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

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085964 Decimal expansion of the prime zeta function at 4. 15
0, 7, 6, 9, 9, 3, 1, 3, 9, 7, 6, 4, 2, 4, 6, 8, 4, 4, 9, 4, 2, 6, 1, 9, 2, 9, 5, 9, 3, 3, 1, 5, 7, 8, 7, 0, 1, 6, 2, 0, 4, 1, 0, 5, 9, 7, 1, 4, 8, 4, 3, 1, 9, 0, 2, 6, 4, 9, 3, 8, 0, 0, 8, 8, 5, 9, 2, 1, 6, 5, 7, 0, 4, 8, 7, 5, 6, 4, 2, 0, 6, 5, 1, 0, 3, 3, 3, 1, 0, 6, 7, 8, 5, 3, 9, 6, 2, 8, 9, 5, 4, 2, 0, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

H. Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint.

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

Eric Weisstein's World of Mathematics, Prime Zeta Function

FORMULA

P(4) = Sum_{p prime>=2} 1/p^4 = Sum_{n=1..inf} mobius(n)*log(zeta(4*n))/n

Equals A086034 + A085993 + 1/16. [From R. J. Mathar, Jul 22 2010]

EXAMPLE

0.0769931397642468449426...

MAPLE

A085964:= proc(i) print(evalf(add(1/ithprime(k)^4, k=1..i), 100)); end:

A085964(100000); Paolo P. Lava, May 29 2012

MATHEMATICA

Clear[s]; s[n_] := s[n] = Sum[ MoebiusMu[k]*Log[Zeta[4*k]]/k, {k, 1, n}] // RealDigits[#, 10, 104]& // First // Prepend[#, 0]&; s[100]; s[n = 200]; While[s[n] != s[n - 100], n = n + 100]; s[n] (* Jean-Fran├žois Alcover, Feb 14 2013 *)

CROSSREFS

Cf. A085548, A085541, A085965 - A085969,

Sequence in context: A201766 A197588 A021569 * A082121 A215338 A176414

Adjacent sequences:  A085961 A085962 A085963 * A085965 A085966 A085967

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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified April 21 02:07 EDT 2014. Contains 240824 sequences.