login
This site is supported by donations to The OEIS Foundation.

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005596 Decimal expansion of Artin's constant product(1-1/(p^2-p), p=prime).
(Formerly M2608)
27
3, 7, 3, 9, 5, 5, 8, 1, 3, 6, 1, 9, 2, 0, 2, 2, 8, 8, 0, 5, 4, 7, 2, 8, 0, 5, 4, 3, 4, 6, 4, 1, 6, 4, 1, 5, 1, 1, 1, 6, 2, 9, 2, 4, 8, 6, 0, 6, 1, 5, 0, 0, 4, 2, 0, 9, 4, 7, 4, 2, 8, 0, 2, 4, 1, 7, 3, 5, 0, 1, 8, 2, 0, 4, 0, 0, 2, 8, 0, 8, 2, 3, 4, 4, 3, 0, 4, 3, 1, 7, 0, 8, 7, 2, 5, 0, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

P. Moree, The formal series Witt transform, Disc. Math., 295 (2005), 143-160. See p. 159.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

H. Cohen, High-precision calculation of Hardy-Littlewood constants, (1998). - From N. J. A. Sloane, Jan 26 2013

R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, constant A_1^(1).

Pieter Moree, Artin's primitive root conjecture - a survey, math.NT/0412262

G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]

G. Niklasch, Artin's constant

Simon Plouffe, The Artin's Constant=product(1-1/p**2-p), p=prime)

T. O. Silva, Plouffe's Inverter, The first 500 digits of Artin's constant

Eric Weisstein's World of Mathematics, Artin's constant

Eric Weisstein's World of Mathematics, Full Reptend Prime

Index entries for sequences related to Artin's conjecture

FORMULA

Equals product_{j=2..infinity} 1/Zeta(j)^A006206(j), where Zeta(.)=A013661, A002117 etc. is Riemann's zeta function. [From R. J. Mathar, Feb 14 2009]

EXAMPLE

0.37395581361920228805472805434641641511162924860615...

CROSSREFS

Cf. A048296, A065414, A001913, A001122.

Sequence in context: A131917 A019785 A074176 * A159566 A096385 A205723

Adjacent sequences:  A005593 A005594 A005595 * A005597 A005598 A005599

KEYWORD

nonn,cons,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Tom\'as Oliveira e Silva (http://www.ieeta.pt/~tos)

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

Pari code removed by D. S. McNeil, Dec 26 2010

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified April 18 11:12 EDT 2014. Contains 240707 sequences.