A159671 Continued fraction expansion of Landau's constant L.

0, 1, 1, 5, 3, 1, 1, 2, 1, 1, 6, 3, 1, 8, 11, 2, 1, 1, 27, 4, 1, 1, 2, 3, 3, 3, 1, 1, 4, 1, 3, 11, 1, 1, 3, 1, 1, 1, 2, 3, 26, 10, 3, 1, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 7, 4, 1, 2, 2, 1, 1, 6, 2, 10, 2, 6, 6, 1, 3, 1, 2, 4, 2, 1, 2, 5, 1, 1, 1, 1, 1, 4, 11, 9, 1, 1, 1, 2, 1, 2, 5, 2, 4, 1, 48, 1, 8, 1, 8, 7, 1, 3

Offset: 0

Author

Harry J. Smith, Apr 19 2009

Keywords

• nonn

Comments

Terms are computed using the conjectured formula.

Examples

			L = 0.543258965342976706952728...= 0 + 1/(1 + 1/(1 + 1/(5 + 1/(3 + ...)))).
		

Links

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

Programs

PARI

{ default(realprecision, 1080); x=contfrac(gamma(1/3)*gamma(5/6)/gamma(1/6)); d=0; for (n=0, 1000, write("b159671.txt", n, " ", x[n+1])); }

Formula

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