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

1,2

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)

References

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

Links

Table of n, a(n) for n=1..102.

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.

Example

zeta(1.72864723899818361813510301...) = 2.

Mathematica

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

Prog

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

Crossrefs

Cf. A129374, A247667.

Sequence in context: A198564 A388507 A259072 * A363538 A048836 A198673

Adjacent sequences: A107308 A107309 A107310 * A107312 A107313 A107314

Keyword

nonn,cons

Author

Ralf Stephan, May 20 2005

Status

approved