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The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

Number Theory

A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

A number n such that sigma^2(n)=sigma(sigma(n))=2n, where sigma(n) is the divisor function is called a superperfect number. Even superperfect numbers are just 2^(p-1), where ...

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, ...

The representation of a number as a sum of powers of a base b, followed by expression of each of the exponents as a sum of powers of b, etc., until the process stops. For ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...