A392160 Decimal expansion of 2*sqrt(3)*Pi^2/(27*zeta(3)).

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

Offset

1,3

Comments

This constant gives a sharp upper bound to the lim sup of the ratio between the density of prime triples in the set of coprime triples in S intersection Z_{+}^3 and that of prime triples in the set of coprime triples in Z_{+}^3, where S = {(z_0, z_1, z_2) : z_0^2 - z_1^2 + z_2^2 - z_0*z_2 = 0} (see Geng et al. link).

Links

Table of n, a(n) for n=1..100.

Liang Geng, Wei He, and Rongwei Yang, The Density of Primes in the Eigensurface of S_3, arXiv:2512.21488 [math.NT], 2025. See p. 4.

Example

1.0534200433692442051034824799149890631081481213...

Mathematica

RealDigits[2Sqrt[3]Pi^2/(27*Zeta[3]), 10, 100][[1]]

Crossrefs

Cf. A002117, A002194, A002388, A164102, A291050, A346933, A392159 (lower bound).

Sequence in context: A004486 A011426 A293509 * A090343 A135448 A243359

Adjacent sequences: A392157 A392158 A392159 * A392161 A392162 A392163

Keyword

nonn,cons

Author

Stefano Spezia, Jan 01 2026

Status

approved