Trott’s constant is the unique number whose digits equal its continued fraction coefficients.

Uniqueness assumes the number is expanded into a simple continued fraction, i.e. one with all numerators equal to 1.

See OEIS sequence A039662.

Trott’s constant is the unique number whose digits equal its continued fraction coefficients.

Uniqueness assumes the number is expanded into a simple continued fraction, i.e. one with all numerators equal to 1.

See OEIS sequence A039662.

I’m curious about whether a Trott’s constant exists for every number base, in particular binary.

Yeah, neither existence or uniqueness is clear to me, in any base.

John, based on what do you claim existence and/or uniqueness? Both seem to the least uncertain.

Trott proved it in 1999, but I haven’t read the proof.