𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Beatty sequences and Langford sequences

✍ Scribed by Roger B. Eggleton; Aviezri S. Fraenkel; R.Jaime Simpson


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
830 KB
Volume
111
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Langford sequences: perfect and hooked
✍ James E. Simpson πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 562 KB

Asequence{d,d+l...., d f m -1) of m consecutive positive integers is said to be perfect if the integers {1,2, . . . , 2m} can be arranged in disjoint pairs {(q, bi): 1 si G m} so that {bi-a,: l~i~m}={d,d+l,..., d+m-1). A sequence is hooked if the set {1,2,...,2m-1,2m + 1) can be arranged in pairs to

Prime divisors in Beatty sequences
✍ William D. Banks; Igor E. Shparlinski πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 137 KB

We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence Ξ±n + Ξ² , n = 1, 2, . . . , where Ξ±, Ξ² ∈ R, and Ξ± > 0 is irrational. For example, we show that where Ξ©(k) and Ο‰(k) denote the number of prime divisors of an integer k = 0 counted with and without m

Extended Langford Sequences with Small D
✍ VΓ‘clav Linek; Zhike Jiang πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 284 KB

A k-extended Langford sequence of defect d and length m is a sequence s 1 , s 2 , ..., s 2m+1 in which s k ==, where = is the null symbol, and each other member of the sequence comes from the set [d, d+1, ..., d+m&1]. Each j # [d, d+1, ..., d+m&1] occurs exactly twice in the sequence, and the two oc

A Generating Function Technique for Beat
✍ Kevin O'Bryant πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 178 KB

Let g(x, n), with x Β₯ R + , be a step function for each n. Assuming certain technical hypotheses, we give a constant a and function f such that ; . n=1 g(x, n) can be written in the form a+; 0 < r < x f(r), where the summation is extended over all points in (0, x) at which some g( β€’ , n) is not cont