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A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

The golden ratio has decimal expansion phi=1.618033988749894848... (OEIS A001622). It can be computed to 10^(10) digits of precision in 24 CPU-minutes on modern hardware and ...

The decimal expansion of the Golomb-Dickman constant is given by lambda=0.6243299885... (OEIS A084945). Mitchell (1968) computed lambda to 53 decimal places. lambda has been ...

Consider the recurrence equation defined by a_0=m and a_n=|_sqrt(2a_(n-1)(a_(n-1)+1))_|, (1) where |_x_| is the floor function. Graham and Pollak actually defined a_1=m, but ...

Graham's biggest little hexagon is the largest possible (not necessarily regular) convex hexagon with polygon diameter 1 (i.e., for which no two of the vertices are more than ...

For an integer n>=2, let gpf(x) denote the greatest prime factor of n, i.e., the number p_k in the factorization n=p_1^(a_1)...p_k^(a_k), with p_i<p_j for i<j. For n=2, 3, ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

Let the sum of the squares of the digits of a positive integer s_0 be represented by s_1. In a similar way, let the sum of the squares of the digits of s_1 be represented by ...

A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...