Multi-parametric Extensions of Newman’s Phenomenon
نویسنده
چکیده
Consider the sequence (3k)k≥0 written in base two representation and reduce the sum of digits s2(3k) mod 2. A well-known result of Newman [10] says that the resulting sequence shows an overplus of 0’s with respect to 1’s. It is also known [3] that, asymptotically speaking, s2(7k)k≥0 is more often 0 than 1 or 2. We investigate similar phenomena for the sequence (7k + i)k≥0 with 0 < i ≤ 6 as well as give a two-parametric family of arithmetic progressions where overplus phenomena can be observed. This paper sharpens and extends results obtained by Drmota and Ska lba [3], continuing work presented by Drmota and the author in [4].
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