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

0,4

Comments

Terms are computed using the conjectured formula.

Links

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

Formula

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

Example

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

Prog

(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])); }

Crossrefs

Sequence in context: A111142 A179626 A174965 * A094853 A096937 A097527

Adjacent sequences: A159668 A159669 A159670 * A159672 A159673 A159674

Keyword

nonn

Author

Harry J. Smith, Apr 19 2009

Status

approved