A386734 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} Integral_{z=0..1} {1/(x+y+z)} dx dy dz, where {} denotes fractional part.

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

Offset

0,2

Links

Table of n, a(n) for n=0..104.

Ovidiu Furdui, Multiple Fractional Part Integrals and Euler's Constant, Miskolc Mathematical Notes, Vol. 17, No. 1 (2016), pp. 255-266.

Formula

Equals 9*log(3)/2 - 6*log(2) - zeta(3)/2.

Example

0.18384376406702461207534175664658126707821355787059...

Mathematica

RealDigits[9*Log[3]/2 - 6*Log[2] - Zeta[3]/2, 10, 120][[1]]

Prog

(PARI) 9*log(3)/2 - 6*log(2) - zeta(3)/2

Crossrefs

Cf. A002117, A002162, A002391, A153810, A386733, A386736, A386737.

Sequence in context: A199598 A387773 A011106 * A131641 A190408 A343851

Adjacent sequences: A386731 A386732 A386733 * A386735 A386736 A386737

Keyword

nonn,cons

Author

Amiram Eldar, Aug 01 2025

Status

approved