Search: id:A065442
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%I A065442
%S A065442 1,6,0,6,6,9,5,1,5,2,4,1,5,2,9,1,7,6,3,7,8,3,3,0,1,5,2,3,1,9,0,9,2,4,5,
%T A065442 8,0,4,8,0,5,7,9,6,7,1,5,0,5,7,5,6,4,3,5,7,7,8,0,7,9,5,5,3,6,9,1,4,1,8,
%U A065442 4,2,0,7,4,3,4,8,6,6,9,0,5,6,5,7,1,1,8,0,1,6,7,0,1,5,5,5,7,5,8,9,7,0,4
%N A065442 Decimal expansion of Erdos-Borwein constant Sum_{k=1..inf} 1/(2^k-1).
%D A065442 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
%H A065442 Harry J. Smith, <a href="b065442.txt">Table of n, a(n) for n=1,...,2000</
               a>
%H A065442 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/dig/dig.html">
               Digital Search Tree Constants</a>
%H A065442 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Erdos-BorweinConstant.html">Link to a section of The World of Mathematics.</
               a>
%H A065442 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TreeSearching.html">Tree Searching</a>
%H A065442 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DoubleSeries.html">Double Series</a>
%H A065442 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IrrationalNumber.html">Irrational Number</a>
%F A065442 Note Sum_{k=1..inf} d(k)/2^k = Sum_{k=1..inf} 1/(2^k-1).
%e A065442 1.60669515241529176378330152319092458048057967150575643577807955369...
%t A065442 RealDigits[ Sum[1/(2^k - 1), {k, 350}], 10, 111][[1]] (* Robert G. Wilson 
               v Nov 05 2006 *)
%o A065442 (PARI) {A065442(n)= s=0; for(x=1,n,s=s+1.0/(2^x-1)); s }
%o A065442 (PARI) { default(realprecision, 2080); x=suminf(k=1, 1/(2^k - 1)); for 
               (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065442.txt", n, " ", 
               d)) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 19 2009]
%Y A065442 See A038631 for continued fraction.
%Y A065442 Sequence in context: A092605 A004016 A093577 this_sequence A141462 A055955 
               A165071
%Y A065442 Adjacent sequences: A065439 A065440 A065441 this_sequence A065443 A065444 
               A065445
%K A065442 nonn,cons
%O A065442 1,2
%A A065442 N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2001
%E A065442 More terms from Randall L. Rathbun, Jan 16 2002

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