A107311 Decimal expansion of the solution to zeta(x) = 2.

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

Offset: 1

Author

Ralf Stephan, May 20 2005

Keywords

• nonn
• cons

Comments

From Artur Jasinski, Dec 21 2024: (Start)

Borwein et al. (2007) proved (Theorem 3.1) that the real parts of the zeros of the partials sums of the Riemman zeta functions are not greater than this constant.

Conjecture 1: the real parts of the zeros of the prime zeta function are not greater than this constant.

Conjecture 2: the real parts of the zeros of the anyone subset of the prime zeta function are not greater than this constant. (End)

Examples

			zeta(1.72864723899818361813510301...) = 2.
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's Composition Constant, p. 293.

Links

• Peter Borwein, Greg Fee, Ron Ferguson, and Alexa van der Waal, Zeros of Partial Sums of the Riemann Zeta Function, Experiment. Math. 16(1) (2007), pp. 21-40. See p. 25.
• Einar Hille, A problem in "factorisatio numerorum", Acta Arithmetica, 2(1);134-144, 1936.
• Hsien-Kuei Hwang, Distribution of the number of factors in random ordered factorizations of integers, Journal of Number Theory 81:1 (2000), pp. 61-92.
• M. Klazar and F. Luca, On the maximal order of numbers in the "factorisatio numerorum" problem, arXiv:math/0505352 [math.NT], 2005-2006.

Crossrefs

Cf. A129374, A247667.

Programs

Mathematica

x /. FindRoot[ Zeta[x] == 2, {x, 2}, WorkingPrecision -> 102] // RealDigits // First (* Jean-François Alcover, Mar 19 2013 *)

PARI

solve(X=1.5,2,zeta(X)-2)