A349604 Decimal expansion of the positive real solution to (1 - 1/2^x) * zeta(x) = 2.

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

Offset: 1

Author

Amiram Eldar, Nov 23 2021

Keywords

• nonn
• cons

Comments

This constant, c, appears in the inequality A074206(n) <= n^c for odd n (Baustian and Bobkov, 2020).

Examples

			1.37778516983754118384089490370869137916464016638683...
		

Links

• Falko Baustian and Vladimir Bobkov, On asymptotic behavior of Dirichlet inverse, International Journal of Number Theory, Vol. 16, No. 6 (2020), pp. 1337-1354; arXiv preprint, arXiv:1903.12445 [math.NT], 2019-2020.

Crossrefs

Cf. A074206, A107311.

Programs

Mathematica

RealDigits[s /. FindRoot[(1 - 1/2^s)*Zeta[s] == 2, {s, 2}, WorkingPrecision -> 110], 10, 100][[1]]

PARI

solve(x=1.1, 2, (1-1/2^x)*zeta(x) - 2) \\ Michel Marcus, Nov 23 2021