The sum-of-digits function on arithmetic progressions
نویسندگان
چکیده
منابع مشابه
On Arithmetic Progressions of Integers with a Distinct Sum of Digits
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the base-b representation. Further let q be a positive integer. In this paper we study the length k of arithmetic progressions n, n+ q, . . . , n+ q(k − 1) such that sb(n), sb(n+ q), . . . , sb(n+ q(k − 1)) are (pairwise) distinct. More specifically, let Lb,q denote the supremum of k as n varies in ...
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We consider the set of squares n2, n < 2k, and split up the sum of binary digits s(n2) into two parts s[<k](n 2) + s[≥k](n 2), where s[<k](n 2) = s(n2 mod 2k) collects the first k digits and s[≥k](n 2) = s(bn2/2kc) collects the remaining digits. We present very precise results on the distribution on s[<k](n 2) and s[≥k](n 2). For example, we provide asymptotic formulas for the numbers #{n < 2k ...
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In celebration of G.E. Andrews' 60 th birthday.
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ژورنال
عنوان ژورنال: Moscow Journal of Combinatorics and Number Theory
سال: 2020
ISSN: 2640-7361,2220-5438
DOI: 10.2140/moscow.2020.9.43