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A274641 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).

%I A274641 #41 Aug 16 2020 12:41:36
%S A274641 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 A274641 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 A274641 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 A274641 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 A274641 See A274640 for further information.
%C A274641 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 A274641 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 A274641 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 A274641 Rémy Sigrist, <a href="/A274641/a274641.png">Colored representation of the spiral for -500 <= x, y <= 500</a>
%H A274641 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 A274641 From _Jon E. Schoenfield_, Dec 26 2016: (Start)
%e A274641 The spiral begins:
%e A274641 .
%e A274641    8--15---1---3---6--13--10--11---0---4---7
%e A274641    |                                       |
%e A274641   16   7--14--13--12--11---8---9---5---6   2
%e A274641    |   |                               |   |
%e A274641    0   1   3--10---9---2---7---6---8  12  14
%e A274641    |   |   |                       |   |   |
%e A274641    7   8   6   2---4---5---0---1   3  11  10
%e A274641    |   |   |   |               |   |   |   |
%e A274641   10  11   7   0   1---3---2   5   4   9  13
%e A274641    |   |   |   |   |       |   |   |   |   |
%e A274641   14   6   5   4   2   0---1   3   7  10  11
%e A274641    |   |   |   |   |           |   |   |   |
%e A274641   13   9   2   1   3---4---5---0   6   8  12
%e A274641    |   |   |   |                   |   |   |
%e A274641    6  10   8   5---0---1---3---4---2   7   9
%e A274641    |   |   |                           |   |
%e A274641    3  12   4---6---7---8---9--10--11---5   0
%e A274641    |   |                                   |
%e A274641   11  13---9---8---5--12---4---2--14--15---6
%e A274641    |
%e A274641    9--14---0--11--15---7--13--12--10--17--16
%e A274641 .
%e A274641 (End)
%Y A274641 Cf. A274640 (if start with 1 at center), A324481 (position of first n).
%Y A274641 For the eight spokes see A324774-A324781.
%K A274641 nonn
%O A274641 0,3
%A A274641 _N. J. A. Sloane_, Jul 09 2016, based on the entry A274640 from _Zak Seidov_ and _Kerry Mitchell_, Jun 30 2016