Search: id:A113011
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%I A113011
%S A113011 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,
%T A113011 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,
%U A113011 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
%N A113011 Decimal expansion of 1/(e^(1/2)-1).
%C A113011 Has continued fraction 1+2/(3+4/(5+6/7+...)).
%C A113011 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.
%H A113011 Leonhard Euler, <a href="http://arXiv.org/abs/math/0508227">On the formation 
               of continued fractions</a>, see p. 14.
%H A113011 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ContinuedFraction.html">Continued Fraction</a>
%e A113011 1.54149408253679828413110344447251463834045923684188210947413695663...
%t A113011 First@ RealDigits[ 1 / (Exp[1/2] - 1), 10, 111] (* Or *)
%t A113011 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 *)
%Y A113011 Cf. A113012, A113013.
%Y A113011 Sequence in context: A136042 A166044 A087707 this_sequence A130815 A084129 
               A011503
%Y A113011 Adjacent sequences: A113008 A113009 A113010 this_sequence A113012 A113013 
               A113014
%K A113011 nonn,cons
%O A113011 1,2
%A A113011 Eric Weisstein (eric(AT)weisstein.com), following a suggestion of Grover 
               W. Hughes, Oct 09, 2005
%E A113011 Simpler definition from T. D. Noe (noe(AT)sspectra.com), Oct 09 2005
%E A113011 Euler reference from David Harden, Oct 09, 2005
%E A113011 ArXiv URL replaced by its non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 23 2009

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