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A157697 Decimal expansion of sqrt(2/3). 3
8, 1, 6, 4, 9, 6, 5, 8, 0, 9, 2, 7, 7, 2, 6, 0, 3, 2, 7, 3, 2, 4, 2, 8, 0, 2, 4, 9, 0, 1, 9, 6, 3, 7, 9, 7, 3, 2, 1, 9, 8, 2, 4, 9, 3, 5, 5, 2, 2, 2, 3, 3, 7, 6, 1, 4, 4, 2, 3, 0, 8, 5, 5, 7, 5, 0, 3, 2, 0, 1, 2, 5, 8, 1, 9, 1, 0, 5, 0, 0, 8, 8, 4, 6, 6, 1, 9, 8, 1, 1, 0, 3, 4, 8, 8, 0, 0, 7, 8, 2, 7, 2, 8, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals sum_{n=0..infinity} (-1)^n*binomial(2n,n)/8^n = 1/A115754 . Averaging this constant with sqrt(2) = A002193 = sum_{n=0..inf} binomial(2n,n)/8^n yields A145439.

Height (from a vertex to the opposite face) of regular tetrahedron with unit edge. - Stanislav Sykora, May 31 2012

REFERENCES

Jolley, Summation of Series, Dover (1961) eq. (168) on page 32.

LINKS

Table of n, a(n) for n=0..104.

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.

FORMULA

= 1-(1/2)/2 +(1*3)/(2*4)/2^2 - (1*3*5)/(2*4*6)/2^3+... [Jolley]

EXAMPLE

0.816496580927726056140063577...

MAPLE

evalf(sqrt(2/3)) ;

MATHEMATICA

RealDigits[N[Sqrt[2/3], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011*)

CROSSREFS

Sequence in context: A033812 A019717 A007404 * A240982 A182551 A005486

Adjacent sequences:  A157694 A157695 A157696 * A157698 A157699 A157700

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Mar 04 2009

STATUS

approved

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Last modified September 2 23:10 EDT 2014. Contains 246369 sequences.