منابع مشابه
On Sums of Primes from Beatty Sequences
Ever since the days of Euler and Goldbach, number-theorists have been fascinated by additive representations of the integers as sums of primes. The most famous result in this field is I.M. Vinogradov’s three primes theorem [7], which states that every sufficiently large odd integer is the sum of three primes. Over the years, a number of authors have studied variants of the three primes theorem ...
متن کاملPrimes in Beatty Sequences in Short Intervals
In this paper we show that sieve methods used previously to investigate primes in short intervals and corresponding Goldbach type problems can be modified to obtain results on primes in Beatty sequences in short intervals.
متن کاملPrimes in Intersections of Beatty Sequences
In this note we consider the question of whether there are infinitely many primes in the intersection of two or more Beatty sequences ⌊ξjn+ ηj⌋, n ∈ N, j = 1, . . . , k. We begin with a straightforward sufficient condition for a set of Beatty sequences to contain infinitely many primes in their intersection. We then consider two sequences when one ξj is rational. However, the main result we est...
متن کاملSubstitution Invariant Beatty Sequences
with θ irrational and taken to satisfy 0 < θ < 1; plainly this may be assumed without loss of generality. Evidently (fn) is a sequence of zeros and ones. Denote by w0 and w1 words on the alphabet {0, 1} ; that is, finite strings in the letters 0 and 1. Then the sequence (fn) is said to be invariant under the substitution W given by W : 0 −→ w0, 1 −→ w1, if the infinite strings fθ = f1f2f3 . . ....
متن کاملINTERSECTING RATIONAL BEATTY SEQUENCES Jamie
A rational Beatty sequence has the form {�pi/q + b� : i ∈ Z} where p > q > 0 and gcd(p, q) = 1. We call p/q the modulus of the sequence and b the offset. Morikawa gave a condition on the moduli of two Beatty sequences such that they would be disjoint for a suitable choice of offsets. Holzman and Fraenkel showed that the sequence formed by the intersection of two Beatty sequences with moduli p1/...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.04.003