Soldner's constant continued fraction is the continued fraction of Soldner's constant 
, given by [1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2,
...] (OEIS A099803).
The positions at which the numbers 1, 2, ... occur in the continued fraction are 0, 1, 6, 2, 47, 28, 21, 107, 114, ....
The high-water marks are 1, 2, 4, 47, 99, 294, 527, 616, 1152, ... (OEIS A099804), which occur at positions 0, 1, 2, 11, 69, 125, 201, 584, 1591, 2435, ... (OEIS A229230).
Let the continued fraction of 
be denoted ![[a_0;a_1,a_2,...]](/images/equations/SoldnersConstantContinuedFraction/Inline3.svg)
and let the denominators
of the convergents be denoted 
, 
,
..., 
. The plots above show successive values of 
, 
, 
, which appear to converge
to Khinchin's constant (left figure) and 
, which appear to converge
to the Lévy constant (right figure), although
neither of these limits has been rigorously established.
