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A340866 Decimal expansion of the Mertens constant C(5,4). 5
1, 2, 9, 9, 3, 6, 4, 5, 4, 7, 9, 1, 4, 9, 7, 7, 9, 8, 8, 1, 6, 0, 8, 4, 0, 0, 1, 4, 9, 6, 4, 2, 6, 5, 9, 0, 9, 5, 0, 2, 5, 7, 4, 9, 7, 0, 4, 0, 8, 3, 2, 9, 6, 6, 2, 0, 1, 6, 7, 8, 1, 7, 7, 0, 3, 1, 2, 9, 2, 2, 8, 7, 8, 8, 3, 5, 4, 4, 0, 3, 5, 8, 0, 6, 4, 7, 6, 4, 7, 6, 9, 7, 6, 7, 6, 5, 7, 9, 3, 0, 2, 9, 4, 0, 9, 3, 5, 5, 0, 7, 6, 3, 7, 3, 7, 4, 3, 2, 1, 5, 4, 2, 7, 1, 1, 9, 0, 7, 0, 3, 3, 5, 4, 0, 9, 8, 6, 0, 6, 1, 4, 5, 0, 3, 2, 9, 7, 2, 5, 8, 8, 4, 3, 6, 1, 1, 5, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Data taken from Alessandro Languasco and Alessandro Zaccagnini 2007 p. 4.

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..497

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). [in this table on page 4, the last correct digit is a(108), beyond the level there certified. - Vaclav Kotesovec, Jan 26 2021]

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

Equals A340839*5^(1/4)*sqrt(A340004/(2*A340127)).

Equals (13*Pi^2/(24*sqrt(5)*exp(gamma)*log((1+sqrt(5))/2))*A340629/A340809)^(1/4). - Vaclav Kotesovec, Jan 25 2021

EXAMPLE

1.299364547914977988160840014964265909502574970408329662016...

MATHEMATICA

(* Using Vaclav Kotesovec's function Z from A301430. *)

$MaxExtraPrecision = 1000; digits = 121;

digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][[1]];

digitize[(13*Pi^2 / (24*Sqrt[5] * Exp[EulerGamma] * Log[(1 + Sqrt[5])/2]) * Z[5, 1, 2]^2 / (Z[5, 1, 4] * Z[5, 4, 4]))^(1/4)]

CROSSREFS

Cf. A340004, A340127, A340839, A340711.

Sequence in context: A023400 A153637 A137618 * A021338 A021889 A309927

Adjacent sequences:  A340863 A340864 A340865 * A340867 A340868 A340869

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Jan 24 2021

EXTENSIONS

Corrected by Vaclav Kotesovec, Jan 25 2021

More digits from Vaclav Kotesovec, Jan 26 2021

STATUS

approved

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Last modified September 18 01:03 EDT 2021. Contains 347498 sequences. (Running on oeis4.)