A157291 Decimal expansion of Zeta(5)/Zeta(10).

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Comments

The product_{p = primes = A000040} (1+1/p^5), the fifth-power analog to A082020.

Examples

			1.035897477277500224... = (1+1/2^5)*(1+1/3^5)*(1+1/5^5)*(1+1/7^5)*...
		

Crossrefs

Cf. A013663, A013668, A050997, A082020.

Cf. A005117, A113850.

Programs

Maple

evalf(Zeta(5)/Zeta(10)) ;

Mathematica

RealDigits[Zeta[5]/Zeta[10],10,120][[1]] (* Harvey P. Dale, Apr 06 2013 *)

Formula

Equals A013663/A013668 = Product_{i>=1} (1+1/A050997(i)).

Equals Sum_{k>=1} 1/A005117(k)^5 = 1 + Sum_{k>=1} 1/A113850(k). - Amiram Eldar, May 22 2020

Equals 93555 * zeta(5) / Pi^10. - Vaclav Kotesovec, May 22 2020