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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

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)
34
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, 8, 9, 8, 1, 6, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

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

Ivan Cherednik, A note on Artin's constant, arXiv:0810.2325 [math.NT], 2008.

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

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, arXiv:math/0412262 [math.NT], 204-2012.

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

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

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

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. - R. J. Mathar, Feb 14 2009

EXAMPLE

0.37395581361920228805472805434641641511162924860615...

MATHEMATICA

a = Exp[-NSum[ (LucasL[n] - 1)/n PrimeZetaP[n], {n, 2, Infinity}, PrecisionGoal -> 500, WorkingPrecision -> 500, NSumTerms -> 100000]]; RealDigits[a, 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 taken from Mathematica's Help file on PrimeZetaP *)

PROG

(PARI) prodinf(n=2, 1/zeta(n)^(sumdiv(n, d, moebius(n/d)*(fibonacci(d-1)+fibonacci(d+1)))/n)) \\ Charles R Greathouse IV, Aug 27 2014

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

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Tomás Oliveira e Silva (http://www.ieeta.pt/~tos)

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 10:15 EST 2016. Contains 278971 sequences.