OFFSET
0,1
COMMENTS
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
EXAMPLE
exp(-1/(2*sqrt(2))) = 0.70218850132655959623818747974621806350453051703896...
MAPLE
evalf(exp(-1/(2*sqrt(2))), 120); # Muniru A Asiru, Oct 07 2018
MATHEMATICA
RealDigits[Exp[-1/(2*2^(1/2))], 10, 100][[1]]
PROG
(PARI) exp(-1/sqrt(8)) \\ Charles R Greathouse IV, Apr 21 2016
(Magma) SetDefaultRealField(RealField(100)); Exp(-1/Sqrt(8)); // G. C. Greubel, Oct 06 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Geoffrey Critzer, Oct 26 2013
STATUS
approved