%I #17 Oct 27 2022 10:13:52

%S 0,10,20,30,40,50,60,70,80,18,100,12,2,23,102,90,49,104,101,103,16,

%T 105,106,107,78,8,81,1,21,22,24,25,26,29,19,9,39,91,14,11,13,15,17,31,

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

%H 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 Gleb Ivanov, <a href="/A358048/a358048.py.txt">Python program</a>.

%e The square spiral begins:

%e .

%e .

%e 49--90--102---23---2 22

%e | | |

%e 104 40---30---20 12 21

%e | | | | |

%e 101 50 0---10 100 1

%e | | | |

%e 103 60---70---80---18 81

%e | |

%e 16--105--106--107--78---8

%e .

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

%K nonn,base

%O 0,2

%A _Eric Angelini_ and _Scott R. Shannon_, Oct 27 2022