login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339083 Decimal expansion of Sum_{k>=0} (zeta(4*k+2)-1). 2
6, 6, 3, 3, 3, 7, 0, 2, 3, 7, 3, 4, 2, 9, 0, 5, 8, 7, 0, 6, 7, 0, 2, 5, 3, 9, 7, 3, 7, 5, 0, 0, 0, 2, 4, 5, 2, 2, 2, 8, 2, 8, 1, 3, 3, 2, 0, 1, 9, 0, 8, 3, 3, 2, 7, 8, 7, 5, 3, 1, 2, 4, 2, 1, 9, 5, 0, 7, 7, 1, 2, 3, 9, 5, 9, 1, 5, 5, 0, 1, 0, 8, 7, 1, 7, 8, 2, 7, 7, 5, 8, 7, 9, 6, 9, 7, 7, 4, 5, 9, 3, 8, 2, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Sum_{k>=1} zeta(4*k)-1 see A256919.
Sum_{k>=1} zeta(4*k+1)-1 see A339097.
Sum_{k>=0} zeta(4*k+3)-1 see A338858.
For additional comments and generalization see A339604.
LINKS
FORMULA
Equals Sum_{k>=2} k^2/(k^4-1).
Equals -1/8 + Pi*coth(Pi)/4 = -1/8 + A338815 = 3/4 - A256919.
EXAMPLE
0.663337023734290587067025397375...
MATHEMATICA
RealDigits[N[Sum[Zeta[4 n + 2] - 1, {n, 0, Infinity}], 105]][[1]]
PROG
(PARI) suminf(k=0, zeta(4*k+2)-1) \\ Michel Marcus, Dec 24 2020
CROSSREFS
Sequence in context: A011484 A146761 A010498 * A240502 A112112 A193085
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 24 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)