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A164833
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Decimal expansion of Pi/8 - log(2)/2.
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5
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0, 4, 6, 1, 2, 5, 4, 9, 1, 4, 1, 8, 7, 5, 1, 5, 0, 0, 0, 9, 9, 2, 1, 4, 3, 6, 2, 1, 8, 0, 8, 4, 9, 5, 7, 6, 4, 8, 6, 8, 9, 6, 1, 0, 7, 7, 4, 1, 7, 6, 0, 6, 0, 0, 5, 6, 1, 5, 2, 8, 0, 6, 9, 2, 9, 1, 7, 8, 0, 2, 3, 9, 8, 0, 0, 9, 2, 8, 7, 6, 7, 0, 2, 5, 5, 7, 2, 6, 8, 9, 6, 6, 9, 5, 5, 5, 2, 8, 9, 7, 2, 6, 7, 6, 7, 7, 7, 0, 3, 0, 3, 8, 7, 4, 9, 4, 5, 4, 6
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OFFSET
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0,2
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COMMENTS
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Digits and formula given at Waldschmidt, p. 4.
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REFERENCES
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Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 251).
A. J. Van Der Poorten, Effectively computable bounds for the solutions of certain Diophantine equations, Acta Arith., 33 (1977), pp. 195-207.
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LINKS
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FORMULA
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Equals Sum_{n>=0} Sum_{m>=0} 1/((4*n+3)^(2*m+1)).
Equals Sum_{k>=1} 1/( (4k-2)*(4k-1)*(4k)) ). - Bruno Berselli, Mar 17 2014
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EXAMPLE
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0.0461254914187515000992143621808495764868961077417606...
1/(2*3*4) + 1/(6*7*8) + 1/(10*11*12) + 1/(14*15*16) + ... [Bruno Berselli, Mar 17 2014]
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MAPLE
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MATHEMATICA
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Join[{0}, RealDigits[Pi/8-Log[2]/2, 10, 120][[1]]] (* Harvey P. Dale, Nov 13 2012 *)
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PROG
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(PARI) default(realprecision, 130); (Pi - 4*log(2))/8 \\ G. C. Greubel, Aug 11 2019
(Magma) SetDefaultRealField(RealField(130)); R:= RealField(); (Pi(R)-4*Log(2))/8; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx((pi-4*log(2))/8, digits=130) # G. C. Greubel, Aug 11 2019
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CROSSREFS
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Cf. A239362: Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)) ).
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KEYWORD
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AUTHOR
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EXTENSIONS
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Normalized offset and leading zeros - R. J. Mathar, Sep 27 2009
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STATUS
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approved
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