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%I #27 Sep 08 2022 08:46:05
%S 7,0,2,1,8,8,5,0,1,3,2,6,5,5,9,5,9,6,2,3,8,1,8,7,4,7,9,7,4,6,2,1,8,0,
%T 6,3,5,0,4,5,3,0,5,1,7,0,3,8,9,6,2,0,7,6,6,6,2,8,9,4,3,2,8,6,8,7,8,7,
%U 9,6,3,0,8,2,3,5,4,5,3,0,1,1,2,8,1,7,9,1,7,7,2,1,4,5,2,8,4,2,8,4
%N Decimal expansion of exp(-1/(2*sqrt(2))).
%C Let {x} denote the fractional part of a real number x. Let p(k) = A001333(k) and q(k) = A000129(k), the numerators and denominators of the continued fraction convergents to sqrt(2). exp(-1/(2*sqrt(2))) is the limit as k goes to infinity of the sequence b(n) = b(2k) = {q(2k)*sqrt(2)}^(2k) = q(2k)*sqrt(2) - p(2k) +1. b(n) is a subsequence of a(n) = {n*sqrt(2)}^n. b(n) can be used to demonstrate that a(n) is divergent.
%H G. C. Greubel, <a href="/A227958/b227958.txt">Table of n, a(n) for n = 0..10000</a>
%e exp(-1/(2*sqrt(2))) = 0.70218850132655959623818747974621806350453051703896...
%p evalf(exp(-1/(2*sqrt(2))),120); # _Muniru A Asiru_, Oct 07 2018
%t RealDigits[Exp[-1/(2*2^(1/2))],10,100][[1]]
%o (PARI) exp(-1/sqrt(8)) \\ _Charles R Greathouse IV_, Apr 21 2016
%o (Magma) SetDefaultRealField(RealField(100)); Exp(-1/Sqrt(8)); // _G. C. Greubel_, Oct 06 2018
%K cons,nonn
%O 0,1
%A _Geoffrey Critzer_, Oct 26 2013
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