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 A308629 #28 Jun 13 2019 11:19:28
%S A308629 1,2,4,4,5,6,8,6,10,10,9,12,13,11,15,15,15,17,18,17,20,21,19,23,24,22,
%T A308629 26,26,24,29,29,27,32,31,30,35,33,32,38,36,35,41,38,38,44,41,39,48,43,
%U A308629 42,51,45,45,53,48,47,56,51,50,59,53,52,62,56,55,65,58
%N A308629 Lengths between nodes on a square spiral, such that the n-th node is closer to the (n-2)-th node than to the (n-1)-th node.
%C A308629 Consider a square spiral which begins at the origin and spirals counterclockwise. We define (0, 0) and (1, 0) as the first two nodes. From here, we wish to find the first point along the spiral path which is closer to (0, 0) than to (1, 0). This point would be (0, 1), which is 2 unit lengths away from the previous node. Hence 2 is the first number in our sequence. Likewise, 4 is the next number, as we have to travel 4 unit lengths along the square spiral to reach a point closer to (1, 0) than to (0, 1), and so on.
%C A308629 Based on an empirical observation of the first several terms, I conjecture that lim_{n->infinity} a(n)/n = 8/9.
%H A308629 Brian Barsotti, <a href="/A308629/a308629.png">Square Spiral Illustration</a>
%H A308629 Rémy Sigrist, <a href="/A308629/a308629_1.png">Scatterplot of the first 1000 nodes</a>
%H A308629 Rémy Sigrist, <a href="/A308629/a308629.gp.txt">PARI program for A308629</a>
%o A308629 (PARI) See Links section.
%K A308629 nonn
%O A308629 1,2
%A A308629 _Brian Barsotti_, Jun 11 2019
%E A308629 More terms from _Rémy Sigrist_, Jun 12 2019