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

1,2

Comments

Data taken from Alessandro Languasco and Alessandro Zaccagnini 2007.

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.

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:

A = ((13*sqrt(5)*Pi^2*exp(-gamma))/(150*log((1+sqrt(5))/2))*A340628/A340808)^(1/4).

Example

1.225238438539084580057609774749220527540595509391649938767...

Crossrefs

Cf. A077761, A083343, A091589, A138312, A161529, A230767, A238114, A271971, A340127, A340794, A340866.

Sequence in context: A133501 A254176 A371012 * A257090 A360910 A339664

Adjacent sequences: A340836 A340837 A340838 * A340840 A340841 A340842

Keyword

nonn,cons,changed

Author

Artur Jasinski, Jan 23 2021

Extensions

Last 11 digits corrected by Vaclav Kotesovec, Jan 25 2021

More digits from Vaclav Kotesovec, Jan 26 2021

Status

approved