A254968 Decimal expansion of the mean reciprocal Euclidean distance from a point in a unit cube to a given vertex of the cube (named B_3(-1) in Bailey's paper).

1, 1, 9, 0, 0, 3, 8, 6, 8, 1, 9, 8, 9, 7, 7, 6, 7, 5, 3, 3, 2, 1, 9, 0, 8, 6, 7, 5, 1, 4, 2, 0, 7, 6, 9, 4, 4, 9, 9, 1, 1, 8, 0, 6, 0, 7, 3, 5, 7, 4, 9, 8, 2, 6, 4, 4, 0, 8, 9, 7, 2, 2, 3, 7, 3, 0, 3, 7, 3, 6, 1, 7, 6, 5, 5, 3, 1, 1, 3, 7, 1, 4, 4, 5, 4, 3, 1, 9, 8, 1, 3, 8, 3, 9, 6, 2, 3, 4, 0, 8, 3, 3, 9, 1, 6

Offset

1,3

Links

Table of n, a(n) for n=1..105.

D. H. Bailey, J. M. Borwein and R. E. Crandall, Box Integrals, J. Comp. Appl. Math., Vol. 206, No. 1 (2007), pp. 196-208.

D. H. Bailey, J. M. Borwein, and R. E. Crandall, Advances in the theory of box integrals, Math. Comp. 79 (271) (2010) 1839-1866, Table 2.

Eric Weisstein's MathWorld, Box Integral.

Formula

Equals B_3(-1) = (3/2)*log(2 + sqrt(3)) - Pi/4.

Equals log(7 + 4*sqrt(3)) - Pi/4 - arcsinh(1/sqrt(2)).

Example

1.1900386819897767533219086751420769449911806073574982644...

Mathematica

RealDigits[(3/2)*Log[2 + Sqrt[3]] - Pi/4, 10, 105] // First

Crossrefs

Cf. A130590, A244920, A244921.

Sequence in context: A097671 A112628 A198871 * A019940 A257435 A366193

Adjacent sequences: A254965 A254966 A254967 * A254969 A254970 A254971

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Feb 11 2015

Extensions

Name corrected by Amiram Eldar, Jun 04 2023

Status

approved