---74 2049  258
       |    |    |                             |    |    |
     169 1296   41   80--129--256--132---12  516  288  517
       |    |    |    |                   |    |    |    |
    8208  138 1040   40   16----3----2  128   72  513 5120
       |    |    |    |    |         |    |    |    |    |
     672   84  136   20    8    0----1   64   65 1026 8192
       |    |    |    |    |              |    |    |    |
     273  162   17   10    4---32---48---33 1024  160 1028
       |    |    |    |                        |    |    |
     546   81  514    5---66---68--512--272----9 1280  648
       |    |    |                                  |    |
     277  170   21---34---69--130--260--520-1088---35 1360
       |    |                                            |
     554   85--522--257-2050--261--544--276--552-1344---43
       |
     321--642--324--650--325--674--337--680--340-2056-4160

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A394166, A396603.

Sequence in context: A372793 A363920 A074270 * A254522 A007120 A092973

Adjacent sequences: A396722 A396723 A396724 * A396726 A396727 A396733

Keyword

nonn,base

Author

Rémy Sigrist, Jun 03 2026

Status

approved