A358968 Decimal expansion of the real part of the smallest complex zero of the prime zeta function in absolutely convergent zone.

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, 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, 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

Offset

1,3

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=1..115.

Eric Weisstein's World of Mathematics, Prime Zeta Function

Example

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

Mathematica

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 *)

Crossrefs

Cf. A358923, A358924, A358969.

Sequence in context: A111507 A117236 A349141 * A246771 A176397 A245724

Adjacent sequences: A358965 A358966 A358967 * A358969 A358970 A358971

Keyword

nonn,cons

Author

Artur Jasinski, Dec 07 2022

Status

approved