A081760 Decimal expansion of the conjectured Landau's constant L.

5, 4, 3, 2, 5, 8, 9, 6, 5, 3, 4, 2, 9, 7, 6, 7, 0, 6, 9, 5, 2, 7, 2, 8, 2, 9, 5, 3, 0, 0, 6, 1, 3, 2, 3, 1, 1, 3, 8, 8, 6, 3, 2, 9, 3, 7, 5, 8, 3, 5, 6, 9, 8, 8, 9, 5, 5, 7, 3, 2, 5, 6, 9, 1, 0, 0, 4, 3, 4, 6, 8, 7, 0, 1, 5, 3, 0, 7, 8, 3, 7, 3, 1, 2, 8, 5, 2, 1, 2, 7, 1, 0, 2, 2, 5, 9, 7, 1, 0, 8, 5, 7, 5, 3

Offset

0,1

Comments

Terms are computed using the conjectured formula.

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 7.1, p. 456.

Links

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

Eric Weisstein's World of Mathematics, Landau constant.

Formula

It is conjectured that L = 0.5432589653429767... = Gamma(1/3)*Gamma(5/6)/Gamma(1/6).

Equivalently 2^(5/3) * Pi^2 / (3 * Gamma(1/3)^3). - Vaclav Kotesovec, Jun 10 2018

Equivalently Product_{k>=0} (18*k^2 + 21*k + 3)/(18*k^2 + 21*k + 5). - Antonio Graciá Llorente, May 02 2024

Mathematica

Gamma[1/3]*Gamma[5/6]/Gamma[1/6] // RealDigits[#, 10, 104]& // First (* Jean-François Alcover, Feb 25 2014 *)

Prog

(PARI) { default(realprecision, 1080); x=gamma(1/3)*gamma(5/6)/gamma(1/6); d=0; for (n=0, 1000, x=(x-d)*10; d=floor(x); write("b081760.txt", n, " ", d)); } \\ Harry J. Smith, Apr 13 2009

Crossrefs

Sequence in context: A003561 A201327 A329457 * A261218 A094097 A145330

Adjacent sequences: A081757 A081758 A081759 * A081761 A081762 A081763

Keyword

cons,nonn

Author

Benoit Cloitre, Apr 09 2003

Status

approved