A386736 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} Integral_{z=0..1} {1/(x+y+z)}^2 dx dy dz, where {} denotes fractional part.

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

Offset

0,1

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 6*log(2) - 3*log(3) -(zeta(2) + zeta(3))/6.

Example

0.3885477223540393286722981299552364311798731004354002...

Mathematica

RealDigits[6*Log[2] - 3*Log[3] - (Zeta[2] + Zeta[3])/6, 10, 120][[1]]

Prog

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

Crossrefs

Cf. A002117, A002162, A002391, A013661, A386734, A386735, A386737.

Sequence in context: A371941 A232182 A118817 * A179553 A384287 A157471

Adjacent sequences: A386733 A386734 A386735 * A386737 A386738 A386739

Keyword

nonn,cons

Author

Amiram Eldar, Aug 01 2025

Status

approved