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A363247 a(0) = 0. a(n) = the smallest nonnegative integer, excluding a(n-1), not occurring in all occurrences of a(n-1)'s eight neighbors thus far in a square spiral.

%I A363247 #40 May 31 2023 22:35:54
%S A363247 0,1,2,3,4,1,5,2,4,5,3,6,0,7,1,8,0,9,2,8,6,4,7,8,10,0,11,1,10,2,11,4,
%T A363247 12,2,13,3,9,5,12,3,14,0,15,1,14,5,13,4,15,2,16,1,17,0,18,1,19,0,20,1,
%U A363247 21,0,22,1,23,0,24,1,25,0,26,1,27,0,28,2,17,3
%N A363247 a(0) = 0. a(n) = the smallest nonnegative integer, excluding a(n-1), not occurring in all occurrences of a(n-1)'s eight neighbors thus far in a square spiral.
%H A363247 Scott R. Shannon, <a href="/A363247/b363247.txt">Table of n, a(n) for n = 0..10000</a>
%H A363247 Scott R. Shannon, <a href="/A363247/a363247.png">Image of the first 10000 terms on the square spiral</a>. The value colors are scaled across the spectrum from red to violet to show their relative size. Zoom in to see the numbers.
%e A363247 The spiral begins:
%e A363247   0---8---1---7---0
%e A363247   |               |
%e A363247   9   4---3---2   6
%e A363247   |   |       |   |
%e A363247   2   1   0---1   3   .
%e A363247   |   |           |   .
%e A363247   8   5---2---4---5   .
%e A363247   |                   |
%e A363247   6---4---7---8---10--0
%e A363247 a(0) = 0
%e A363247 a(1) = 1. Smallest integer that's not a neighbor to every 0 = 1.
%e A363247 a(2) = 2. Smallest integer that's not a neighbor to every 1 = 2.
%e A363247 a(3) = 3. Smallest integer that's not a neighbor to every 2 = 3.
%e A363247 a(4) = 4. Smallest integer that's not a neighbor to every 3 = 4.
%e A363247 a(5) = 1. Smallest integer that's not a neighbor to every 4 = 1.
%Y A363247 Cf. A275609, A358048.
%K A363247 nonn
%O A363247 0,3
%A A363247 _Gavin Lupo_, May 24 2023