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 A211020 #60 Jan 14 2023 10:51:34
%S A211020 0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T A211020 4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,
%U A211020 6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A211020 Number of circles in the structure of A211000 after n-th stage.
%C A211020 For n >= 13 the structure looks like essentially a column of tangent circles of radius 1. The circles are centered on a straight line which is parallel to the axis "y". The structure arises from the prime numbers A000040.
%H A211020 Paolo Xausa, <a href="/A211020/b211020.txt">Table of n, a(n) for n = 0..9999</a>
%H A211020 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 A211020 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%e A211020 From _Paolo Xausa_, Jan 09 2023: (Start)
%e A211020 In the following diagrams the A211000 structure is shown at the end of the n-th stage (Q-toothpicks are depicted as straight lines instead of circle arcs; circles are depicted as rhombi).
%e A211020 n 0 5 11 13 15 34 41 65
%e A211020 a(n) 0 0 1 2 3 4 5 6
%e A211020 .
%e A211020 /\
%e A211020 \/
%e A211020 \
%e A211020 /
%e A211020 /\ /\
%e A211020 \/ \/
%e A211020 /\ /\ /\ /\ /\/\ /\/\ /\/\
%e A211020 \ \ \ \ \/ \/ \/
%e A211020 \ \ \ /\ /\ /\ /\
%e A211020 / / / \/ \/ \/ \/
%e A211020 / /\ /\ /\ /\ /\
%e A211020 \ \/ \/ \/ \/ \/
%e A211020 /\ /\ /\ /\ /\ /\
%e A211020 \/ \/ \/ \/ \/ \/
%e A211020 (End)
%t A211020 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 A211020 A211020[100] (* _Paolo Xausa_, Jan 06 2023 *)
%Y A211020 Cf. A187210, A210838, A210841.
%Y A211020 Cf. A211000, A211001, A211002, A211003.
%Y A211020 Cf. A211010, A211011, A211021, A211022, A211023.
%Y A211020 Cf. A355478, A357434.
%K A211020 nonn
%O A211020 0,14
%A A211020 _Omar E. Pol_, Mar 30 2012
%E A211020 Offset changed to 0 and a(0) prepended by _Paolo Xausa_, Jan 06 2023