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The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

A (-1,1)-matrix is a matrix whose elements consist only of the numbers -1 or 1. For an n×n (-1,1)-matrix, the largest possible determinants (Hadamard's maximum determinant ...

Feynman (1997, p. 116) noticed the curious fact that the decimal expansion 1/(243)=0.004115226337448559... (1) repeats pairs of the digits 0, 1, 2, 3, ... separated by the ...

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle ...

Cantor dust is a fractal that can be constructed using string rewriting beginning with a cell [0] and iterating the rules {0->[0 0 0; 0 0 0; 0 0 0],1->[1 0 1; 0 0 0; 1 0 1]}. ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

Sequences of integers generated in the Collatz problem. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...

The two-dimensional Hammersley point set of order m is defined by taking all numbers in the range from 0 to 2^m-1 and interpreting them as binary fractions. Calling these ...

A matrix H with elements H_(ij)=(i+j-1)^(-1) (1) for i,j=1, 2, ..., n. Hilbert matrices are implemented in the Wolfram Language by HilbertMatrix[m, n]. The figure above shows ...