|
| |
|
|
A136271
|
|
Decimal expansion of sum log(p)/p^2 over the primes p=2,3,5,7,11,...
|
|
9
|
|
|
|
4, 9, 3, 0, 9, 1, 1, 0, 9, 3, 6, 8, 7, 6, 4, 4, 6, 2, 1, 9, 7, 8, 2, 6, 2, 0, 5, 0, 5, 6, 4, 9, 1, 2, 5, 8, 0, 5, 5, 5, 8, 8, 1, 2, 6, 3, 4, 6, 4, 6, 8, 2, 9, 0, 7, 1, 3, 3, 2, 7, 1, 2, 0, 3, 2, 1, 3, 3, 6, 7, 7, 3, 6, 7, 9, 5, 7, 8, 5, 2, 0, 3, 5, 5, 0, 7, 6, 0, 0, 4, 2, 1, 8, 1, 6, 9, 3, 1, 1, 2, 4, 2, 4, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
The negative first derivative of the Prime Zeta function at 2.
|
|
|
REFERENCES
|
Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
|
|
|
LINKS
|
Table of n, a(n) for n=0..103.
Henri Cohen, High-precision computation of Hardy-Littlewood constants, preprint 1998.
Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]
R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], Table 2.
J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV
|
|
|
FORMULA
|
Equals Sum_{n >= 1} log(A000040(n))/A001248(n).
|
|
|
EXAMPLE
|
0.4930911093687...
|
|
|
MATHEMATICA
|
RealDigits[PrimeZetaP'[2], 10, 104] // First (* Jean-François Alcover, Sep 11 2015 *)
|
|
|
CROSSREFS
|
Cf. A303493-A303499.
Sequence in context: A011262 A073843 A073842 * A113970 A021957 A096301
Adjacent sequences: A136268 A136269 A136270 * A136272 A136273 A136274
|
|
|
KEYWORD
|
cons,nonn
|
|
|
AUTHOR
|
R. J. Mathar, Mar 09 2008
|
|
|
EXTENSIONS
|
Removed 6 digits where preprints disagree. Added zero to an A-number in formula. Corrected Cohen preprint year. Added 2nd link. - R. J. Mathar, Nov 27 2008
More digits from Jean-François Alcover, Sep 11 2015
|
|
|
STATUS
|
approved
|
| |
|
|
