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A337108 Square spiral constructed by greedy algorithm, so that each diagonal and antidiagonal contains distinct numbers.

%I A337108 #14 Mar 19 2025 18:17:35
%S A337108 0,0,1,1,1,0,2,1,2,2,0,2,3,3,2,3,3,2,0,2,4,3,1,3,4,4,3,0,4,4,5,5,5,1,
%T A337108 4,5,5,4,5,0,3,4,6,5,5,1,6,5,6,6,5,6,0,6,3,6,7,7,4,7,1,7,6,7,7,6,3,6,
%U A337108 0,6,7,6,8,7,8,7,1,7,4,7,8,8,7,4,2,0,2
%N A337108 Square spiral constructed by greedy algorithm, so that each diagonal and antidiagonal contains distinct numbers.
%C A337108 This sequence is a variant of A308896; here we walk a bishop, there a rook.
%C A337108 Visually, we have a superposition of two images that we can separate by considering the parity of the x and y coordinates (see illustrations in Links section).
%H A337108 Rémy Sigrist, <a href="/A337108/b337108.txt">Table of n, a(n) for n = 0..10200</a>
%H A337108 Rémy Sigrist, <a href="/A337108/a337108.png">Colored representation of the spiral for -512 <= x, y <= 512</a>
%H A337108 Rémy Sigrist, <a href="/A337108/a337108_1.png">Colored representation of the spiral for -512 <= x, y <= 512 and x any y have the same parity</a>
%H A337108 Rémy Sigrist, <a href="/A337108/a337108_2.png">Colored representation of the spiral for -512 <= x, y <= 512 and x and y have different parity</a>
%H A337108 Rémy Sigrist, <a href="/A337108/a337108.gp.txt">PARI program for A337108</a>
%F A337108 a(n) = 0 iff n belongs to A035608.
%e A337108 The spiral begins:
%e A337108         7----7----6----7----1----7----4----7----7
%e A337108         |                                       |
%e A337108         6    5----5----4----1----5----5----5    6
%e A337108         |    |                             |    |
%e A337108         3    4    3----3----2----3----3    4    3
%e A337108         |    |    |                   |    |    |
%e A337108         6    5    2    1----1----1    2    4    6
%e A337108         |    |    |    |         |    |    |    |
%e A337108         0    0    0    0    0----0    0    0    0
%e A337108         |    |    |    |              |    |    |
%e A337108         6    3    2    2----1----2----2    3    6
%e A337108         |    |    |                        |    |
%e A337108         7    4    4----3----1----3----4----4    5
%e A337108         |    |                                  |
%e A337108         6    6----5----5----1----6----5----6----6
%e A337108         |
%e A337108         8----7----8----7----1----7----4----7----8
%o A337108 (PARI) \\ See Links section.
%Y A337108 See A274641 and A308896 for similar sequences.
%Y A337108 Cf. A035608.
%K A337108 nonn
%O A337108 0,7
%A A337108 _Rémy Sigrist_, Aug 16 2020