Search Results for ""

Given two starting numbers (a_1,a_2), the following table gives the unique sequences {a_i} that contain no three-term arithmetic progressions. Sloane sequence A003278 1, 2, ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...

A cryptarithmetic in which the letters used to represent distinct digits are derived from related words or meaningful phrases. The term was coined by Hunter in 1955 (Madachy ...

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

An algorithm for computing an Egyptian fraction (Stewart 1992).

The Cauchy product of two sequences f(n) and g(n) defined for nonnegative integers n is defined by (f degreesg)(n)=sum_(k=0)^nf(k)g(n-k).

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

A number puzzle in which a group of arithmetical operations has some or all of its digits replaced by letters or symbols, and where the original digits must be found. In such ...