A242070 Decimal expansion of the supremum of all real s such that zeta'(s+i*t) = 0 for some real t.

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

Offset

1,1

Links

Table of n, a(n) for n=1..100.

J. Arias de Reyna, J. van de Lune, Some bounds and limits in the theory of Riemann's zeta function. arXiv:1107.5134 [math.NT]

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 28.

Formula

The unique solution y > 1 of the equation zeta'(y)/zeta(y) = -2^(y + 1)*log(2)/(4^y - 1).

Example

2.81301402025289836752725540121668696384614056054026221526643874...

Mathematica

y /. FindRoot[Zeta'[y]/Zeta[y] == -2^(y + 1)*Log[2]/(4^y - 1), {y, 2}, WorkingPrecision -> 100] // RealDigits // First

Crossrefs

Cf. A242069.

Sequence in context: A202539 A197287 A081882 * A155694 A200689 A143198

Adjacent sequences: A242067 A242068 A242069 * A242071 A242072 A242073

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 14 2014

Status

approved