login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085994 Decimal expansion of the Riemann zeta prime modulo function at 5 for primes of the form 4k+3. 5
0, 0, 4, 1, 8, 1, 5, 4, 3, 4, 4, 9, 7, 0, 2, 4, 5, 9, 6, 1, 4, 3, 0, 6, 3, 3, 4, 3, 5, 2, 8, 1, 4, 6, 2, 7, 1, 5, 4, 2, 5, 4, 5, 4, 3, 0, 2, 0, 8, 5, 2, 1, 8, 4, 3, 5, 3, 3, 9, 6, 7, 4, 1, 2, 5, 1, 3, 4, 5, 5, 7, 4, 1, 5, 9, 9, 5, 0, 9, 1, 9, 5, 0, 5, 6, 7, 2, 7, 4, 9, 3, 5, 2, 6, 8, 9, 5, 7, 6, 9, 2, 2, 8, 3, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..104.

P. Flajolet and I. Vardi, Zeta Function Expansions of Classical Constants, Unpublished manuscript. 1996.

X. Gourdon and P. Sebah, Some Constants from Number theory.

FORMULA

Zeta_R(5) = Sum_{r prime=3 mod 4} 1/r^5 = (1/2)*Sum_{n=0..inf} mobius(2*n+1)*log(b((2*n+1)*5))/(2*n+1), where b(x)=(1-2^(-x))*zeta(x)/L(x) and L(x) is the Dirichlet Beta function.

EXAMPLE

0.0041815434497024...

MATHEMATICA

b[x_] = (1 - 2^(-x))*(Zeta[x]/DirichletBeta[x]); $MaxExtraPrecision = 200; m = 40; Join[{0, 0}, RealDigits[(1/2)*NSum[MoebiusMu[2n + 1]* Log[b[(2n + 1)*5]]/(2n + 1), {n, 0, m}, AccuracyGoal -> 120, NSumTerms -> m, PrecisionGoal -> 120, WorkingPrecision -> 120] ][[1]]][[1 ;; 105]] (* Jean-Fran├žois Alcover, Jun 22 2011, updated Mar 14 2018 *)

CROSSREFS

Cf. A085991, A085992, A085993.

Sequence in context: A297402 A239666 A101512 * A179836 A040019 A240776

Adjacent sequences:  A085991 A085992 A085993 * A085995 A085996 A085997

KEYWORD

cons,nonn

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 16 03:17 EST 2019. Contains 319184 sequences. (Running on oeis4.)