This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A107311 #55 Dec 29 2024 23:50:41
%S A107311 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,
%T A107311 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,
%U A107311 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
%N A107311 Decimal expansion of the solution to zeta(x) = 2.
%C A107311 From _Artur Jasinski_, Dec 21 2024: (Start)
%C A107311 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.
%C A107311 Conjecture 1: the real parts of the zeros of the prime zeta function are not greater than this constant.
%C A107311 Conjecture 2: the real parts of the zeros of the anyone subset of the prime zeta function are not greater than this constant. (End)
%D A107311 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's Composition Constant, p. 293.
%H A107311 Peter Borwein, Greg Fee, Ron Ferguson, and Alexa van der Waal, <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-16/issue-1/Zeros-of-Partial-Summs-of-the-Riemann-Zeta-Function/em/1175789799.full">Zeros of Partial Sums of the Riemann Zeta Function</a>, Experiment. Math. 16(1) (2007), pp. 21-40. See p. 25.
%H A107311 Einar Hille, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa2/aa215.pdf">A problem in "factorisatio numerorum"</a>, Acta Arithmetica, 2(1);134-144, 1936.
%H A107311 Hsien-Kuei Hwang, <a href="https://doi.org/10.1006/jnth.1999.2467">Distribution of the number of factors in random ordered factorizations of integers</a>, Journal of Number Theory 81:1 (2000), pp. 61-92.
%H A107311 M. Klazar and F. Luca, <a href="https://arxiv.org/abs/math/0505352">On the maximal order of numbers in the "factorisatio numerorum" problem</a>, arXiv:math/0505352 [math.NT], 2005-2006.
%e A107311 zeta(1.72864723899818361813510301...) = 2.
%t A107311 x /. FindRoot[ Zeta[x] == 2, {x, 2}, WorkingPrecision -> 102] // RealDigits // First (* _Jean-François Alcover_, Mar 19 2013 *)
%o A107311 (PARI) solve(X=1.5,2,zeta(X)-2)
%Y A107311 Cf. A129374, A247667.
%K A107311 nonn,cons
%O A107311 1,2
%A A107311 _Ralf Stephan_, May 20 2005