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For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

Legion's number of the first kind is defined as L_1 = 666^(666) (1) = 27154..._()_(1871 digits)98016, (2) where 666 is the beast number. It has 1881 decimal digits. Legion's ...

An addition chain for a number n is a sequence 1=a_0<a_1<...<a_r=n, such that each member after a_0 is the sum of two earlier (not necessarily distinct) ones. The number r is ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

The base-2 transcendental number 0.11011011111011011111..._2 (1) (OEIS A014578), where the nth bit is 1 if n is not divisible by 3 and is the complement of the (n/3)th bit if ...

The abundance of a number n, sometimes also called the abundancy (a term which in this work, is reserved for a different but related quantity), is the quantity ...

The cototient of a positive number n is defined as n-phi(n), where n is the totient function. It is therefore the number of positive integers <=n that have at least one prime ...

Define the harmonic mean of the divisors of n H(n)=(sigma_0(n))/(sum_(d|n)1/d), where sigma_0(n) is the divisor function (the number of divisors of n). For n=1, 2, ..., the ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...