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%I #11 Aug 18 2020 04:27:39
%S 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 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 0,6,7,6,8,7,8,7,1,7,4,7,8,8,7,4,2,0,2
%N Square spiral constructed by greedy algorithm, so that each diagonal and antidiagonal contains distinct numbers.
%C This sequence is a variant of A308896; here we walk a bishop, there a rook.
%C 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 Rémy Sigrist, <a href="/A337108/b337108.txt">Table of n, a(n) for n = 0..10200</a>
%H Rémy Sigrist, <a href="/A337108/a337108.png">Colored representation of the spiral for -512 <= x, y <= 512</a>
%H 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 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 Rémy Sigrist, <a href="/A337108/a337108.gp.txt">PARI program for A337108</a>
%F a(n) = 0 iff n belongs to A035608.
%e The spiral begins:
%e 7----7----6----7----1----7----4----7----7
%e | |
%e 6 5----5----4----1----5----5----5 6
%e | | | |
%e 3 4 3----3----2----3----3 4 3
%e | | | | | |
%e 6 5 2 1----1----1 2 4 6
%e | | | | | | | |
%e 0 0 0 0 0----0 0 0 0
%e | | | | | | |
%e 6 3 2 2----1----2----2 3 6
%e | | | | |
%e 7 4 4----3----1----3----4----4 5
%e | | |
%e 6 6----5----5----1----6----5----6----6
%e |
%e 8----7----8----7----1----7----4----7----8
%o (PARI) See Links section.
%Y See A274641 and A308896 for similar sequences.
%Y Cf. A035608.
%K nonn
%O 0,7
%A _Rémy Sigrist_, Aug 16 2020