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%I #41 Aug 16 2020 12:41:36
%S 0,1,2,3,1,2,3,4,5,0,3,5,1,0,5,4,2,0,4,1,5,0,1,3,4,2,6,7,4,3,8,6,7,2,
%T 9,10,3,6,7,5,2,8,4,6,7,8,9,10,11,5,7,8,10,9,11,12,6,5,9,8,11,12,13,
%U 14,7,1,8,11,6,9,10,12,13,9,8,5,12,4,2,14,15,6,0,9,12,11,13,10,14,2,7,4,0,11,10,13,6,3,1,15,8,16,0,7,10
%N Counterclockwise square spiral constructed by greedy algorithm, so that each row, column, and diagonal contains distinct numbers. Start with 0 (so in this version a(n) = A274640(n) - 1).
%C See A274640 for further information.
%C Presumably every row, column, and diagonal is a permutation of the natural numbers, but is there a proof? - _N. J. A. Sloane_, Jul 10 2016
%H N. J. A. Sloane, <a href="/A274641/b274641.txt">Table of n, a(n) for n = 0..20000</a> [Based on Alois Heinz's b-file for A274640]
%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.
%H Rémy Sigrist, <a href="/A274641/a274641.png">Colored representation of the spiral for -500 <= x, y <= 500</a>
%H N. J. A. Sloane, <a href="/A195264/a195264.pdf">Confessions of a Sequence Addict (AofA2017)</a>, slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
%e From _Jon E. Schoenfield_, Dec 26 2016: (Start)
%e The spiral begins:
%e .
%e 8--15---1---3---6--13--10--11---0---4---7
%e | |
%e 16 7--14--13--12--11---8---9---5---6 2
%e | | | |
%e 0 1 3--10---9---2---7---6---8 12 14
%e | | | | | |
%e 7 8 6 2---4---5---0---1 3 11 10
%e | | | | | | | |
%e 10 11 7 0 1---3---2 5 4 9 13
%e | | | | | | | | | |
%e 14 6 5 4 2 0---1 3 7 10 11
%e | | | | | | | | |
%e 13 9 2 1 3---4---5---0 6 8 12
%e | | | | | | |
%e 6 10 8 5---0---1---3---4---2 7 9
%e | | | | |
%e 3 12 4---6---7---8---9--10--11---5 0
%e | | |
%e 11 13---9---8---5--12---4---2--14--15---6
%e |
%e 9--14---0--11--15---7--13--12--10--17--16
%e .
%e (End)
%Y Cf. A274640 (if start with 1 at center), A324481 (position of first n).
%Y For the eight spokes see A324774-A324781.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jul 09 2016, based on the entry A274640 from _Zak Seidov_ and _Kerry Mitchell_, Jun 30 2016
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