%I #31 Jun 01 2023 01:55:54
%S 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,
%T 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,
%U 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
%N Decimal expansion of 1/zeta(5).
%C Decimal expansion of 1/zeta(5), the inverse of A013663.
%C The Riemann zeta(5) function has no known closed-form formula. It is not known if this value is irrational, let alone transcendental.
%H Karl-Heinz Hofmann, <a href="/A343308/b343308.txt">Table of n, a(n) for n = 0..10000</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Riemann_%CE%B6_function">Riemann Zeta function</a>.
%F Equals 1/A013663.
%F Equals Sum_{k>=1} mobius(k) / k^5. - _Sean A. Irvine_, Aug 28 2021
%F Equals Product_{p prime} (1 - 1/p^5). - _Amiram Eldar_, Jun 01 2023
%e 0.9643873404292624591264365884449845712376504613516...
%t RealDigits[1/Zeta[5], 10, 100][[1]] (* _Amiram Eldar_, Apr 11 2021 *)
%o (PARI) 1/zeta(5) \\ _Michel Marcus_, Aug 29 2021
%Y Cf. A013663, A059956, A088453, A215267.
%K nonn,cons
%O 0,1
%A _Karl-Heinz Hofmann_, Apr 11 2021