Some Arithmetic Properties of Certain Sequences
نویسندگان
چکیده
In an earlier paper it was argued that two sequences, denoted by {Un} and {Wn}, constitute the sextic analogues of the well-known Lucas sequences {un} and {vn}. While a number of the properties of {Un} and {Wn} were presented, several arithmetic properties of these sequences were only mentioned in passing. In this paper we discuss the derived sequences {Dn} and {En}, where Dn = gcd(Wn − 6R n, Un) and En = gcd(Wn, Un), in greater detail and show that they possess many number theoretic properties analogous to those of {un} and {vn}, respectively. The second author is supported by NSERC of Canada.
منابع مشابه
Entropy Properties of Certain Record Statistics and Some Characterization Results
In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...
متن کاملOn the total version of geometric-arithmetic index
The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.
متن کاملLong Period Sequences Generated by the Logistic Map over Finite Fields with Control Parameter Four
Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using finite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of s...
متن کاملCuts and overspill properties in models of bounded arithmetic
In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...
متن کاملSome Results on the Arithmetic Correlation of Sequences
In this paper we study various properties of arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. Here we analyze the arithmetic autocorrelations of non-binary `-sequences, showing that they are nearly optimal. We analyze the expected autoand cross-correlations of sequences with fixed shift. We study sequences with the arithmetic sh...
متن کامل