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An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

A digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...

The mean clustering coefficient of a graph G is the average of the local clustering coefficients of G. It is implemented in the Wolfram Language as ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

A maze, also known as a labyrinth, as is a set of passages (with impermeable walls). The goal of the maze is to start at one given point and find a path through the passages ...

A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this ...

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

A (Delta,D)-graph is a graph with maximum vertex degree Delta and diameter at most D. The order of a graph with degree Delta of diameter D is bounded by ...