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%I #8 Apr 10 2021 22:27:03
%S 1,8,7,7,7,9,0,3,1,3,2,3,0,4,2,7,7,0,4,3,3,0,1,0,5,2,9,1,2,4,3,8,7,9,
%T 7,0,8,8,2,6,6,3,6,7,7,5,5,7,9,0,0,5,4,0,2,3,5,7,1,2,0,9,0,4,4,4,6,3,
%U 1,1,2,6,1,5,5,0,2,5,9,2,6,5,2,3,9,5,4,7,9,2,3,7,2,8,6,6,0,1,3,0,5,1,6,2,1
%N Decimal expansion of the integral over cos(Pi*x)*x^(1/x) between 1/e and e.
%C Strangely close to A037077 which is a sum of the integrand from 1 to infinity.
%H Marvin Ray Burns, <a href="http://www.mapleprimes.com/blog/marvinrayburns/mrbconstantj">Author's original inquiry</a>
%H R. J. Mathar, <a href="http://arxiv.org/abs/0912.3844">Numerical evaluation of the oscillatory integral over exp(i*pi*x)x^(1/x) between 1 and infinity</a>, arXiv:0912.3844
%e 0.187779...
%p Int( cos(Pi*x)*x^(1/x),x=exp(-1)..exp(1)) ; evalf(%) ; # _R. J. Mathar_, May 07 2010
%t RealDigits[ Re[NIntegrate[(-1)^n*n^(1/n), {n, 1/E, E}, WorkingPrecision -> 200]]]
%Y A157852 is the same integral from 1 to infinity.
%K nonn,cons
%O 0,2
%A _Marvin Ray Burns_, May 04 2010
%E Definition simplified, keyword:cons inserted, offset corrected by _R. J. Mathar_, May 07 2010
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