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SUMMARY:Bartosz Sobolewski (Jagiellonian University in Kraków and Montanu
 niversität Leoben)
DTSTART:20240213T130000Z
DTEND:20240213T140000Z
DTSTAMP:20260423T021342Z
UID:OWNS/126
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/126/">B
 lock occurrences in the binary expansion of n and n+t</a>\nby Bartosz Sobo
 lewski (Jagiellonian University in Kraków and Montanuniversität Leoben) 
 as part of One World Numeration seminar\n\n\nAbstract\nLet $s(n)$ denote t
 he sum of binary digits of a nonnegative integer $n$. In 2012 Cusick asked
  whether for every nonnegative integer $t$ the set of $n$ satisfying $s(n+
 t) \\geq s(n)$ has natural density strictly greater than $1/2$. So far it 
 is known that the answer is affirmative for almost all $t$ (in the sense o
 f density) and $s(n+t) - s(n)$ has approximately Gaussian distribution. Du
 ring the talk we consider an analogue of this problem concerning the funct
 ion $r(n)$\, which counts the occurrences of the block $11$ in the binary 
 expansion of $n$.  In particular\, we prove that the distribution of $r(n+
 t)-r(n)$ is approximately Gaussian as well. We also discuss a generalizati
 on to an arbitrary block of binary digits. This is a joint work with Lukas
  Spiegelhofer.\n
LOCATION:https://researchseminars.org/talk/OWNS/126/
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