A393256 Decimal expansion of Pi*G - (3/8)*zeta(3), where G is Catalan's constant (A006752).

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

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Michael Penn, So much to learn/review in one integral!, YouTube video, 2020.

Formula

Equals Integral_{x=0..oo} log(1 + x)*log(1 + 1/(x^2))/x dx.

Equals A393257 - (3/8)*A002117.

Example

2.42681944292331329475267835595475405357798454042...

Mathematica

First[RealDigits[Pi*Catalan - 3*Zeta[3]/8, 10, 100]] (* or *)
First[RealDigits[Integrate[Log[1 + x]*Log[1 + 1/x^2]/x, {x, 0, Infinity}], 10, 100]]

Crossrefs

Cf. A000796, A002117, A006752, A393257.

Sequence in context: A303347 A382660 A325971 * A250222 A026251 A205721

Adjacent sequences: A393253 A393254 A393255 * A393257 A393258 A393259

Keyword

nonn,cons,easy

Author

Paolo Xausa, Feb 07 2026

Status

approved