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A098021
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Irrational rotation of the square root of 2 as an implicit sequence with an uneven Cantor cartoon.
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4
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5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 63, 68, 75, 80, 87, 92, 99, 104, 109, 116, 121, 128, 133, 138, 145, 150, 157, 162, 169, 174, 179, 186, 191, 198, 203, 208, 215, 220, 227, 232, 237, 244, 249, 256, 261, 268, 273, 278, 285, 290, 297, 302, 307, 314, 319, 326
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: A098021 is the sequence of positions of 0 in the zero-one sequence [nr+2r]-[nr]-[2r], where r=sqrt(2) and [ ]=floor; see A187967. [From Clark Kimberling, Mar 17 2011 ]
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FORMULA
| f(n)= n*sqrt(2) (mod 1), g(x)=-1 if 0<=x<=1/3, g(x)=0 if 1/3<x<=2/3 & g(x)=1 if 1/3<x<=1, a(n)=n If f[n+2]-2*f[n+1]+f[n]-g[f[n+1]]=0.
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MATHEMATICA
| f[n_] := Mod[Sqrt[2]*n, 1]; g[x_] := -1 /; 0 <= x <= 1/3; g[x_] := 0 /; 1/3 < x <= 2/3; g[x_] := 1 /; 2/3 < x <= 1; a = Delete[ Union[ Table[ If [Simplify[f[n + 2] - 2*f[n + 1] + f[n]] - g[f[n + 1]] == 0, n, 0], {n, 330}]], 1]
ListPlot[a, PlotJoined-> True]
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CROSSREFS
| Cf. A187967.
Sequence in context: A140138 A190492 A190562 * A098022 A190550 A071978
Adjacent sequences: A098018 A098019 A098020 * A098022 A098023 A098024
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2004
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 25 2004
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