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A function f(x) is logarithmically convex on the interval [a,b] if f>0 and lnf(x) is convex on [a,b]. If f(x) and g(x) are logarithmically convex on the interval [a,b], then ...

A closed three-dimensional figure (which may, according to some terminology conventions, be self-intersecting). Kern and Bland (1948, p. 18) define a solid as any limited ...

An interprime is the average of consecutive (but not necessarily twin) odd primes. The first few terms are 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, ... (OEIS A024675). The first ...

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers ...

A number n is practical if for all k<=n, k is the sum of distinct proper divisors of n. Defined in 1948 by A. K. Srinivasen. All even perfect numbers are practical. The ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...

The continued fraction for Apéry's constant zeta(3) is [1; 4, 1, 18, 1, 1, 1, 4, 1, ...] (OEIS A013631). The positions at which the numbers 1, 2, ... occur in the continued ...