On random sequences of integers
نویسندگان
چکیده
منابع مشابه
On Sequences of Positive Integers
where [a, b, . . .] denotes the least common multiple of a, b, . . . . For the first term above represents the density of the multiples of a1 , the second represents the density of those multiples of a 2 that are not multiples of a 1 , and so on . Now suppose we start from an infinite sequence a,, a2 , . . . (arranged in increasing order) instead of from a finite set . It is plain that A(ai, a2...
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Let a 1 < a, < . . . be an infinite sequence of integers of positive lower logarithmic density, in other words 1 (1) lim sup > 0. X=+logxa;<x a i DAVENPORT and ERDŐS [1] proved that then there exists an infinite subsequence a,,, < a„, ` . . . satisfying a,, ./a,, .+, . In this note we will give various sharpenings of this result . The sequence a1 < a2 < . . . will be denoted by A, an infinite s...
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What I want to describe is a kind of experimental mathematics, ideal for doing at times when honest thinking is not going well. The requirements are a small computer (pencil and paper suffice, though the calculations are tedious), and Neil Sloane’s “A Handbook of Integer Sequences” [15]. This book, a kind of hitch-hikers’ guide to the universe N”, consists mainly of a list of 2372 sequences of ...
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We collect together here the concepts and results which we will need in the sequel; details and proofs are to be found in [HP 1, 2]. Let X1, X2, · · · , Xk be independently distributed random integer variables such that Xj takes values in the range 1 ≤ Xj ≤ nj with equal likelihood. Let m be a fixed but arbitrary modulus. We refer to (n1, n2, · · · , nk;m), abbreviated to (n, k;m), as a system....
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Extending earlier work of R Donaghey and P J Cameron we investigate some canon ical eigen sequences associated with transformations of integer sequences Several known sequences appear in a new setting for instance the sequences such as studied by T Tsuzuku H O Foulkes and A Kerber in connection with multiply transi tive groups are eigen sequences for the binomial transform Many interesting new ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12474-0