A386733 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} {1/(x+y)} dx dy, where {} denotes fractional part.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Ovidui Furdui, Problem 150, Problems, Missouri J. Math. Sci., Vol. 16, No. 2 (2004), p. 130; Huizeng Qin, Solution to Problem 150, ibid., Vol. 17, No. 3 (2005), pp. 197-199.

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

Formula

Equals 2*log(2) - Pi^2/12 = A016627 - A072691.

Example

0.56382732769577740059825665959334054154152531811711...

Mathematica

RealDigits[2*Log[2] - Pi^2/12, 10, 120][[1]]

Prog

(PARI) 2*log(2) - zeta(2)/2

Crossrefs

Cf. A016627, A072691, A153810, A345208, A386734, A386735.

Sequence in context: A123852 A329197 A153614 * A328905 A195709 A257837

Adjacent sequences: A386730 A386731 A386732 * A386734 A386735 A386736

Keyword

nonn,cons

Author

Amiram Eldar, Aug 01 2025

Status

approved