Motivated by the concepts of Sidel’nikov sequences and two-prime generator (or Jacobi sequences) we introduce and analyze some new binary sequences called two-prime Sidel’nikov sequences. In the cases of twin primes and cousin primes equivalent 3 modulo 4 we show that these sequences are balanced. In the general case, besides balancedness we also study the autocorrelation, the correlation measu...

where a, b and (yn)n>o take values in some specified ring and a and b are fixed elements which do not depend on the Integer index n. A solution (yn)„^0 ^ completely specified once the values of yQ and yx are given. It is customary to denote by Fn(a, b) the solution corresponding to the choice y0 = 0, yt = l, and by Ln(a, b) the solution corresponding to the choice y0 = 2, yx = a. Loosely speaki...

In this paper we use Faa di Bruno's formula to associate Bell polynomial values differential equations of the form $y^{\prime}=f(y)$. That is, partial polynomials represent solution such an equation and compute special polynomials.

In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = Axn +Bxn−k +Cxn−l +Dxn−σ + bxn−k +hxn−l dxn−k + exn−l , n = 0,1,2, ....., where the coefficients A,B,C,D,b,d,e,h ∈ (0,∞), while k, l and σ are positive integers. The initial conditions x−σ ,...,x−l ,...,x−k, ...,x−1,x0 are arbitrary ...