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...which are not multiplicatively independent are said to be multiplicatively dependent. As examples, 36 and 216 are multiplicatively dependent since <math>36^3=(6^2)^3=(6^3)^2=216^2</math>, whereas 2 and 3 are multipli ...

...]] and [[mathematical logic]], a '''Meertens number''' in a given [[number base]] <math>b</math> is a [[natural number]] that is its own [[Gödel numbering| ...th>n</math> be a natural number. We define the '''Meertens function''' for base <math>b > 1</math> <math>F_{b} : \mathbb{N} \rightarrow \mathbb{N}</math> t ...

In [[number theory]], a '''pernicious number''' is a positive integer such that the [[Hamming weight]] of its [[Binary numeral system|binary repr ...anxin|last=Cai|author-link=Tianxin Cai|title=Perfect Numbers And Fibonacci Sequences|page=50|publisher=World Scientific|year=2022|isbn=978-9811244094}}</ref> ...

...s. For any positive [[integer]] ''n'', let ''f''&hairsp;(''n'') denote the integer given by the [[recurrence relation|recurrence]] {{nowrap|1=''f''&hairsp;('' The [[integer part]]s of their square roots, ...

...finitely many weakly prime numbers in any base. Furthermore, for any fixed base there is a positive proportion of such primes.<ref>{{cite journal|author=[[ ...proved that there exist an infinite number of "delicate primes" under any base.<ref name=":12" /> ...

...to the sum of its digits each raised to the power of itself. An example in base 10 is 3435, because <math>3435 = 3^3 + 4^4 + 3^3 + 5^5</math>. The term "Mu Let <math>n</math> be a natural number which can be written in base <math>b</math> as the k-digit number <math>d_{k-1}d_{k-2}...d_{1}d_{0}</mat ...

[[Category:Base-dependent integer sequences]] ...

...f name=Cobham>{{Cite journal|last=Cobham|first=Alan|year=1969|title=On the base-dependence of sets of numbers recognizable by finite automata|journal=Mathe ...resentation of a natural number <math display="inline">n</math> in [[Radix|base]] <math display="inline">b</math> is the sequence of digits <math>n_0n_1\cd ...

...onic series]], formed by omitting all terms whose denominator expressed in base 10 contains the digit 9. That is, it is the sum ...e most large integers contain every digit. For example, a random 100-digit integer is very likely to contain at least one '9', causing it to be excluded from ...

...xt|Madritsch|Wagner|2010}} provide asymptotic formulas for the number of [[integer partition]]s in which all parts are fibbinary.{{r|madwag}} ...rcube graph]] <math>Q_d</math> of dimension <math>d</math> is indexed by [[integer]]s from 0 to <math>2^d-1</math>, so that two [[vertex (graph theory)|vertic ...

...ce]]s with links to their entries in the [[On-Line Encyclopedia of Integer Sequences]]. ...'') :{{=}} ''σ''₁(''n'')}} is the sum of divisors of a positive integer {{math|''n''}}. ...

...], a '''perfect digital invariant (PDI)''' is a number in a given [[number base]] (<math>b</math>) that is the sum of its own digits each raised to a given ...tion''' (also known as a '''happy function''', from [[happy number]]s) for base <math>b > 1</math> and power <math>p > 0</math> <math>F_{p, b} : \mathbb{N} ...

...] or [[cyclic shift|shift]] cyclically when they are multiplied by another integer <math>n</math>. Examples are: For any [[Coprime integers|integer coprime]] to 10, its reciprocal is a repeating decimal without any non-recu ...

{{defn|no=|[[Axiom of dependent choice]] A weak form of the axiom of choice}} {{defn|defn=The [[bounding number]], the least size of an unbounded family of sequences of natural numbers}} ...

...arth]] could have begun using only relatively short [[Genetic code|genetic sequences]], which in theory were too short to store all essential information.<ref n ..."/> However, to encode a system as complex as a protein, longer nucleotide sequences are needed, which increases the probability of a mutation even more and req ...

...[[moving average]] filter of length ''m'', where ''m'' is a positive, odd integer. The KZ filter belongs to the class of [[low-pass filter]]s. The KZ filter ...interval {{math|[ −(''m'' − 1)/2 , (''m'' − 1)/2 ]}} where ''m'' is an odd integer. Therefore, the coefficient {{math|''a''{{su|''b'' = ''s''|''p'' = ''m'','' ...

{{defn|Any of the positive [[integer]]s that occurs as a [[coefficient]] in the [[binomial theorem]] is a '''bin ...elf depends on the variable ''x'', so that ''y'' and ''z'' are therefore [[dependent variable]]s, then ''z'', via the intermediate variable of ''y'', depends on ...

...nction|spaces of square-integrable functions]], [[Sequence space|spaces of sequences]], [[Sobolev space]]s consisting of [[generalized function]]s, and [[Hardy ...ly if <math>x</math> and <math>y</math> are [[linear independence|linearly dependent]]. ...

In Figure 9, ''q'' is the diffraction order it can have values of any integer (positive, negative or zero).<ref>{{cite book|last1=Baba|first1=A|last2=Kan ...lts demonstrate that SPR imaging is a promising tool for monitoring single base mismatches and screen out the hybridized molecules.<ref name="Smith et al"/ ...

{{defn|In mathematics and [[digital electronics]], a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typ {{defn|A device that can be instructed to carry out sequences of arithmetic or [[Boolean algebra|logical]] operations automatically via { ...