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The Eulerian number <n; k> gives the number of permutations of {1,2,...,n} having k permutation ascents (Graham et al. 1994, p. 267). Note that a slightly different ...

A palindromic number is a number (in some base b) that is the same when written forwards or backwards, i.e., of the form a_1a_2...a_2a_1. The first few palindromic numbers ...

An almost perfect number, also known as a least deficient or slightly defective (Singh 1997) number, is a positive integer n for which the divisor function satisfies ...

A quasiperfect number, called a "slightly excessive number" by Singh (1997), is a "least" abundant number, i.e., one such that sigma(n)=2n+1. Quasiperfect numbers are ...

Let the stick number s(K) of a knot K be the least number of straight sticks needed to make a knot K. The smallest stick number of any knot is s(T)=6, where T is the trefoil ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

There are two definitions of the Fermat number. The less common is a number of the form 2^n+1 obtained by setting x=1 in a Fermat polynomial, the first few of which are 3, 5, ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...