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A247674 Decimal expansion of the integral over the square [0,1]x[0,1] of sqrt(1+(x-y)^2) dx dy. 5
1, 0, 7, 6, 6, 3, 5, 7, 3, 2, 8, 9, 5, 1, 7, 8, 0, 0, 8, 9, 6, 5, 3, 7, 9, 7, 5, 0, 2, 4, 3, 2, 2, 6, 2, 8, 2, 8, 3, 8, 2, 6, 9, 7, 0, 3, 1, 3, 5, 9, 8, 6, 0, 5, 3, 0, 2, 7, 7, 3, 5, 6, 9, 5, 9, 8, 9, 7, 9, 9, 6, 9, 1, 4, 0, 1, 3, 2, 3, 7, 4, 1, 5, 5, 0, 2, 4, 4, 3, 8, 0, 4, 6, 7, 7, 0, 8, 8, 5, 1, 9, 4, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

D. H. Bailey, J. M. Borwein, Highly Parallel, High-Precision Numerical Integration p. 9. (2005) Lawrence Berkeley National Laboratory

FORMULA

Equals 2/3 - sqrt(2)/3 + arcsinh(1).

Equals 2*A244921 + A247674 = (2 + sqrt(2) + 5*log(1+sqrt(2)))/3.

EXAMPLE

1.076635732895178008965379750243226282838269703135986...

MATHEMATICA

RealDigits[2/3 - Sqrt[2]/3 + ArcSinh[1], 10, 103] // First

PROG

(PARI) default(realprecision, 100); (2 + sqrt(2) + 5*log(1+sqrt(2)))/3 \\ G. C. Greubel, Aug 31 2018

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); (2 + Sqrt(2) + 5*Log(1+Sqrt(2)))/3; // G. C. Greubel, Aug 31 2018

CROSSREFS

Cf. A244921.

Sequence in context: A265304 A102769 A031348 * A109696 A257233 A110948

Adjacent sequences:  A247671 A247672 A247673 * A247675 A247676 A247677

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 22 2014

STATUS

approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)