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A343308 Decimal expansion of 1/zeta(5).

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