|
| |
|
|
A085541
|
|
Decimal expansion of the prime zeta function at 3.
|
|
14
|
|
|
|
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]]
(* From 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 (hillcino368(AT)gmail.com), Jul 02 2003
|
|
|
EXTENSIONS
|
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003
|
|
|
STATUS
|
approved
|
| |
|
|
