login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221711 Decimal expansion of sum 1/(p^2 * log p) over the primes p=2,3,5,7,11,... 3
5, 0, 7, 7, 8, 2, 1, 8, 7, 8, 5, 9, 1, 9, 9, 3, 1, 8, 7, 7, 4, 3, 7, 5, 1, 0, 3, 7, 9, 4, 7, 0, 5, 5, 7, 0, 4, 6, 6, 9, 7, 3, 6, 7, 1, 7, 0, 4, 3, 2, 0, 6, 9, 8, 5, 7, 3, 9, 8, 0, 2, 1, 2, 3, 4, 8, 2, 7, 2, 8, 6, 9, 0, 1, 3, 7, 4, 1, 3, 1, 1, 5, 1, 0, 4, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..86.

Karim Belabas, Henri Cohen, Computation of sum_{p prime} 1/(p^s log(p)), PARI/GP script, 2020.

H. Cohen, High-precision calculation of Hardy-Littlewood constants, (1998).

Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]

R. J. Mathar, Twenty digits of some integrals of the prime zeta function, arXiv:0811.4739, Section 2.4.

EXAMPLE

0.50778218785919931877437510379470557...

PROG

(PARI) See Belabas, Cohen link. Run as SumEulerlog(2) after setting the required precision.

CROSSREFS

Cf. A137245.

Sequence in context: A021201 A112254 A180660 * A200400 A190147 A108745

Adjacent sequences:  A221708 A221709 A221710 * A221712 A221713 A221714

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Jan 26 2013

EXTENSIONS

More terms from Hugo Pfoertner, Feb 01 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 16:27 EST 2021. Contains 340363 sequences. (Running on oeis4.)