login
Decimal expansion of 105*zeta(3)/Pi^4.
3

%I #16 Jan 25 2024 02:46:47

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

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

%U 2,3,3,0,0,4,6,2,3,6,9,3,6,9,2,9,8,7,8,6,0,6,7,2,1,4,0,7,4,2,0,0,7,1,2,7

%N Decimal expansion of 105*zeta(3)/Pi^4.

%H H. Riesel and R. C. Vaughan, <a href="https://doi.org/10.1007/BF02384300">On sums of primes</a>, Ark. Mat., Volume 21, Number 1-2 (1983), 45-74 (p. 47).

%F Equals Product_{p>=3} 1+1/(p*(p-1)) where p are successive odd primes.

%F Equals A082695*2/3.

%F Equals Sum_{k>=1} A001615(k)/k^4. - _Amiram Eldar_, Jan 25 2024

%e 1.295730957880506136704713575049842291458572334511870477351090459267...

%t RealDigits[N[105 Zeta[3]/Pi^4, 105]][[1]]

%o (PARI) prodeulerrat(1+1/(p*(p-1)),1,3) \\ _Hugo Pfoertner_, Dec 23 2020

%Y Cf. A002117, A001615, A005597, A082695.

%K nonn,cons

%O 1,2

%A _Artur Jasinski_, Dec 23 2020