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An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

The Leibniz harmonic triangle is the number triangle given by 1/11/2 1/21/3 1/6 1/31/4 1/(12) 1/(12) 1/41/5 1/(20) 1/(30) 1/(20) 1/5 (1) (OEIS A003506), where each fraction ...

A near noble number is a real number 0<nu<1 whose continued fraction is periodic, and the periodic sequence of terms is composed of a string of p-1 1s followed by an integer ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

The "ternary" Champernowne constant can be defined by concatenating the ternary representations of the integers C_3 = 0.(1)(2)(1,0)(1,1)(1,2)(2,0)..._3 (1) = ...

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 ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

The constant lambda=1.303577269034296... (OEIS A014715) giving the asymptotic rate of growth Clambda^n of the number of digits in the nth term of the look and say sequence, ...