A358021 Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its eight surrounding neighbors.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 30, 44, 10, 55, 11, 20, 13, 66, 12, 33, 14, 22, 15, 23, 16, 24, 57, 18, 25, 36, 27, 48, 26, 34, 56, 47, 28, 50, 49, 58, 60, 29, 35, 67, 38, 40, 77, 59, 37, 19, 68, 39, 46, 70, 41, 80, 31, 65, 90, 17, 88, 21, 93, 51, 43, 69, 71, 32, 111, 73, 81, 64, 72, 89, 42, 91

Offset

0,3

Comments

The sequence is finite; after a(264) = 177 the square at coordinate (-8,-1) relative to the starting square is reached which has the four neighbors 177, 409, 256, 308. These numbers include all digits 0 to 9 so the next term does not exist. The largest used number is a(241) = 7777 while smallest unused number is 120.

Links

Table of n, a(n) for n=0..75.

Example

The square spiral begins:
                       .
                       .
  13--20--11--55--10  36
   |               |   |
  66   4---3---2  44  25
   |   |       |   |   |
  12   5   0---1  30  18
   |   |           |   |
  33   6---7---8---9  57
   |                   |
  14--22--15--23--16--24
.
a(10) = 30 as when the tenth square is filled its surrounding neighbors are 1, 2, 8, 9, and 30 is the smallest unused number that does not contain those digits.

Crossrefs

Cf. A358048, A344325, A344367, A354111, A343530.

Sequence in context: A072941 A225655 A024658 * A349864 A004849 A261279

Adjacent sequences: A358018 A358019 A358020 * A358022 A358023 A358024

Keyword

nonn,base,fini

Author

Scott R. Shannon and Eric Angelini, Oct 24 2022

Status

approved