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Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by ...

An n×n magic square for which every pair of numbers symmetrically opposite the center sum to n^2+1. The Lo Shu is associative but not panmagic. The numbers of associative ...

Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A k-automatic set is a set of integers whose base-k representations form a regular language, i.e., a language accepted by a finite automaton or state machine. If bases a and ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

Let P(x) be defined as the power series whose nth term has a coefficient equal to the nth prime p_n, P(x) = 1+sum_(k=1)^(infty)p_kx^k (1) = 1+2x+3x^2+5x^3+7x^4+11x^5+.... (2) ...

Every irrational number x has an approximation constant c(x) defined by c(x)=lim inf_(q->infty)q|qx-p|, where p=nint(qx) is the nearest integer to qx and lim inf is the ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...