Difference between revisions of "Template:Classes of natural numbers"

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}}
 
}}
  
|group8 = [[Pseudoprime]]s
+
|group8 = [[Number base|Base]]-dependent<br/> numbers
|list8 =  
+
|list8 = {{Navbox|subgroup
* [[Carmichael number]]
+
|group1 = [[Numerical digit|Digit]]-based [[arithmetic dynamics]]
* [[Catalan pseudoprime]]
+
|list1 =
* [[Elliptic pseudoprime]]
+
* [[Digit sum]]
* [[Euler pseudoprime]]
+
* [[Digital root]]
* [[Euler–Jacobi pseudoprime]]
+
** [[Multiplicative digital root|Multiplicative]]
* [[Fermat pseudoprime]]
+
* [[Dudeney number|Dudeney]]
* [[Frobenius pseudoprime]]
+
* [[Factorion]]
* [[Lucas pseudoprime]]
+
* [[Happy number|Happy]]
* [[Somer–Lucas pseudoprime]]
+
* [[Lychrel number|Lychrel]]
* [[Strong pseudoprime]]
+
* [[Meertens number|Meertens]]
 +
* [[Missing-digit sum]]
 +
* [[Narcissistic number|Narcissistic]]
 +
* [[Perfect digit-to-digit invariant]]
 +
* [[Perfect digital invariant]]
 +
* [[Persistence of a number|Persistence]]
 +
** [[Additive persistence|Additive]]
 +
** [[Multiplicative persistence|Multiplicative]]
 +
* [[Self number|Self]]
 +
* [[Sum-product number|Sum-product]]
 +
 
 +
|group2 = Digit-composition related
 +
|list2 =
 +
* [[Palindromic number|Palindromic]]
 +
* [[Pandigital number|Pandigital]]
 +
* [[Repdigit]]
 +
* [[Repunit]]
 +
* [[Self-descriptive number|Self-descriptive]]
 +
* [[Smarandache–Wellin number|Smarandache–Wellin]]
 +
* [[Strictly non-palindromic number|Strictly non-palindromic]]
 +
* [[Undulating number|Undulating]]
 +
 
 +
|group3 = Digit-[[permutation]] related
 +
|list3 =
 +
* [[Cyclic number|Cyclic]]
 +
* [[Digit-reassembly number|Digit-reassembly]]
 +
* [[Parasitic number|Parasitic]]
 +
* [[Primeval number|Primeval]]
 +
* [[Transposable integer|Transposable]]
 +
 
 +
|group4 = [[Divisor]] related
 +
|list4 =  
 +
* [[Equidigital number|Equidigital]]
 +
* [[Extravagant number|Extravagant]]
 +
* [[Frugal number|Frugal]]
 +
* [[Harshad number|Harshad]]
 +
* [[Pernicious number|Pernicious]]
 +
* [[Polydivisible number|Polydivisible]]
 +
* [[Vampire number|Vampire]]
 +
 
 +
|group5 = [[P-adic number]] related
 +
|list5 =
 +
* [[Automorphic number|Automorphic]]
 +
 
 +
|group6 = Other
 +
|list6 =
 +
* [[Friedman number|Friedman]]
 +
* [[Kaprekar number|Kaprekar]]
 +
* [[Keith number|Keith]]
 +
}}
  
 
|group9 = Combinatorial<br/> numbers
 
|group9 = Combinatorial<br/> numbers
Line 165: Line 214:
 
* [[Schröder–Hipparchus number|Schröder–Hipparchus]]
 
* [[Schröder–Hipparchus number|Schröder–Hipparchus]]
  
|group10 = [[Arithmetic function]]s
+
|group10 = [[Pseudoprime]]s
|list10 = {{Navbox|subgroup
+
|list10 =
 +
* [[Carmichael number]]
 +
* [[Catalan pseudoprime]]
 +
* [[Elliptic pseudoprime]]
 +
* [[Euler pseudoprime]]
 +
* [[Euler–Jacobi pseudoprime]]
 +
* [[Fermat pseudoprime]]
 +
* [[Frobenius pseudoprime]]
 +
* [[Lucas pseudoprime]]
 +
* [[Somer–Lucas pseudoprime]]
 +
* [[Strong pseudoprime]]
 +
 
 +
|group11 = [[Arithmetic function]]s
 +
|list11 = {{Navbox|subgroup
 
  |group1 = By properties of [[Divisor function|σ(''n'')]]
 
  |group1 = By properties of [[Divisor function|σ(''n'')]]
 
  |list1 =  
 
  |list1 =  
Line 219: Line 281:
 
}}
 
}}
  
|group11 = Dividing a quotient
+
|group12 = Dividing a quotient
|list11 =  
+
|list12 =  
 
