Catalan Numbers, Primes and Twin Primes
نویسندگان
چکیده
with C0 = 1. Their appearances occur in a dazzling variety of combinatorial settings where they are used to enumerate all manner of geometric and algebraic objects (see Richard Stanley’s collection [28, Chap. 6]; an online Addendum is continuously updated). Quite a lot is known about the divisibility of the Catalan numbers; see [2, 10]. They are obviously closely related to the middle binomial numbers and not surprisingly, there is a considerable literature on their divisibility too; see [13, 5, 18, 14, 16, 15]. The aim of this paper is to observe a connection between Catalan numbers, primes and twin primes.
منابع مشابه
Research Statement Dominic Klyve
My research concerns explicit inequalities in elementary number theory. Specifically, I am interested in the distribution of twin primes, along with theoretical and computational techniques for putting explicit bounds on classes numbers such as twin primes. One important method I use to examine the density of twins is to look for bounds on Brun’s Constant. 1. Motivation and Background Twin prim...
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