This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A293729 #18 Jul 29 2023 05:06:57 %S A293729 0,1,1,0,0,1,1,0,0,1,-3,-3,-2,-2,-4,-4,-1,-1,-5,-5,-2,-3,-3,-2,-2,-3, %T A293729 -3,-2,-2,-3,1,1,0,0,2,2,-1,-1,3,3,-1,-1,0,0,-2,-5,-4,-4,-5,-5,-4,-4, %U A293729 -5,-1,-1,-6,-6,-3,-4,-4,-3,-3,-4,-4,-1,-2,-2,-1,-1,-2 %N A293729 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) = X-coordinate of P(n). %C A293729 See A293730 for the corresponding Y-coordinates. %C A293729 The following diagram depicts the angle t cited in the name: %C A293729 . P(n)* . %C A293729 . | t . %C A293729 . | . %C A293729 . | . %C A293729 . |. %C A293729 . P(n-1)* %C A293729 . / %C A293729 . / %C A293729 . P(n-2)* %C A293729 This sequence has building features in common with A293539. %C A293729 This sequence has fractal features: the representation of the first 200,000 points of the sequence seems chaotic; however, many portions of the sequence are duplicated elsewhere, possibly after rotating them by an integral multiple of 90 degrees (see representation of such duplication in Links section). %C A293729 The variant P' of this sequence where we minimize the angle t in case of a tie has simple patterns that repeat themselves in a square spiral (see representation of P' in Links section). %H A293729 Rémy Sigrist, <a href="/A293729/b293729.txt">Table of n, a(n) for n = 1..10000</a> %H A293729 Rémy Sigrist, <a href="/A293729/a293729.png">Representation of P(n) for n=1..100, with lines joining consecutive points</a> %H A293729 Rémy Sigrist, <a href="/A293729/a293729_1.png">Colorized representation of P(n) for n=1..200000</a> %H A293729 Rémy Sigrist, <a href="/A293729/a293729_2.png">Representation of P(n) with duplicate pattern highlighted</a> %H A293729 Rémy Sigrist, <a href="/A293729/a293729_3.png">Representation of the variant P'(n) for n=1..10000</a> %H A293729 Rémy Sigrist, <a href="/A293729/a293729.gp.txt">PARI program for A293729</a> %e A293729 See representation of first points in Links section. %Y A293729 Cf. A293539, A293730. %K A293729 sign,look %O A293729 1,11 %A A293729 _Rémy Sigrist_, Oct 15 2017