cp's OEIS Frontend

A293772 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) = X-coordinate of P(n).

%I A293772 #14 Oct 16 2017 09:53:26
%S A293772 0,1,1,0,-1,-1,0,2,2,1,0,-1,-2,-2,-1,1,3,3,2,1,-1,-2,-3,-3,-2,-1,1,2,
%T A293772 4,4,3,2,0,-3,-4,-4,-3,-2,-1,1,2,3,4,4,3,1,-2,-5,-5,-4,-1,0,1,3,4,5,5,
%U A293772 4,3,1,-2,-3,-6,-6,-5,-3,0,1,2,3,4,5,5,4,2,-1,-4
%N A293772 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) = X-coordinate of P(n).
%C A293772 See A293773 for the corresponding Y-coordinates.
%C A293772 The following diagram depicts the angle t cited in the name:
%C A293772 .      P(n)*    .
%C A293772 .          | t .
%C A293772 .          |  .
%C A293772 .          | .
%C A293772 .          |.
%C A293772 .    P(n-1)*
%C A293772 .         /
%C A293772 .        /
%C A293772 . P(n-2)*
%C A293772 This sequence has building features in common with A293680.
%C A293772 The representation of the first thousands points of the sequence shows a spiral.
%H A293772 Rémy Sigrist, <a href="/A293772/b293772.txt">Table of n, a(n) for n = 1..10000</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772.png">Representation of P(n) for n=1..100, with lines joining consecutive points</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772_1.png">Representation of P(n) for n=1..1000, with lines joining consecutive points</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772_2.png">Representation of P(n) for n=1..100000</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772_3.png">Scatterplot of a(n) for n=1..100000</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772_4.png">Scatterplot of (n, a(n)) when A293773(n) >= 0 and n <= 100000</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772_5.png">Scatterplot of (n, a(n)) when A293773(n) < 0 and n <= 100000</a>
%H A293772 Rémy Sigrist, <a href="/A293772/a293772.gp.txt">PARI program for A293772</a>
%e A293772 See representation of first points in Links section.
%o A293772 (PARI) See Links section.
%Y A293772 Cf. A293680, A293773.
%K A293772 sign,look
%O A293772 1,8
%A A293772 _Rémy Sigrist_, Oct 16 2017