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A105459
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Decimal expansion of Hlawka's Schneckenkonstante K = -2.157782...
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1
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2, 1, 5, 7, 7, 8, 2, 9, 9, 6, 6, 5, 9, 4, 4, 6, 2, 2, 0, 9, 2, 9, 1, 4, 2, 7, 8, 6, 8, 2, 9, 5, 7, 7, 7, 2, 3, 5, 0, 4, 1, 3, 9, 5, 9, 8, 6, 0, 7, 5, 6, 2, 4, 5, 5, 1, 5, 4, 8, 9, 5, 5, 5, 0, 8, 5, 8, 8, 6, 9, 6, 4, 6, 7, 9, 6, 6, 0, 6, 4, 8, 1, 4, 9, 6, 6, 9, 4, 2, 9, 8, 9, 4, 6, 3, 9, 6, 0, 8, 9, 8
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| D. Brink, The spiral of Theodorus and sums of zeta-values at the half-integers, Amer. Math. Monthly (to appear).
P. J. Davis, Spirals from Theodorus to Chaos, A K Peters, Wellesley, MA, 1993.
E. Hlawka, Gleichverteilung und Quadratwurzelschnecke, Monatsh. Math., 89 (1980) 19-44.
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FORMULA
| sum_{x=1}^{n-1}\frac{1}{arctan(x)}=2\sqrt{n}+K+o(1).
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CROSSREFS
| Cf. A185051 for continued fraction expansion.
Sequence in context: A093545 A193762 A198422 * A183946 A005297 A014551
Adjacent sequences: A105456 A105457 A105458 * A105460 A105461 A105462
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KEYWORD
| nonn,cons
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AUTHOR
| David Brink (brink(AT)math.ku.dk), Jun 13 2011
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