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

0,2

Comments

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

Links

Table of n, a(n) for n=0..70.

Eric Angelini, More inspiring spirals (1), personal blog CinquanteSignes.blogspot.com, Oct. 23, 2022.

Gleb Ivanov, Python program.

Example

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.

Crossrefs

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

Sequence in context: A299970 A342143 A344331 * A037997 A044850 A282150

Adjacent sequences: A358045 A358046 A358047 * A358049 A358050 A358051

Keyword

nonn,base

Author

Eric Angelini and Scott R. Shannon, Oct 27 2022

Status

approved