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A085541 Decimal expansion of the prime zeta function at 3. 15
1, 7, 4, 7, 6, 2, 6, 3, 9, 2, 9, 9, 4, 4, 3, 5, 3, 6, 4, 2, 3, 1, 1, 3, 3, 1, 4, 6, 6, 5, 7, 0, 6, 7, 0, 0, 9, 7, 5, 4, 1, 2, 1, 2, 1, 9, 2, 6, 1, 4, 9, 2, 8, 9, 8, 8, 8, 6, 7, 2, 0, 1, 6, 7, 0, 1, 6, 3, 1, 5, 8, 9, 5, 2, 8, 1, 2, 9, 5, 8, 7, 6, 3, 5, 6, 3, 4, 2, 0, 0, 5, 3, 6, 9, 7, 2, 5, 6, 0, 5, 4, 6, 7, 9, 1 (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

Gerhard Niklasch and Pieter Moree, Some number-theoretical constants [Cached copy]

Eric Weisstein's World of Mathematics, Prime Zeta Function

FORMULA

P(3) = Sum_{p prime>=2} 1/p^3 = Sum_{n=1..inf} mobius(n)*log(zeta(3*n))/n - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003

Equals A086033 + A085992 +1/8. [From R. J. Mathar, Jul 22 2010]

EXAMPLE

0.1747626392994435364231...

MAPLE

A085541:= proc(i) print(evalf(add(1/ithprime(k)^3, k=1..i), 100)); end:

A085541(100000); # Paolo P. Lava, May 29 2012

MATHEMATICA

(* If Mathematica version >= 7.0 then RealDigits[PrimeZetaP[3]//N[#, 105]&][[1]] else : *) m = 200; $MaxExtraPrecision = 200; PrimeZetaP[s_] := NSum[MoebiusMu[k]*Log[Zeta[k*s]]/k, {k, 1, m}, AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m]; RealDigits[PrimeZetaP[3]][[1]][[1 ;; 105]] (* Jean-François Alcover, Jun 24 2011 *)

PROG

(PARI) recip3(n) = { v=0; p=1; forprime(y=2, n, v=v+1./y^3; ); print(v) }

CROSSREFS

Cf. A085548, A085964 (at 4).

Sequence in context: A153186 A085469 A050996 * A133055 A195384 A021576

Adjacent sequences:  A085538 A085539 A085540 * A085542 A085543 A085544

KEYWORD

easy,nonn,cons

AUTHOR

Cino Hilliard, Jul 02 2003

EXTENSIONS

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

STATUS

approved

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Last modified August 22 03:58 EDT 2014. Contains 245921 sequences.