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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.

%I A358048 #17 Oct 27 2022 10:13:52
%S A358048 0,10,20,30,40,50,60,70,80,18,100,12,2,23,102,90,49,104,101,103,16,
%T A358048 105,106,107,78,8,81,1,21,22,24,25,26,29,19,9,39,91,14,11,13,15,17,31,
%U A358048 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
%N 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.
%C A358048 The sequence is conjectured to be a permutation of the nonnegative integers.
%H A358048 Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/10/more-inspiring-spirals-1.html">More inspiring spirals (1)</a>, personal blog CinquanteSignes.blogspot.com, Oct. 23, 2022.
%H A358048 Gleb Ivanov, <a href="/A358048/a358048.py.txt">Python program</a>.
%e A358048 The square spiral begins:
%e A358048                            .
%e A358048                            .
%e A358048    49--90--102---23---2   22
%e A358048    |                  |    |
%e A358048   104  40---30---20   12  21
%e A358048    |   |          |   |    |
%e A358048   101  50    0---10  100   1
%e A358048    |   |              |    |
%e A358048   103  60---70---80---18  81
%e A358048    |                       |
%e A358048    16--105--106--107--78---8
%e A358048 .
%e A358048 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.
%Y A358048 Cf. A358021, A344325, A344367, A354111, A343530.
%K A358048 nonn,base
%O A358048 0,2
%A A358048 _Eric Angelini_ and _Scott R. Shannon_, Oct 27 2022