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A293773 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 i < j < k, P(k) does not lie on the vector (P(i), P(j)), and for any n > 2, P(n) is the closest lattice point 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/2, and in case of a tie, minimize the angle t; a(n) = Y-coordinate of P(n). 2

%I #10 Oct 16 2017 12:54:56

%S 0,0,1,1,0,-1,-1,0,1,2,2,1,-1,-2,-2,-1,1,2,3,3,2,1,-1,-2,-3,-3,-2,-1,

%T 2,3,4,4,3,1,0,-1,-3,-4,-4,-3,-2,0,4,5,5,4,2,-1,-2,-3,-5,-5,-4,-1,1,4,

%U 5,6,6,5,3,2,-2,-3,-4,-5,-6,-6,-5,-3,0,6,7,7,6,4

%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 i < j < k, P(k) does not lie on the vector (P(i), P(j)), and for any n > 2, P(n) is the closest lattice point 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/2, and in case of a tie, minimize the angle t; a(n) = Y-coordinate of P(n).

%C See A293772 for the corresponding X-coordinates and additional comments.

%H Rémy Sigrist, <a href="/A293773/b293773.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A293773/a293773.png">Scatterplot of a(n) for n=1..100000</a>

%Y Cf. A293772.

%K sign,look

%O 1,10

%A _Rémy Sigrist_, Oct 16 2017

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