Search Results for ""

The forward difference is a finite difference defined by Deltaa_n=a_(n+1)-a_n. (1) Higher order differences are obtained by repeated operations of the forward difference ...

An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example, p_1 = {3,8,5,10,9,4,6,1,7,2} (1) p_2 = ...

The second theorem of Mertens states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by sum_(p<=x)1/p=lnlnx+B_1+o(1), where p is a ...

The sequence produced by starting with a_1=1 and applying the greedy algorithm in the following way: for each k>=2, let a_k be the least integer exceeding a_(k-1) for which ...

Consider the decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

A cyclic number is an (n-1)-digit integer that, when multiplied by 1, 2, 3, ..., n-1, produces the same digits in a different order. Cyclic numbers are generated by the full ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

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' ...