A Trott constant is a real number whose decimal digits are equal to the terms of
its continued fraction.

The first Trott constant
(OEIS A039662) was discovered by M. Trott
in 1999. While it is theoretically possible to extend this sequence arbitrarily far,
it is impractical to do so since agreement after 639 terms is so close that the number
of consecutive term pairs of "90" that would immediately follow the 639th
term would exceed
(Schoenfield 2010).

The second Trott constant is the number (OEIS A091694;
Trott 2004, p. 70) which is equal to its non-simple continued
fraction

The third Trott constant is the number (OEIS A113307;
M. Trott, pers. comm., Oct. 24, 2005) which is equal to its non-simple
continued fraction

Very little seems to be known about the existence and uniqueness of such numbers.