A358129 Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its four orthogonally adjacent neighbors.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 11, 22, 10, 24, 13, 25, 16, 23, 14, 26, 15, 28, 17, 30, 12, 33, 18, 27, 19, 32, 40, 29, 31, 42, 36, 21, 34, 50, 41, 35, 44, 37, 45, 38, 46, 39, 47, 53, 48, 55, 49, 52, 43, 56, 70, 51, 60, 57, 61, 54, 63, 58, 64, 59, 66, 71, 62, 73, 68, 72, 65, 74, 69, 77, 90, 75

Offset: 0

Author

Scott R. Shannon and Eric Angelini, Oct 30 2022

Keywords

• nonn
• base

Comments

This sequence is similar to A358021 except here only the four orthogonally adjacent neighbors are considered. It is unknown if the sequence eventually terminates; if it does, it does so after more than 1.5 million terms. In that range on numerous occasions the only available number is one containing only the digit 7. For example a(862833) = 7...7, where there are forty-nine 7's.

Examples

			The square spiral begins:
                       .
                       .
  25--13--24--10--22  19
   |               |   |
  16   4---3---2  11  27
   |   |       |   |   |
  23   5   0---1  20  18
   |   |           |   |
  14   6---7---8---9  33
   |                   |
  26--15--28--17--30--12
.
a(10) = 20 as when the tenth cell is filled its two orthogonal neighbors use the digits 1 and 9, and 20 is the smallest unused number that does not contain either of those digits.
		

Links

• Scott R. Shannon, Image of the first 500000 terms. The values are scaled across the spectrum from red to violet, with the value ranges increasing towards the violet end to give more color weighting to the larger numbers.

Crossrefs

Cf. A358021, A358048, A344325, A344367, A354111, A343530.