A358969 Decimal expansion of the imaginary part of the smallest complex zero of the prime zeta function in the absolutely convergent zone.

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, 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, 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

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..116.

Eric Weisstein's World of Mathematics, Prime Zeta Function

Example

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

Mathematica

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 *)

Crossrefs

Cf. A358923, A358924, A358968.

Sequence in context: A104691 A011160 A068960 * A205129 A236290 A105273

Adjacent sequences: A358966 A358967 A358968 * A358970 A358971 A358972

Keyword

nonn,cons

Author

Artur Jasinski, Dec 07 2022

Status

approved