A358048 Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that every number shares a digit with each of its eight surrounding neighbors.

0, 10, 20, 30, 40, 50, 60, 70, 80, 18, 100, 12, 2, 23, 102, 90, 49, 104, 101, 103, 16, 105, 106, 107, 78, 8, 81, 1, 21, 22, 24, 25, 26, 29, 19, 9, 39, 91, 14, 11, 13, 15, 17, 31, 41, 51, 71, 87, 28, 38, 48, 108, 61, 112, 27, 32, 34, 42, 52, 62, 69, 59, 79, 89, 83, 93, 94, 109, 110, 111, 113

Offset: 0

Author

Eric Angelini and Scott R. Shannon, Oct 27 2022

Keywords

• nonn
• base

Comments

The sequence is conjectured to be a permutation of the nonnegative integers.

Examples

			The square spiral begins:
                           .
                           .
   49--90--102---23---2   22
   |                  |    |
  104  40---30---20   12  21
   |   |          |   |    |
  101  50    0---10  100   1
   |   |              |    |
  103  60---70---80---18  81
   |                       |
   16--105--106--107--78---8
.
a(11) = 12 as when the eleventh square is filled its surrounding neighbors are 10, 20, 100, and 12 is the smallest unused number that shares a digit with each of these three numbers.
		

Links

• Eric Angelini, More inspiring spirals (1), personal blog CinquanteSignes.blogspot.com, Oct. 23, 2022.
• Gleb Ivanov, Python program.

Crossrefs

Cf. A358021, A344325, A344367, A354111, A343530.