A211011 Value on the axis "y" of the endpoint of the structure (or curve) of A211000 at n-th stage.

0, 1, 0, -1, -2, -3, -4, -5, -6, -7, -6, -5, -4, -3, -2, -1, -2, -3, -4, -5, -6, -7, -6, -5, -4, -3, -4, -5, -4, -3, -2, -1, 0, 1, 0, -1, 0, 1, 2, 3, 2, 1, 0, -1, -2, -3, -2, -1, 0, 1, 0, -1, 0, 1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 6, 7, 8, 9, 8, 7, 6, 5

Offset: 0

Author

Omar E. Pol, Mar 30 2012

Keywords

• sign
• look

Comments

For n >= 13 the 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. Note that all odd numbers > 1 are located on the main axis of the structure. For the number of circles after n-th stage see A211020. For the values on the axis "x" see A211010. For the values for the n-th prime see A211023.

Examples

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..9999
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Bisection of A211000.

Cf. A187210, A210838, A210841, A211001-A211003, A211010, A211020-A211024.

Programs

Mathematica

A211011[nmax_]:=Module[{ep={0,0},angle=3/4Pi,turn=Pi/2},Join[{0},Table[If[!PrimeQ[n],If[n>5&&PrimeQ[n-1],turn*=-1];angle-=turn];Last[ep=AngleVector[ep,{Sqrt[2],angle}]],{n,0,nmax-1}]]];
A211011[100] (* Paolo Xausa, Jan 14 2023 *)

Formula

abs(a(n)-a(n+1)) = 1.