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A211023
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Value on the axis "y" of the endpoint of the structure of A211000 if the index is prime.
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7
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0, -1, -3, -5, -5, -3, -3, -5, -5, -3, -1, 1, 1, -1, -1, 1, 3, 5, 7, 7, 5, 3, 3, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 3, 1, -1, -3, -5, -5, -3, -1, 1, 3, 5, 5, 3, 3, 3, 3, 5, 5, 3, 1, -1, -3, -5, -7, -9, -11, -11, -9, -7, -5, -5, -7, -7, -5, -3, -1, 1, 1, -1, -1, 1, 3
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OFFSET
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1,3
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COMMENTS
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a(n) is also the value on the axis "y" of the n-th inflection point in the structure of A211000.
The behavior seems to be as modular arithmetic but in a growing structure. The structure of A211000 looks like essentially a column of tangent circles of radius 1. The structure of A211000 arises from the prime numbers A000040.
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LINKS
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FORMULA
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MATHEMATICA
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A211023[upto_]:=Module[{ep={0, 0}, angle=3/4Pi, turn=Pi/2}, Table[If[!PrimeQ[n], If[n>5&&PrimeQ[n-1], turn*=-1]; angle-=turn]; ep=AngleVector[ep, {Sqrt[2], angle}]; If[PrimeQ[n+1], Last[ep], Nothing], {n, 0, upto-1}]];
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CROSSREFS
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Cf. A187210, A211000, A211001, A211002, A211003, A211010, A211011, A211020, A211021, A211022, A211024.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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