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The omega constant is defined as W(1)=0.5671432904... (1) (OEIS A030178), where W(x) is the Lambert W-function. It is available in the Wolfram Language using the function ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A fraction containing each of the digits 1 through 9 is called a pandigital fraction. The following table gives the number of pandigital fractions which represent simple unit ...

The golden ratio phi can be written in terms of a nested radical in the beautiful form phi=sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))), (1) which can be written recursively as ...

A permutation of n distinct, ordered items in which none of the items is in its original ordered position is known as a derangement. If some, but not necessarily all, of the ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

The number of partitions of n with k or fewer addends, or equivalently, into partitions with no element greater than k. This function is denoted q(n,k) or q_k(n). (Note that ...