A358968 - OEIS

%I #26 Feb 17 2023 22:27:02

%S 1,0,6,1,9,2,4,1,7,5,9,2,2,0,7,0,7,6,0,8,4,9,9,6,1,7,9,5,6,9,4,6,1,1,

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

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

%N Decimal expansion of the real part of the smallest complex zero of the prime zeta function in absolutely convergent zone.

%C The absolutely convergent zone of P(z) is for Re(z) > 1 where P(z) is the prime zeta function.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>

%e P(1.06192417592207076084996... + i*23.71733039185105166927978...) = 0.

%t Re[z /. FindRoot[PrimeZetaP[z] == If[$VersionNumber < 12.3, 0, 2*Pi*I], {z, 1 + 23.7*I},  WorkingPrecision -> 120]] (* after _Vaclav Kotesovec_ at A358923 *)

%Y Cf. A358923, A358924, A358969.

%K nonn,cons

%O 1,3

%A _Artur Jasinski_, Dec 07 2022