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A113011
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Decimal expansion of 1/(e^(1/2)-1).
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6
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1, 5, 4, 1, 4, 9, 4, 0, 8, 2, 5, 3, 6, 7, 9, 8, 2, 8, 4, 1, 3, 1, 1, 0, 3, 4, 4, 4, 4, 7, 2, 5, 1, 4, 6, 3, 8, 3, 4, 0, 4, 5, 9, 2, 3, 6, 8, 4, 1, 8, 8, 2, 1, 0, 9, 4, 7, 4, 1, 3, 6, 9, 5, 6, 6, 3, 7, 5, 4, 2, 6, 3, 9, 1, 4, 3, 3, 1, 4, 8, 0, 7, 0, 7, 1, 8, 2, 5, 7, 2, 4, 0, 8, 5, 0, 0, 7, 7, 4, 2, 2, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Has continued fraction 1+2/(3+4/(5+6/7+...)).
Simple continued fraction is 1, 1, 1, 5, 1, 1, 9, 1, 1, 13, 1, 1, 17, 1, {1, 4k+1, 1}, ..., . - Robert G. Wilson v, Jul 01 2007.
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LINKS
| Leonhard Euler, On the formation of continued fractions, see p. 14.
Eric Weisstein's World of Mathematics, Continued Fraction
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EXAMPLE
| 1.54149408253679828413110344447251463834045923684188210947413695663...
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MATHEMATICA
| First@ RealDigits[ 1 / (Exp[1/2] - 1), 10, 111] (* Or *)
First@ RealDigits@ N[Fold[Last@#2 + First@#2/#1 &, 1, Partition[ Reverse@ Range@130, 2]], 111] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007 *)
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CROSSREFS
| Cf. A113012, A113013.
Sequence in context: A190287 A087707 A198352 * A130815 A084129 A011503
Adjacent sequences: A113008 A113009 A113010 * A113012 A113013 A113014
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), following a suggestion of Grover W. Hughes, Oct 09, 2005
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EXTENSIONS
| Simpler definition from T. D. Noe (noe(AT)sspectra.com), Oct 09 2005
Euler reference from David Harden, Oct 09, 2005
ArXiv URL replaced by its non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009
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