A081760 - OEIS

%I #34 Dec 20 2024 09:37:03

%S 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,

%T 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,

%U 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

%N Decimal expansion of the conjectured Landau's constant L.

%C Terms are computed using the conjectured formula.

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

%H Harry J. Smith, <a href="/A081760/b081760.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LandauConstant.html">Landau constant</a>.

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

%F Equivalently 2^(5/3) * Pi^2 / (3 * Gamma(1/3)^3). - _Vaclav Kotesovec_, Jun 10 2018

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

%t Gamma[1/3]*Gamma[5/6]/Gamma[1/6] // RealDigits[#, 10, 104]& // First (* _Jean-François Alcover_, Feb 25 2014 *)

%o (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

%K cons,nonn

%O 0,1

%A _Benoit Cloitre_, Apr 09 2003