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.
6 thoughts on “Trott’s constant”
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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.
The link suggests the digit expansion and the continued fraction only agree for a finite number of terms. Other numbers have that property, so uniqueness could only hold if claim is they agree for all terms.
It seems nothing was provided until 2021. See https://math.stackexchange.com/questions/2106795/how-are-trott-constants-found-are-there-mathematical-results