A211021 Numbers n such that a new circle appears in the structure of A211000.

11, 13, 15, 34, 41, 65, 71, 75, 275, 281, 285, 437, 443, 561, 567, 575, 581, 591, 597, 605, 611, 617, 647, 663, 957, 971, 1025, 1037, 1043, 1055, 1067, 1073, 1091, 1113, 1153, 1165, 1711, 2243, 3377, 3467, 5809, 7937, 7955, 8021, 8043, 8057, 8063

Offset: 1

Author

Omar E. Pol, Mar 31 2012

Keywords

• nonn

Comments

Also where the positive records occur in A211020.

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.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..250
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A187210, A211000-A211003, A211010, A211011, A211020, A211022-A211024.

Programs

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}]]];
Flatten[Position[Differences[A211020[1000]],1]] (* Paolo Xausa, Jan 16 2023 *)