OFFSET
0,5
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.
LINKS
FORMULA
abs(a(n)-a(n+1)) = 1.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
sign,look
AUTHOR
Omar E. Pol, Mar 30 2012
STATUS
approved