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Define the juggler sequence for a positive integer a_1=n as the sequence of numbers produced by the iteration a_(k+1)={|_a_k^(1/2)_| for even a_k; |_a_k^(3/2)_| for odd a_k, ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

A Smarandache-like function which is defined where S_k(n) is defined as the smallest integer for which n|S_k(n)^k. The Smarandache S_k(n) function can therefore be obtained ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...

The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The bull graph is a simple graph on 5 nodes and 5 edges whose name derives from its resemblance to a schematic illustration of a bull or ram (whose face is the triangle and ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph. The Harries-Wong graph ...