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A211020 Number of circles in the structure of A211000 after n-th stage. 14
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, 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, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,14
COMMENTS
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.
LINKS
EXAMPLE
From Paolo Xausa, Jan 09 2023: (Start)
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).
n 0 5 11 13 15 34 41 65
a(n) 0 0 1 2 3 4 5 6
.
/\
\/
\
/
/\ /\
\/ \/
/\ /\ /\ /\ /\/\ /\/\ /\/\
\ \ \ \ \/ \/ \/
\ \ \ /\ /\ /\ /\
/ / / \/ \/ \/ \/
/ /\ /\ /\ /\ /\
\ \/ \/ \/ \/ \/
/\ /\ /\ /\ /\ /\
\/ \/ \/ \/ \/ \/
(End)
MATHEMATICA
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}]]];
A211020[100] (* Paolo Xausa, Jan 06 2023 *)
CROSSREFS
Sequence in context: A165024 A300402 A326166 * A157639 A010096 A230864
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 30 2012
EXTENSIONS
Offset changed to 0 and a(0) prepended by Paolo Xausa, Jan 06 2023
STATUS
approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)