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

Author

Omar E. Pol, Apr 14 2012

Keywords

• nonn

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.

Examples

			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
		

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

Crossrefs

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

Programs

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 *)