A358969 - OEIS

%I #28 Feb 17 2023 22:27:42

%S 2,3,7,1,7,3,3,0,3,9,1,8,5,1,0,5,1,6,6,9,2,7,9,7,8,0,2,1,5,3,1,8,5,8,

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

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

%N Decimal expansion of the imaginary part of the smallest complex zero of the prime zeta function in the 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 Im[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, A358968.

%K nonn,cons

%O 2,1

%A _Artur Jasinski_, Dec 07 2022