A387378 Decimal expansion of the smallest positive real solution > 0.5 to zeta(z) = zeta(1-z).
1, 9, 0, 6, 7, 7, 5, 0, 8, 4, 7, 0, 6, 9, 6, 6, 2, 0, 7, 2, 7, 9, 1, 4, 5, 8, 3, 6, 5, 6, 2, 3, 4, 4, 7, 3, 0, 3, 3, 8, 4, 2, 0, 1, 7, 3, 2, 6, 5, 8, 5, 3, 9, 8, 3, 3, 4, 7, 4, 6, 1, 7, 7, 8, 5, 4, 3, 6, 0, 0, 6, 4, 1, 7, 3, 5, 7, 9, 7, 2, 7, 1, 1, 7, 3, 1, 5, 9, 1, 4, 0, 1, 2, 1, 0, 6, 5, 0, 2, 2, 6, 2, 2, 6, 8, 2, 1, 6, 5, 0, 8, 6, 7, 9, 2, 6, 0, 7, 6, 2
Offset: 2
Examples
19.06775084706966207279...
Programs
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Mathematica
RealDigits[x /. FindRoot[Zeta[x] == Zeta[1 - x], {x, 19}, WorkingPrecision -> 120]][[1]]
Formula
zeta(19.067750847069662...) = zeta(1-19.067750847069662...) = 1.000001820649741...
Smallest positive real root > 0.5 of the equation Gamma(z) = (2^(z-1))*(Pi^z)*sec((Pi*z)/2).
Equals A365281 + 1/2. - Amiram Eldar, Aug 28 2025
Comments