A342683 - OEIS

%I #21 Jun 01 2023 01:56:09

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

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

%U 8,5,7,4,6,2,0,9,4,0,4,5,4,2,6,5,1,5,9

%N Decimal expansion of 1/zeta(8).

%C 1/zeta(8) is the probability that 8 randomly selected numbers will be coprime.

%H Karl-Heinz Hofmann, <a href="/A342683/b342683.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals 1/A013666 = 9450/Pi^8.

%F From _Amiram Eldar_, Jun 01 2023: (Start)

%F Equals Sum_{k>=1} mu(k)/k^8, where mu is the Möbius function (A008683).

%F Equals Product_{p prime} (1 - 1/p^8). (End)

%e 0.9959392011255151468348364728055453240050227784589...

%p evalf(9450/Pi^8,100) ; # _R. J. Mathar_, Jun 04 2021

%t RealDigits[1/Zeta[8], 10, 100][[1]] (* _Amiram Eldar_, May 18 2021 *)

%o (PARI) 1/zeta(8)

%Y Cf. A008683, A059956, A215267, A343359, A013666.

%K nonn,cons

%O 0,1

%A _Karl-Heinz Hofmann_, May 18 2021