A384541 Decimal expansion of (1/32)*(2 - gamma)*Pi, where gamma is the Euler-Mascheroni constant.

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

Offset

0,2

Links

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

Mats Granvik, Why are these integrals equivalent to the Riemann Hypothesis?.

Formula

Equals lim_{k->oo} Integral_{t=0..oo} (1 - 12*t^2)/((1 + 4*t^2)^3)*Integral_{sigma=1/2..oo} Re(IndefiniteIntegral) dsigma dt where IndefiniteIntegral = Integral_{s} Sum_{n=2..k} 1/n^s + (1/k^(s - 1))/(s - 1) ds and s has been substituted with s = sigma + i*t.

Equals lim_{k->oo} -Pi/32*(Sum_{n=2..k} 1/n - (1 + log(k))). - Mats Granvik, May 30 2026

Example

0.13968152546212446804100475735274892966520858179305033...

Mathematica

RealDigits[-(1/32)*(-2 + EulerGamma)*Pi, 10, 105][[1]]

Crossrefs

Cf. A014963, A191898, A001620, A000796.

Sequence in context: A153416 A269226 A205557 * A193078 A021256 A349850

Adjacent sequences: A384538 A384539 A384540 * A384542 A384543 A384544

Keyword

nonn,cons,changed

Author

Mats Granvik, Jun 02 2025

Status

approved