On digital blocks of polynomial values and extractions in the Rudin–Shapiro sequence
نویسندگان
چکیده
منابع مشابه
On Polynomial Extractions of the Rudin–shapiro Sequence
Let P (x) ∈ Z[x] be an integer-valued polynomial taking only positive values and let d be any fixed positive integer. The aim of this short note is to show, by elementary means, that for any sufficiently large integer N ≥ N0(P, d) there exists n such that P (n) contains exactly N occurrences of the block (q − 1, q − 1, . . . , q − 1) in its digital expansion in base q. The method of proof is co...
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On simultaneous digital expansions of polynomial values
Let sq denote the q-ary sum-of-digits function and let P1(X), P2(X) ∈ Z[X] with P1(N), P2(N) ⊂ N be polynomials of degree h, l ≥ 1, h 6= l, respectively. In this note we show that (sq(P1(n))/sq(P2(n)))n≥1 is dense in R. This extends work by Stolarsky (1978) and Hare, Laishram and Stoll (2011).
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 2016
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/2016009