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DigitCount




Mathematica Notation

Traditional Notation









Number Theory Functions > DigitCount[n,b] > Series representations > Other series representations





http://functions.wolfram.com/13.10.06.0001.01









  


  








Input Form





DigitCount[n, 2, 1] == n - Sum[Floor[n/2^k], {k, 1, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DigitCount", "[", RowBox[List["n", ",", "2", ",", "1"]], "]"]], "\[Equal]", RowBox[List["n", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["Floor", "[", FractionBox["n", SuperscriptBox["2", "k"]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mi> s </mi> <mn> 2 </mn> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> n </mi> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mo> &#8970; </mo> <mfrac> <mi> n </mi> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <ci> n </ci> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <floor /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DigitCount", "[", RowBox[List["n_", ",", "2", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["n", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["Floor", "[", FractionBox["n", SuperscriptBox["2", "k"]], "]"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29