A211024 Sum of all visible nodes in the structure of A211000 at n-th stage.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 59, 71, 79, 93, 105, 117, 121, 133, 141, 153, 165, 177, 181, 193, 201, 209, 213, 217, 221, 237, 253, 285, 318, 350, 354, 358, 362, 400, 439, 479, 483, 491, 499, 527, 543, 559, 563, 575, 583, 591, 595, 599, 603

Offset

0,3

Comments

First differs from A000217 at a(11). For n >= 13 the Q-toothpick structure of A211000 looks like essentially a column of tangent circles of radius 1. The structure arises from the prime numbers A000040. The behavior seems to be as modular arithmetic but in a growing structure.

Links

Paolo Xausa, Table of n, a(n) for n = 0..9999 (terms 0..4999 from Carole Dubois)

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

Example

Consider the illustration of the nodes in structure of A211000:
-----------------------------------------------------
After 9 stages    After 10 stages    After 11 stages
-----------------------------------------------------
.
.    1                 1                  1
.  0   2             0   2              0   2
.        3                 3                  3
.          4                 4                  4
.        5                 5                  5
.      6                 6                  6
.        7                 7                 11
.          8            10   8             10   8
.        9                 9                  9
.
----------------------------------------------------
We can see that:
a(9)  = 0+1+2+3+4+5+6+7+8+9 = a(8)+9 = 45
a(10) = 0+1+2+3+4+5+6+7+8+9+10 = a(9)+10 = 55
a(11) = 0+1+2+3+4+5+6+8+9+10+11 = a(10)-7+11 = 59

Mathematica

A211024[nmax_]:=Module[{ep={0, 0}, node=Association[], angle=3/4Pi, turn=Pi/2}, Join[{0}, Table[If[!PrimeQ[n], If[n>5&&PrimeQ[n-1], turn*=-1]; angle-=turn]; ep=AngleVector[ep, {Sqrt[2], angle}]; node[ep]=n+1; Total[node], {n, 0, nmax-1}]]];
A211024[100] (* Paolo Xausa, Jan 16 2023 *)

Crossrefs

Cf. A000217, A187210, A211000-A211003, A211010, A211011, A211020-A211023.

Sequence in context: A033442 A105335 A130489 * A261422 A262544 A033443

Adjacent sequences: A211021 A211022 A211023 * A211025 A211026 A211027

Keyword

nonn

Author

Omar E. Pol, Apr 14 2012

Status

approved