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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 for ...

By analogy with the log sine function, define the log cosine function by C_n=int_0^(pi/2)[ln(cosx)]^ndx. (1) The first few cases are given by C_1 = -1/2piln2 (2) C_2 = ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

11 11 1 11 2 2 11 2 4 2 11 3 6 6 3 11 3 9 10 9 3 11 4 12 19 19 12 4 11 4 16 28 38 28 16 4 11 5 20 44 66 66 44 20 5 11 5 25 60 110 126 110 60 25 5 1 (1) Losanitsch's triangle ...

The set of L^p-functions (where p>=1) generalizes L2-space. Instead of square integrable, the measurable function f must be p-integrable for f to be in L^p. On a measure ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

When P and Q are integers such that D=P^2-4Q!=0, define the Lucas sequence {U_k} by U_k=(a^k-b^k)/(a-b) for k>=0, with a and b the two roots of x^2-Px+Q=0. Then define a ...

An n-step Lucas sequence {L_k^((n))}_(k=1)^infty is defined by letting L_k^((n))=-1 for k<0, L_0^((n))=n, and other terms according to the linear recurrence equation ...

The first few numbers not known to produce palindromes when applying the 196-algorithm (i.e., a reverse-then-add sequence) are sometimes known as Lychrel numbers. This term ...