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 A211021 #26 Jan 16 2023 11:16:34
%S A211021 11,13,15,34,41,65,71,75,275,281,285,437,443,561,567,575,581,591,597,
%T A211021 605,611,617,647,663,957,971,1025,1037,1043,1055,1067,1073,1091,1113,
%U A211021 1153,1165,1711,2243,3377,3467,5809,7937,7955,8021,8043,8057,8063
%N A211021 Numbers n such that a new circle appears in the structure of A211000.
%C A211021 Also where the positive records occur in A211020.
%C A211021 The behavior seems to be as modular arithmetic but in a growing structure. The structure of A211000 looks like essentially a column of tangent circles of radius 1. The structure arises from the prime numbers A000040.
%H A211021 Paolo Xausa, <a href="/A211021/b211021.txt">Table of n, a(n) for n = 1..250</a>
%H A211021 N. J. A. Sloane, <a href="http://oeis.org/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H A211021 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%t A211021 A211020[nmax_]:=Module[{ep={{0, 0}}, angle=3/4Pi, turn=Pi/2, cells}, Join[{0}, Table[If[!PrimeQ[n], If[n>5&&PrimeQ[n-1], turn*=-1]; angle-=turn]; AppendTo[ep, AngleVector[Last[ep], {Sqrt[2], angle}]]; cells=FindCycle[Graph[MapApply[UndirectedEdge, Partition[ep, 2, 1]]], {4}, All]; CountDistinct[Map[Sort, Map[First, cells, {2}]]], {n, 0, nmax-1}]]];
%t A211021 Flatten[Position[Differences[A211020[1000]],1]] (* _Paolo Xausa_, Jan 16 2023 *)
%Y A211021 Cf. A187210, A211000-A211003, A211010, A211011, A211020, A211022-A211024.
%K A211021 nonn
%O A211021 1,1
%A A211021 _Omar E. Pol_, Mar 31 2012