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A157697
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Decimal expansion of sqrt(2/3).
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6
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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
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OFFSET
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0,1
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COMMENTS
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Equals Sum_{n>=0} (-1)^n*binomial(2n,n)/8^n = 1/A115754. Averaging this constant with sqrt(2) = A002193 = Sum_{n>=0} 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
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REFERENCES
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Jolley, Summation of Series, Dover (1961) eq. (168) on page 32.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.
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FORMULA
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sqrt(2/3) = 1 - (1/2)/2 + (1*3)/(2*4)/2^2 - (1*3*5)/(2*4*6)/2^3 + ... [Jolley]
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EXAMPLE
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0.816496580927726056140063577...
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MAPLE
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evalf(sqrt(2/3)) ;
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MATHEMATICA
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RealDigits[Sqrt[2/3], 10, 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011*)
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PROG
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(PARI) sqrt(2/3) \\ G. C. Greubel, Mar 30 2018
(MAGMA) Sqrt(2/3); // G. C. Greubel, Mar 30 2018
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CROSSREFS
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Sequence in context: A019717 A007404 A299627 * A281785 A240982 A258146
Adjacent sequences: A157694 A157695 A157696 * A157698 A157699 A157700
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KEYWORD
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cons,easy,nonn
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AUTHOR
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R. J. Mathar, Mar 04 2009
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STATUS
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approved
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