* [[Wieferich prime#Wieferich numbers|Wieferich]]
 
* [[Wieferich prime#Wieferich numbers|Wieferich]]
 
* [[Wall–Sun–Sun prime|Wall–Sun–Sun]]
 
* [[Wall–Sun–Sun prime|Wall–Sun–Sun]]
Line 226: Line 288:
 
* [[Wilson prime#Wilson numbers|Wilson]]
 
* [[Wilson prime#Wilson numbers|Wilson]]
  
|group12 = Other [[prime factor]]<br/> or [[divisor]] related<br/> numbers
+
|group13 = Other [[prime factor]]<br/> or [[divisor]] related<br/> numbers
|list12 =  
+
|list13 =  
 
* [[Blum integer|Blum]]
 
* [[Blum integer|Blum]]
 
* [[Erdős–Nicolas number|Erdős–Nicolas]]
 
* [[Erdős–Nicolas number|Erdős–Nicolas]]
Line 244: Line 306:
 
* [[Super-Poulet number|Super-Poulet]]
 
* [[Super-Poulet number|Super-Poulet]]
 
* [[Zeisel number|Zeisel]]
 
* [[Zeisel number|Zeisel]]
 
|group13 = [[Number base|Base]]-dependent<br/> numbers
 
|list13 = {{Navbox|subgroup
 
|group1 = [[Numerical digit|Digit]]-based [[arithmetic dynamics]]
 
|list1 =
 
* [[Digit sum]]
 
* [[Digital root]]
 
** [[Multiplicative digital root|Multiplicative]]
 
* [[Dudeney number|Dudeney]]
 
* [[Factorion]]
 
* [[Happy number|Happy]]
 
* [[Lychrel number|Lychrel]]
 
* [[Meertens number|Meertens]]
 
* [[Missing-digit sum]]
 
* [[Narcissistic number|Narcissistic]]
 
* [[Perfect digit-to-digit invariant]]
 
* [[Perfect digital invariant]]
 
* [[Persistence of a number|Persistence]]
 
** [[Additive persistence|Additive]]
 
** [[Multiplicative persistence|Multiplicative]]
 
* [[Self number|Self]]
 
* [[Sum-product number|Sum-product]]
 
 
|group2 = Digit-composition related
 
|list2 =
 
* [[Palindromic number|Palindromic]]
 
* [[Pandigital number|Pandigital]]
 
* [[Repdigit]]
 
* [[Repunit]]
 
* [[Self-descriptive number|Self-descriptive]]
 
* [[Smarandache–Wellin number|Smarandache–Wellin]]
 
* [[Strictly non-palindromic number|Strictly non-palindromic]]
 
* [[Undulating number|Undulating]]
 
 
|group3 = Digit-[[permutation]] related
 
|list3 =
 
* [[Cyclic number|Cyclic]]
 
* [[Digit-reassembly number|Digit-reassembly]]
 
* [[Parasitic number|Parasitic]]
 
* [[Primeval number|Primeval]]
 
* [[Transposable integer|Transposable]]
 
 
|group4 = [[Divisor]] related
 
|list4 =
 
* [[Equidigital number|Equidigital]]
 
* [[Extravagant number|Extravagant]]
 
* [[Frugal number|Frugal]]
 
* [[Harshad number|Harshad]]
 
* [[Pernicious number|Pernicious]]
 
* [[Polydivisible number|Polydivisible]]
 
* [[Vampire number|Vampire]]
 
 
|group5 = [[P-adic number]] related
 
|list5 =
 
* [[Automorphic number|Automorphic]]
 
 
|group6 = Other
 
|list6 =
 
* [[Friedman number|Friedman]]
 
* [[Kaprekar number|Kaprekar]]
 
* [[Keith number|Keith]]
 
}}
 
  
 
|group14 = Generated<br/> via a [[Sieve theory|sieve]]
 
|group14 = Generated<br/> via a [[Sieve theory|sieve]]

Revision as of 20:12, 7 October 2019

Template documentation

Initial visibility: currently defaults to autocollapse

To set this template's initial visibility, the |state= parameter may be used:

  • |state=collapsed: {{Classes of natural numbers|state=collapsed}} to show the template collapsed, i.e., hidden apart from its title bar
  • |state=expanded: {{Classes of natural numbers|state=expanded}} to show the template expanded, i.e., fully visible
  • |state=autocollapse: {{Classes of natural numbers|state=autocollapse}}
    • shows the template collapsed to the title bar if there is a {{navbar}}, a {{sidebar}}, or some other table on the page with the collapsible attribute
    • shows the template in its expanded state if there are no other collapsible items on the page

If the |state= parameter in the template on this page is not set, the template's initial visibility is taken from the |default= parameter in the Collapsible option template. For the template on this page, that currently evaluates to autocollapse.

See also