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A085965 Decimal expansion of the prime zeta function at 5. 7
0, 3, 5, 7, 5, 5, 0, 1, 7, 4, 8, 3, 9, 2, 4, 2, 5, 7, 1, 3, 2, 8, 1, 8, 2, 4, 2, 5, 3, 8, 8, 5, 5, 7, 1, 1, 1, 3, 1, 6, 9, 7, 2, 7, 6, 7, 2, 6, 6, 5, 1, 3, 3, 1, 6, 9, 0, 0, 9, 2, 6, 7, 4, 8, 2, 3, 9, 7, 5, 8, 3, 4, 2, 7, 4, 7, 2, 7, 9, 3, 1, 3, 6, 6, 0, 7, 2, 8, 0, 6, 4, 7, 0, 3, 7, 6, 7, 9, 5, 0, 8, 9, 6, 3, 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(5) = Sum_{p prime>=2} 1/p^5 = Sum_{n=1..inf} mobius(n)*log(zeta(5*n))/n.

Equals 1/2^5 +A085994 +A086035. - R. J. Mathar, Jul 14 2012

EXAMPLE

0.0357550174839242571328...

MAPLE

A085965:= proc(i) print(evalf(add(1/ithprime(k)^5, k=1..i), 100)); end:

A085965(100000); # Paolo P. Lava, May 29 2012

MATHEMATICA

s[n_] := s[n] = Sum[ MoebiusMu[k]*Log[Zeta[5*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-François Alcover, Feb 14 2013, from 1st formula *)

RealDigits[ PrimeZetaP[ 5], 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 *)

CROSSREFS

Cf. A085548, A085541, A085964.

Sequence in context: A064537 A023899 A254863 * A238205 A186702 A141710

Adjacent sequences:  A085962 A085963 A085964 * A085966 A085967 A085968

KEYWORD

cons,nonn

AUTHOR

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

STATUS

approved

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Last modified December 5 16:07 EST 2016. Contains 278770 sequences.