Search Results for ""

If the period of a repeating decimal for a/p, where p is prime and a/p is a reduced fraction, has an even number of digits, then dividing the repeating portion into halves ...

The number of digits used to perform a given computation. The concepts of accuracy and precision are both closely related and often confused. While the accuracy of a number x ...

A Mersenne number is a number of the form M_n=2^n-1, (1) where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first ...

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then Lochs' ...

The integer sequence defined by the recurrence relation P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=P(1)=P(2)=1. This is the same recurrence relation as for the ...

The limiting rabbit sequence written as a binary fraction 0.1011010110110..._2 (OEIS A005614), where b_2 denotes a binary number (a number in base-2). The decimal value is ...

A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135=(1+3+5)(1·3·5). (1) Obviously, such a number ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...