Search Results for ""

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...

By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

Consider the process of taking a number, multiplying its digits, then multiplying the digits of numbers derived from it, etc., until the remaining number has only one digit. ...

Approximants derived by expanding a function as a ratio of two power series and determining both the numerator and denominator coefficients. Padé approximations are usually ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

An algebraic integer of the form a+bsqrt(D) where D is squarefree forms a quadratic field and is denoted Q(sqrt(D)). If D>0, the field is called a real quadratic field, and ...

Roundoff error is the difference between an approximation of a number used in computation and its exact (correct) value. In certain types of computation, roundoff error can ...

Consider the consecutive number sequences formed by the concatenation of the first n positive integers: 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and ...