cp's OEIS Frontend

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.

%I A358021 #12 Oct 27 2022 10:13:58
%S A358021 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,
%T A358021 57,18,25,36,27,48,26,34,56,47,28,50,49,58,60,29,35,67,38,40,77,59,37,
%U A358021 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
%N 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.
%C A358021 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.
%e A358021 The square spiral begins:
%e A358021                        .
%e A358021                        .
%e A358021   13--20--11--55--10  36
%e A358021    |               |   |
%e A358021   66   4---3---2  44  25
%e A358021    |   |       |   |   |
%e A358021   12   5   0---1  30  18
%e A358021    |   |           |   |
%e A358021   33   6---7---8---9  57
%e A358021    |                   |
%e A358021   14--22--15--23--16--24
%e A358021 .
%e A358021 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.
%Y A358021 Cf. A358048, A344325, A344367, A354111, A343530.
%K A358021 nonn,base,fini
%O A358021 0,3
%A A358021 _Scott R. Shannon_ and _Eric Angelini_, Oct 24 2022