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A242069 Decimal expansion of the supremum of all real s such that zeta(s+i*t) = 1 for some real t. 3

%I #13 Jan 17 2020 05:43:15

%S 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,

%T 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,

%U 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

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

%H J. Arias de Reyna, J. van de Lune, <a href="http://arxiv.org/abs/1107.5134">Some bounds and limits in the theory of Riemann's zeta function.</a> arXiv:1107.5134 [math.NT]

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 28.

%F The unique solution x > 1 of the equation zeta(x) = (2^x + 1)/(2^x - 1).

%e 1.9401016837436252860174693905255488782302476074457584536287...

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

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Aug 14 2014

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