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Let P be the sequence of distinct lattice points defined by the following rules: P(1) = (0,0), P(2) = (1,0), and for any n > 2, P(n) is the closest lattice point at integer distance to P(n-1) such that the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)), say t, satisfies 0 < t < Pi, and in case of a tie, maximize the angle t; a(n) = Y-coordinate of P(n).
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%I #7 Oct 16 2017 09:54:20

%S 0,0,1,1,-1,-1,2,2,-2,-2,1,0,0,1,1,0,0,1,1,0,4,4,3,3,5,5,2,2,6,6,3,4,

%T 4,3,3,4,4,3,3,4,7,6,6,7,7,3,3,4,4,2,2,5,5,2,5,5,4,8,8,7,7,9,9,6,10,

%U 10,9,9,11,11,8,8,12,12,9,10,10,9,9,10,10,9

%N Let P be the sequence of distinct lattice points defined by the following rules: P(1) = (0,0), P(2) = (1,0), and for any n > 2, P(n) is the closest lattice point at integer distance to P(n-1) such that the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)), say t, satisfies 0 < t < Pi, and in case of a tie, maximize the angle t; a(n) = Y-coordinate of P(n).

%C See A293729 for the corresponding X-coordinates, and additional comments.

%H Rémy Sigrist, <a href="/A293730/b293730.txt">Table of n, a(n) for n = 1..10000</a>

%Y Cf. A293729.

%K sign

%O 1,7

%A _Rémy Sigrist_, Oct 15 2017