The sum-of-digits function of polynomial sequences
نویسندگان
چکیده
منابع مشابه
The sum-of-digits function of polynomial sequences
Let q ≥ 2 be an integer and sq(n) denote the sum of the digits in base q of the positive integer n. The goal of this work is to study a problem of Gelfond concerning the repartition of the sequence (sq(P (n)))n∈N in arithmetic progressions when P ∈ Z[X] is such that P (N) ⊂ N. We answer Gelfond’s question and we show the uniform distribution modulo 1 of the sequence (αsq(P (n)))n∈N for α ∈ R \Q...
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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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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولOn the Sum of Digits of Some Sequences of Integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {an}n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
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By using a generating function approach it is shown that the sum-of-digits function (related to speciic nite and innnite linear recurrences) satisses a central limit theorem. Additionally a local limit theorem is derived.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2011
ISSN: 0024-6107
DOI: 10.1112/jlms/jdr003