A242069 Decimal expansion of the supremum of all real s such that zeta(s+i*t) = 1 for some real t.

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

Offset

1,2

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 x > 1 of the equation zeta(x) = (2^x + 1)/(2^x - 1).

Example

1.9401016837436252860174693905255488782302476074457584536287...

Mathematica

x /. FindRoot[Zeta[x] == (2^x + 1)/(2^x - 1), {x, 2}, WorkingPrecision -> 100] // RealDigits // First

Crossrefs

Sequence in context: A038293 A119516 A193109 * A197828 A116393 A359285

Adjacent sequences: A242066 A242067 A242068 * A242070 A242071 A242072

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 14 2014

Status

approved