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A091505 Decimal expansion of (2 + sqrt(2) + 5*arcsinh(1))/15. 6
5, 2, 1, 4, 0, 5, 4, 3, 3, 1, 6, 4, 7, 2, 0, 6, 7, 8, 3, 3, 0, 9, 8, 2, 3, 5, 6, 6, 0, 7, 2, 4, 3, 9, 7, 4, 9, 1, 4, 0, 3, 1, 5, 6, 7, 7, 7, 9, 0, 0, 8, 3, 4, 1, 7, 9, 6, 2, 1, 0, 5, 1, 8, 7, 5, 0, 5, 0, 7, 8, 9, 3, 3, 0, 4, 8, 1, 5, 8, 3, 1, 8, 6, 7, 9, 2, 8, 1, 3, 2, 9, 2, 5, 2, 6, 1, 4, 5, 2, 4, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Or equally, decimal expansion of (2 + sqrt(2) + 5*log(1+sqrt(2)))/15.

Average distance between two points chosen at random in a unit square.

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Sections 8.1 p. 479 and 8.5 p.498.

L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 49.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Square Line Picking

EXAMPLE

0.5214054331647206783309823566...

MATHEMATICA

RealDigits[(2+Sqrt[2]+5ArcSinh[1])/15, 10, 120][[1]] (* Harvey P. Dale, Jul 18 2011 *)

PROG

(PARI) (2 + sqrt(2) + 5*asinh(1))/15 \\ G. C. Greubel, Jan 11 2017

CROSSREFS

Cf. A091506, A073012.

Sequence in context: A136161 A197383 A266455 * A030357 A212879 A276524

Adjacent sequences:  A091502 A091503 A091504 * A091506 A091507 A091508

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jan 16 2004

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)