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A358969
Decimal expansion of the imaginary part of the smallest complex zero of the prime zeta function in the absolutely convergent zone.
1
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
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
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 07 2022
STATUS
approved