A227958 Decimal expansion of exp(-1/(2*sqrt(2))).

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

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 A335953 * A118858 A261167 A197014

Adjacent sequences: A227955 A227956 A227957 * A227959 A227960 A227961

Keyword

cons,nonn

Author

Geoffrey Critzer, Oct 26 2013

Status

approved