the jacobsthal sequences in finite groups

The Jacobsthal Sequences in Finite Groups

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

On Jacobsthal Binary Sequences

S. Magliveras and W. Wei∗, Florida Atlantic University Let Σ = {0, 1} be the binary alphabet, and A = {0, 01, 11} the set of three strings 0, 01, 11 over Σ. Let A∗ denote the Kleene closure of A, and Z the set of positive integers. A sequence in A∗ is called a Jacobsthal binary sequence. The number of Jacobsthal binary sequences of length n ∈ Z is the n Jacobsthal number. Let k ∈ Z, 1 ≤ k ≤ n. ...

A New Generalization of Jacobsthal Numbers (bi-periodic Jacobsthal Sequences)

The bi-periodic Fibonacci sequence also known as the generalized Fibonacci sequence was fırst introduced into literature in 2009 by Edson and Yayenie [9] after which the bi-periodic Lucas sequence was defined in a similar fashion in 2004 by Bilgici [5]. In this study, we introduce a new generalization of the Jacobsthal numbers which we shall call bi-periodic Jacobsthal sequences similar to the ...

Generating Sequences of Finite Groups

Ternary Modified Collatz Sequences And Jacobsthal Numbers

We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

Weighted Sequences in Finite Cyclic Groups∗

Let p > 7 be a prime, let G = Z/pZ, and let S1 = ∏p i=1 gi and S2 = ∏p i=1 hi be two sequences with terms from G. Suppose that the maximum multiplicity of a term from either S1 or S2 is at most 2p+1 5 . Then we show that, for each g ∈ G, there exists a permutation σ of 1, 2, . . . , p such that g = ∑p i=1(gi · hσ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted...