%I #25 Jan 25 2024 02:45:21
%S 7,3,0,7,6,2,9,6,9,4,0,1,4,3,8,4,9,8,7,2,6,0,3,6,7,3,1,3,0,7,7,1,4,6,
%T 3,9,5,2,8,0,1,1,6,0,5,0,7,9,3,7,4,4,7,0,0,7,1,3,2,5,3,5,6,6,1,6,9,0,
%U 7,6,3,0,6,7,8,4,8,5,5,6,8,2,6,7,0,7,0,0,3,7,1,4,0,9,8,7,9,0,3,2,8,8,6,5
%N Decimal expansion of zeta(3)/zeta(2).
%C Three positive integers b, c, m are randomly selected (with replacement) from {1, 2, ..., n}. Let P(n) be the probability that the congruence b * x == c (mod m) has a solution. zeta(3)/zeta(2) is the limit of P(n) as n goes to infinity.
%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 154.
%F Equals A002117/A013661.
%F Equals Product_{p prime} (1 - 1/(p^2 + p + 1)). - _Amiram Eldar_, Jun 11 2023
%F Equals Sum_{k>=1} A023900(k)/k^3. - _Amiram Eldar_, Jan 25 2024
%e 0.73076296940143849872603673130771463952801160507937...
%t Drop[Flatten[RealDigits[N[Zeta[3]/Zeta[2], 75]]], -2]
%o (PARI) zeta(3)/zeta(2) \\ _Charles R Greathouse IV_, Apr 20 2016
%Y Cf. A002117, A013661, A023900, A222056.
%K nonn,cons
%O 0,1
%A _Geoffrey Critzer_, Jan 18 2015