A340839 Decimal expansion of Mertens constant C(5,1).
1, 2, 2, 5, 2, 3, 8, 4, 3, 8, 5, 3, 9, 0, 8, 4, 5, 8, 0, 0, 5, 7, 6, 0, 9, 7, 7, 4, 7, 4, 9, 2, 2, 0, 5, 2, 7, 5, 4, 0, 5, 9, 5, 5, 0, 9, 3, 9, 1, 6, 4, 9, 9, 3, 8, 7, 6, 7, 3, 3, 3, 6, 4, 4, 3, 0, 2, 6, 7, 3, 1, 4, 2, 9, 6, 4, 4, 1, 7, 6, 1, 9, 2, 7, 3, 8, 4, 1, 6, 1, 9, 5, 6, 2, 7, 3, 6, 5, 2, 9, 5, 6, 6, 7, 5, 6, 7, 9, 6, 2, 7, 9, 0, 4, 2, 5, 9, 6, 3, 2, 4, 0, 2, 1, 1, 0, 0, 4, 8, 0, 7, 6, 8, 7, 9, 3, 3, 7, 6, 5, 5, 0, 4, 6, 7, 8, 7, 4, 2, 6, 0, 3, 2, 5, 0, 1, 1, 5, 3
Offset: 1
Examples
1.225238438539084580057609774749220527540595509391649938767...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.2 Meissel-Mertens constants (pp. 94-95)
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..499
- Alessandro Languasco and Alessandro Zaccagnini, On the constant in the Mertens product for arithmetic progressions. II: Numerical values, Math. Comp. 78 (2009), 315-326.
- Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants - more than 100 correct digits, (2007), 1-134 (digital data relative to the previous paper). [in this table on page 4, the last correct digit is a(109), beyond the level there certified. - _Vaclav Kotesovec_, Jan 26 2021]
- Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants mod q; 3 <= q <= 100, (2007) (GP-PARI procedure 100 digits accuracy).
- Alessandro Languasco and Alessandro Zaccagnini, On the constant in the Mertens product for arithmetic progressions. I. Identities., Funct. Approx. Comment. Math. Volume 42, Number 1 (2010), 17-27.
- For other links see A340711.
Crossrefs
Formula
A = C(5,1)=1.225238438539084580057609774749220527540595509391649938767...
B = C(5,2)=0.546975845411263480238301287430814037751996324100819295153...
C = C(5,3)=0.805951040448267864057376860278430932081288114939010897934...
D = C(5,4)=1.299364547914977988160840014964265909502574970408329662016...
A*B*C*D = 0.70182435445860646228... = (5/4)*exp(-gamma), where gamma is the Euler-Mascheroni constant A001620.
Formula from the article by Languasco and Zaccagnini, 2010, p.9:
Extensions
Last 11 digits corrected by Vaclav Kotesovec, Jan 25 2021
More digits from Vaclav Kotesovec, Jan 26 2021
Comments