A349604 - OEIS

%I #8 Nov 23 2021 09:02:48

%S 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,

%T 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,

%U 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

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

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

%H Falko Baustian and Vladimir Bobkov, <a href="https://doi.org/10.1142/S1793042120500700">On asymptotic behavior of Dirichlet inverse</a>, International Journal of Number Theory, Vol. 16, No. 6 (2020), pp. 1337-1354; <a href="https://arxiv.org/abs/1903.12445">arXiv preprint</a>, arXiv:1903.12445 [math.NT], 2019-2020.

%e 1.37778516983754118384089490370869137916464016638683...

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

%o (PARI) solve(x=1.1, 2, (1-1/2^x)*zeta(x) - 2) \\ _Michel Marcus_, Nov 23 2021

%Y Cf. A074206, A107311.

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Nov 23 2021