A343308 Decimal expansion of 1/zeta(5).

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

Offset: 0

Author

Karl-Heinz Hofmann, Apr 11 2021

Keywords

• nonn
• cons

Comments

Decimal expansion of 1/zeta(5), the inverse of A013663.

The Riemann zeta(5) function has no known closed-form formula. It is not known if this value is irrational, let alone transcendental.

Examples

			0.9643873404292624591264365884449845712376504613516...
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
• OEIS Wiki, Riemann Zeta function.

Crossrefs

Cf. A013663, A059956, A088453, A215267.

Programs

Mathematica

RealDigits[1/Zeta[5], 10, 100][[1]] (* Amiram Eldar, Apr 11 2021 *)

PARI

1/zeta(5) \\ Michel Marcus, Aug 29 2021

Formula

Equals 1/A013663.

Equals Sum_{k>=1} mobius(k) / k^5. - Sean A. Irvine, Aug 28 2021

Equals Product_{p prime} (1 - 1/p^5). - Amiram Eldar, Jun 01 2023