A253905 Decimal expansion of zeta(3)/zeta(2).

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, 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, 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

Offset: 0

Author

Geoffrey Critzer, Jan 18 2015

Keywords

• nonn
• cons

Comments

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.

Examples

			0.73076296940143849872603673130771463952801160507937...
		

Links

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 154.

Crossrefs

Cf. A002117, A013661, A023900, A222056.

Programs

Mathematica

Drop[Flatten[RealDigits[N[Zeta[3]/Zeta[2], 75]]], -2]

PARI

zeta(3)/zeta(2) \\ Charles R Greathouse IV, Apr 20 2016

Formula

Equals A002117/A013661.

Equals Product_{p prime} (1 - 1/(p^2 + p + 1)). - Amiram Eldar, Jun 11 2023

Equals Sum_{k>=1} A023900(k)/k^3. - Amiram Eldar, Jan 25 2024