%I A157852
%S A157852 6,8,7,6,5,2,3
%N A157852 Absolute value of limit_{N -> infinity} (integral((-1)^x*x^(1/x),x=1..2*N).
%C A157852 The continuous counterpart of 1^(1/1)-2^(1/2)+3^(1/3)-4^(1/4)...2*integer 
               as n->infinity.
%C A157852 It is hard to integrate and very slow to converge.
%C A157852 From a numerical integration of the first 5 to 8 periods of the exp(i*pi*x) 
               and estimation of the remainder with a mixed Filon-Euler-Maclaurin 
               approach collecting up to the 5th order of the derivatives, we get 
               0.68765236884 (up to 6th order 0.68765236894, up to 7th order 0.68765236893), 
               all numbers rounded. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 23 2009]
%H A157852 M. R. Burns, <a href="http://marvinrayburns.com/latest.html">Used with 
               other constants to converge closely to rational numbers.</a>
%H A157852 M. R. Burns, <a href="http://www.mapleprimes.com/blog/marvinrayburns/
               mrbconstantc"> Author's public inquiry 1 </a>
%H A157852 M. R. Burns, <a href="http://math2.org/mmb/thread/41959">Author's public 
               inquiry 2 </a>
%e A157852 After integrating from 1 to 5 Million the integral~= 0.6876533456.
%e A157852 After integrating from 1 to 10 Million the integral~= 0.6876528792.
%e A157852 After integrating from 1 to 15 Million the integral~= 0.6876527177.
%e A157852 After integrating from 1 to 20 Million the integral~= 0.6876526145.
%Y A157852 Integrating A037077 instead of summing.
%Y A157852 Sequence in context: A092294 A097668 A133748 this_sequence A088608 A011481 
               A100221
%Y A157852 Adjacent sequences: A157849 A157850 A157851 this_sequence A157853 A157854 
               A157855
%K A157852 nonn,more
%O A157852 1,1
%A A157852 Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Mar 07 2009, Mar 11 2009, 
               Mar 13 2009
%E A157852 Edited by N. J. A. Sloane, Mar 13 2009
%E A157852 Corrected and edited by Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), 
               Apr 03 2009