%I A037077
%S A037077 1,8,7,8,5,9,6,4,2,4,6,2,0,6,7,1,2,0,2,4,8,5,1,7,9,3,4,0,5,4,2,7,3,2,
%T A037077 3,0,0,5,5,9,0,3,0,9,4,9,0,0,1,3,8,7,8,6,1,7,2,0,0,4,6,8,4,0,8,9,4,7,7,
%U A037077 2,3,1,5,6,4,6,6,0,2,1,3,7,0,3,2,9,6,6,5,4,4,3,3,1,7,4,9,6,9,0
%N A037077 Decimal expansion of 1^(1/1)-2^(1/2)+3^(1/3)...
%D A037077 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.
%H A037077 M. R. Burns, <a href="http://pi.lacim.uqam.ca/piDATA/mrburns.txt">MRB 
               constant</a>
%H A037077 M. R. Burns, <a href="http://www.mapleprimes.com/blog/marvinrayburns/
               mrbconstant">Maple Primes</a>
%H A037077 M. R. Burns, <a href="http://marvinrayburns.com/QA-1.mht">Update on the 
               MRB Constant 1</a>. [History and facts]
%H A037077 M. R. Burns, <a href="http://marvinrayburns.com/DEMRB.mht">Update on 
               the MRB Constant 2</a>. [Explicit decimal expansions]
%H A037077 M. R. Burns, <a href="http://marvinrayburns.com/new_on_mrb.html">Update 
               on the MRB Constant 3</a>. [Sinusoidal characteristic]
%H A037077 M. R. Burns, <a href="http://marvinrayburns.com/250KMRB.txt">Update on 
               the MRB Constant 4</a>. [250000 digits]
%H A037077 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/itrexp/itrexp.html">
               Iterated Exponential Constants</a>
%H A037077 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerTower.html">Link to a section of The World of Mathematics</a>
%H A037077 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MRBConstant.html">MRB Constant</a> [From Eric W. Weisstein (eric(AT)weisstein.com), 
               May 01 2009]
%e A037077 0.187859642462067120248517934...
%p A037077 evalf(sum((-1)^n*(n^(1/n)-1),n=1..infinity),100); [From Marvin Ray Burns 
               (bmmmburns(AT)sbcglobal.net), Jun 07 2009]
%t A037077 e=50;ClearAll[a];Clear[m,n,s,d];n=131(Ceiling[e/100]);a[0]=1;For[m=1,
               m<n,a[m]=(1+m)^(1/(1+m));m++ ];Block[{$MaxExtraPrecision=e+1},d=(3+Sqrt[8])^n;
               d=(d+1/d)/2;b=-1;c=-1 d;s=0;For[k=0,k<n,c=b-c;b=(k+n)(k-n)b/((k+1/
               2)(k+1));s=s+c*a[k];k++ ]];Print[N[1/2-s/d,e]];ClearAll[a];Clear[m,
               n,s,d]; (e is the number of digits desired). - Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), 
               Aug 05 2007
%o A037077 (PARI) sumalt(x=1,(-1)^x*((x^(1/x))-1))
%Y A037077 A052110, A157852, A160755 [From Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), 
               Jun 07 2009]
%Y A037077 Sequence in context: A010529 A086911 A103984 this_sequence A094106 A021536 
               A094082
%Y A037077 Adjacent sequences: A037074 A037075 A037076 this_sequence A037078 A037079 
               A037080
%K A037077 cons,nonn
%O A037077 0,2
%A A037077 Marvin Ray Burns (bmmmburns(AT)sbcglobal.net). Entry updated Jan 30 2009, 
               Jun 21 2009