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%I #66 Jan 14 2023 22:00:10
%S 0,1,0,-1,-2,-3,-4,-5,-6,-7,-6,-5,-4,-3,-2,-1,-2,-3,-4,-5,-6,-7,-6,-5,
%T -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,
%U -1,0,1,2,3,2,1,2,3,4,5,6,7,6,5,6,7,8,9,8,7,6,5
%N Value on the axis "y" of the endpoint of the structure (or curve) of A211000 at n-th stage.
%C 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.
%H Paolo Xausa, <a href="/A211011/b211011.txt">Table of n, a(n) for n = 0..9999</a>
%H N. J. A. Sloane, <a href="http://oeis.org/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F abs(a(n)-a(n+1)) = 1.
%e Consider the illustration of the structure of A211000:
%e ------------------------------------------------------
%e . After After After
%e . y 9 stages 10 stages 11 stages
%e ------------------------------------------------------
%e . 2
%e . 1 1 1 1
%e . 0 0 2 0 2 0 2
%e . -1 3 3 3
%e . -2 4 4 4
%e . -3 5 5 5
%e . -4 6 6 6
%e . -5 7 7 11
%e . -6 8 10 8 10 8
%e . -7 9 9 9
%e . -8
%e We can see that a(7) = a(11) = -5.
%t 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}]]];
%t A211011[100] (* _Paolo Xausa_, Jan 14 2023 *)
%Y Bisection of A211000.
%Y Cf. A187210, A210838, A210841, A211001-A211003, A211010, A211020-A211024.
%K sign,look
%O 0,5
%A _Omar E. Pol_, Mar 30 2012
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