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A summation formula related to the binary digits

โœ Scribed by J. Coquet

Publisher
Springer-Verlag
Year
1983
Tongue
English
Weight
250 KB
Volume
73
Category
Article
ISSN
0020-9910

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๐Ÿ“œ SIMILAR VOLUMES

On the Binary Digits of a Power
On the Binary Digits of a Power
โœ Bernt Lindstrรถm ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 399 KB

Let B(m) denote the number of ones in the binary expansion of an integer m 2. We prove that lim sup m ร„ B(m h )ร‚log 2 m=h for integers h 2. We also prove the same result with m h replaced by any polynomial a 0 m h +a 1 m h&1 + } } } +a h with integer coefficients and a 0 >0. ## 1997 Academic Press