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Search: id:A065421
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| A065421 |
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Decimal expansion of Viggo Brun's constant B, also known as the twin primes Brun's constant B_2: Sum (1/p + 1/q) as (p,q) runs through the twin primes. |
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+0
6
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| 1, 9, 0, 2, 1, 6, 0, 5, 8, 3, 1, 0, 4
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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Another constant related to the twin primes is the twin primes constant C_2 (sometimes also denoted PI_2) A005597 defined in connection with the Hardy-Littlewood conjecture concerning the distribution pi_2(x) of the twin primes.
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REFERENCES
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V. Brun, La serie 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + ... ou les denominateurs sont "nombres premiers jumeaux" est convergente ou finie, Bull Sci. Math. 43 (1919) 100-104 and 124-128.
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 14.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 133-135.
D. Shanks and J. W. Wrench, Brun's constant, Math. Comp. 28 (1974) 293-299; 28 (1974) 1183; Math. Rev. 50 #4510.
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LINKS
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C. K. Caldwell, The Prime Glossary, Brun's constant
S. R. Finch, Brun's Constant
P. Sebah, Numbers, constants and computation
T. R. Nicely, Enumeration to 10^14 of the twin primes and Brun's constant.
T. R. Nicely, Prime Constellations Research Project
Wikipedia, Brun's constant
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FORMULA
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(1/3+1/5) + (1/5+1/7) + (1/11+1/13) + ...
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EXAMPLE
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1.902160583190 +- 0.000000001175 [Nicely]
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CROSSREFS
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Cf. A005597 Decimal expansion of twin prime constant C_2 = Product_{ p prime >= 3 } (1-1/(p-1)^2).
Sequence in context: A013570 A065471 A089481 this_sequence A093767 A107091 A153790
Adjacent sequences: A065418 A065419 A065420 this_sequence A065422 A065423 A065424
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KEYWORD
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hard,nonn,cons,nice
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2000
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EXTENSIONS
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Corrected by N. J. A. Sloane (njas(AT)research.att.com), Nov 16, 2001
More terms computed by Pascal Sebah (pascal_sebah(AT)ds-fr.com), Jul 15, 2001
Further terms computed by Pascal Sebah (psebah(AT)yahoo.fr), Aug 22 2002
Commented and edited by Daniel Forgues (squid(AT)zensearch.com), Jul 28 2009
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