منابع مشابه
D-complete Sequences of Integers
An infinite sequence a1 < a2 < · · · is d-complete if every sufficiently large integer is the sum of ai such that no one divides the other. We investigate d-completeness of sets of the form {pαqβ} and {pαqβrγ} with α, β, γ nonnegative.
متن کاملOn 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...
متن کاملOn Divisibility Properties of Sequences of Integers
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...
متن کاملSome sequences of integers
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 ...
متن کاملSome Canonical Sequences of Integers
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: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.12.003