A093066 Decimal expansion of (4 + 17*sqrt(2) - 6*sqrt(3) - 7*Pi + 21*log(1+sqrt(2)) + 42*log(2+sqrt(3)))/75.

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

Offset

0,1

Comments

Average distance between two points chosen at random on two different faces of a unit cube.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, and Eric W. Weisstein, Ten Problems in Experimental Mathematics, The American Mathematical Monthly, Vol. 113, No. 6 (2006), pp. 481-509; ResearchGate link.

Eric Weisstein's World of Mathematics, Cube Line Picking.

Formula

Equals (7/5) * A073012. - Amiram Eldar, May 11 2026

Example

0.92639005517404672921816358654777901444496019010733...

Mathematica

RealDigits[(4 + 17*Sqrt[2] - 6*Sqrt[3] - 7*Pi + 21*Log[1 + Sqrt[2]] + 42*Log[2 + Sqrt[3]])/75, 10, 101][[1]] (* G. C. Greubel, Oct 01 2018 *)

Prog

(PARI) default(realprecision, 100); (4 + 17*sqrt(2) - 6*sqrt(3) - 7*Pi + 21*log(1 + sqrt(2)) + 42*log(2 + sqrt(3)))/75 \\ G. C. Greubel, Oct 01 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (4 + 17*Sqrt(2) - 6*Sqrt(3) - 7*Pi(R) + 21*Log(1 + Sqrt(2)) + 42*Log(2 + Sqrt(3)))/75; // G. C. Greubel, Oct 01 2018

Crossrefs

Cf. A073012.

Sequence in context: A353407 A248318 A298852 * A155168 A239628 A107821

Adjacent sequences: A093063 A093064 A093065 * A093067 A093068 A093069

Keyword

nonn,cons

Author

Eric W. Weisstein, Mar 16 2004

Status

approved