A339925 Decimal expansion of 105*zeta(3)/Pi^4.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..104.

H. Riesel and R. C. Vaughan, On sums of primes, Ark. Mat., Volume 21, Number 1-2 (1983), 45-74 (p. 47).

Formula

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

Equals A082695*2/3.

Equals Sum_{k>=1} A001615(k)/k^4. - Amiram Eldar, Jan 25 2024

Example

1.295730957880506136704713575049842291458572334511870477351090459267...

Mathematica

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

Prog

(PARI) prodeulerrat(1+1/(p*(p-1)), 1, 3) \\ Hugo Pfoertner, Dec 23 2020

Crossrefs

Cf. A002117, A001615, A005597, A082695.

Sequence in context: A051491 A339204 A253169 * A171052 A021342 A069857

Adjacent sequences: A339922 A339923 A339924 * A339926 A339927 A339928

Keyword

nonn,cons

Author

Artur Jasinski, Dec 23 2020

Status

approved