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The number 13.

A friend of a number n is another number m such that (m,n) is a friendly pair.

A permutation of n distinct, ordered items in which none of the items is in its original ordered position is known as a derangement. If some, but not necessarily all, of the ...

The Jacobsthal polynomials are the W-polynomial obtained by setting p(x)=1 and q(x)=2x in the Lucas polynomial sequence. The first few Jacobsthal polynomials are J_1(x) = 1 ...

The asymptotic series for the gamma function is given by (1) (OEIS A001163 and A001164). The coefficient a_n of z^(-n) can given explicitly by ...

A prime number obtained by reading digits around an analog clock. In a clockwise direction, the primes are 2, 3, 5, 7, 11, 23, 67, 89, 4567, 23456789, 23456789101112123, ... ...

A negative number multiplied by another negative number gives a positive number.

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...