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A085964 Decimal expansion of the prime zeta function at 4. 16
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

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 *)

RealDigits[ PrimeZetaP[ 4], 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 *)

CROSSREFS

Cf. A085548, A085541, A085965, A085966, A085967, A085968, 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

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Last modified December 2 15:01 EST 2016. Contains 278678 sequences.