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

1,1

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

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 *)

Crossrefs

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

Sequence in context: A099481 A254412 A215778 * A364003 A214746 A341162

Adjacent sequences: A211018 A211019 A211020 * A211022 A211023 A211024

Keyword

nonn

Author

Omar E. Pol, Mar 31 2012

Status

approved