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!)
A085993 Decimal expansion of the Riemann zeta prime modulo function at 4 for primes of the form 4k+3. 6
0, 1, 2, 8, 4, 3, 5, 5, 5, 6, 1, 0, 2, 1, 7, 5, 5, 3, 3, 4, 3, 6, 2, 2, 5, 3, 4, 6, 1, 9, 5, 1, 9, 0, 1, 8, 3, 3, 4, 5, 5, 3, 1, 4, 9, 7, 7, 1, 0, 0, 8, 4, 5, 8, 1, 1, 7, 1, 2, 6, 4, 8, 3, 0, 2, 0, 4, 1, 6, 0, 7, 2, 9, 6, 9, 6, 8, 6, 4, 1, 7, 5, 7, 3, 5, 3, 1, 2, 7, 8, 6, 9, 8, 1, 7, 3, 2, 5, 3, 0, 7, 8, 0, 9, 9 (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P. Flajolet and I. Vardi, Zeta Function Expansions of Classical Constants, Unpublished manuscript. 1996.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(4) = Sum_{r prime=3 mod 4} 1/r^4 = (1/2)*Sum_{n=0..inf} mobius(2*n+1)*log(b((2*n+1)*4))/(2*n+1), where b(x)=(1-2^(-x))*zeta(x)/L(x) and L(x) is the Dirichlet Beta function.

EXAMPLE

0.0128435556102175...

MATHEMATICA

b[x_] = (1 - 2^(-x))*(Zeta[x]/DirichletBeta[x]); $MaxExtraPrecision = 200; m = 40; Prepend[ RealDigits[ (1/2)*NSum[ MoebiusMu[2n+1]* Log[b[(2n+1)*4]]/(2n+1), {n, 0, m}, AccuracyGoal -> 120, NSumTerms -> m, PrecisionGoal -> 120, WorkingPrecision -> 120] ][[1]], 0][[1 ;; 105]] (* Jean-Fran├žois Alcover, Jun 22 2011, updated Mar 14 2018 *)

CROSSREFS

Cf. A085991, A085992.

Sequence in context: A152626 A093823 A088154 * A010595 A109594 A254446

Adjacent sequences:  A085990 A085991 A085992 * A085994 A085995 A085996

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 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)