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A noble number nu is defined as an irrational number having a continued fraction that becomes an infinite sequence of 1s at some point, nu=[0,a_1,a_2,...,a_n,1^_]. The ...

A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. ...

An octic graph is a regular graph of degree eight. The numbers of simple octic graphs on n=9, 10, 11, ... nodes are 1, 6, 94, 10786, 3459386, ... (OEIS A014378). Examples are ...

An odd permutation is a permutation obtainable from an odd number of two-element swaps, i.e., a permutation with permutation symbol equal to -1. For initial set {1,2,3,4}, ...

An odious number is a nonnegative number that has an odd number of 1s in its binary expansion. The first few odious numbers are therefore 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

A set of two numbers or objects linked in some way is said to be a pair. The pair a and b is usually denoted (a, b), and is generally considered to be ordered, making it a ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...

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 ...