Search results

In mathematics, the '''binary game''' is a [[topological game]] introduced by [[Stanisław Ulam]] in 1935 ...<math>x_0, x_1, x_2, ...</math>. Player I wins the game if and only if the binary number <math>(x_0{}.x_1{}x_2{}x_3{}...)_2 \in{}X</math>, that is, <math>\Si ...

...er|prime]], that is, there is a prime number of 1s when it is written as a binary number.<ref>{{citation|first=Elena|last=Deza|author-link=Elena Deza|title=M ...number]], is a pernicious number. This is because the sum of the digits in binary form is 2, which is a prime number.<ref name=oeis/> ...

{{Short description|Particular kind of species infinite sequences defined via finite decidable properties}} ...is a particular kind of species of [[Sequence#Finite_and_infinite|infinite sequences]] defined via finite [[Decidability_(logic)|decidable]] properties. Here a ...

...bound principle]] of real analysis, even when considering only computable sequences. A common way to resolve this difficulty is to consider only sequences that are accompanied by a [[modulus of convergence]]; no Specker sequence h ...

...written as 1000, 201 and 122. Each number can be written uniquely in skew binary canonical form where there is only '''at most''' one instance of the digit Canonical skew binary representations of the numbers from 0 to 15 are shown in following table:<r ...

...ut making some natural numbers impossible to represent. Simple examples of sequences that are not complete include the [[even and odd numbers|even number]]s, si ...ref>{{Cite journal|last=Brown|first=J. L.|date=1961|title=Note on Complete Sequences of Integers|journal=The American Mathematical Monthly|volume=68|issue=6|pag ...

{{about|sign sequences in mathematics|sequences of roadside signs|Burma-Shave}} Such sequences are commonly studied in [[discrepancy theory]]. ...

A '''binary decision''' is a choice between two alternatives, for instance between taki Binary decisions are basic to many fields. Examples include: ...

...ating function gives a real number between {{math|0}} and {{math|1}} whose binary expansion is the paperfolding word ...to vary at each step we obtain a more general class of sequences. Given a binary sequence (''f''_''i''), we can define a general paperfolding sequ ...

...''Ehrenfeucht–Mycielski sequence''' is a recursively defined sequence of [[binary digits]] with [[pseudorandom]] properties, defined by {{harvs|txt | last1 = ...upper bound would suggest: the position by which all length-<math>i</math> sequences occur, up to the limit of experimental testing, is close to the minimum pos ...

...rloo.ca/journals/JIS/VOL14/Sloane/carry2.html|journal=[[Journal of Integer Sequences]]|volume=14|arxiv=1107.1130|access-date=20 October 2021}}</ref> ==Some standard sequences== ...

...omplexity|worst-case]] number of comparisons used by both [[insertion sort|binary insertion sort]] and [[merge sort]]. However, there are other [[algorithms] ...hat these numbers count the number of comparisons used by [[insertion sort|binary insertion sort]], and conjectured (incorrectly) that they give the minimum ...

{{Short description|Numbers whose binary representation does not contain two consecutive ones}} In [[mathematics]], the '''fibbinary numbers''' are the numbers whose [[binary representation]] does not contain two consecutive ones. That is, they are s ...

{{Short description|Any binary relation equal to its composition with itself}} In mathematics, an '''idempotent binary relation''' is a [[binary relation]] ''R'' on a set ''X'' (a subset of [[Cartesian product]] ''X''&n ...

...ing to determine a range that the search key resides in and performing a [[binary search]] within that range. This takes <math>O(\log i)</math> time, where < .../math> is the index of the element being searched for in the list, whereas binary search would run in <math>O(\log n)</math> time, where <math>n</math> is th ...

...roach to the [[dynamic optimality]] problem on [[online algorithm]]s for [[binary search tree]]s involves reformulating the problem geometrically, in terms o |title=The geometry of binary search trees ...

:''b''_''n'' = 1 if the binary representation of ''n'' contains no block of consecutive 0s of odd length; ...k of consecutive 0s of length 2; whereas ''b''₅ = 0 because the binary representation of 5 is 101, which contains a block of consecutive 0s of len ...

These sequences are named after [[Richard P. Stanley]]. ==Binary–ternary sequence== ...

...s algorithm''' is an efficient method for computers to construct [[optimal binary search tree]]s and [[Huffman coding|alphabetic Huffman codes]], in [[linear ...>n+1</math> leaf nodes, which can be identified (in the order given by the binary tree) with the <math>n+1</math> input weights. ...

==Related sequences== The [[binary logarithm]]s (exponents in the powers of two) of Gould's sequence themselve ...