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

Author

Jean-François Alcover, Aug 14 2014

Keywords

• nonn
• cons
• easy

Examples

			2.81301402025289836752725540121668696384614056054026221526643874...
		

Links

• 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.

Crossrefs

Cf. A242069.

Programs

Mathematica

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

Formula

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