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A227958 Decimal expansion of exp(-1/(2*sqrt(2))). 1
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
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

Sequence in context: A156960 A287697 A067840 * A118858 A261167 A197014

Adjacent sequences:  A227955 A227956 A227957 * A227959 A227960 A227961

KEYWORD

cons,nonn

AUTHOR

Geoffrey Critzer, Oct 26 2013

STATUS

approved

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Last modified January 22 19:16 EST 2020. Contains 331153 sequences. (Running on oeis4.)