Difference between revisions of "Template:Classes of natural numbers"
Jump to navigation
Jump to search
Template documentation
imported>Vpab15 m (update to Sierpiński number) |
|||
| (134 intermediate revisions by 21 users not shown) | |||
| Line 1: | Line 1: | ||
| − | {{Navbox | + | {{Navbox with collapsible groups |
| name = Classes of natural numbers | | name = Classes of natural numbers | ||
| title = Classes of [[natural number]]s | | title = Classes of [[natural number]]s | ||
| Line 5: | Line 5: | ||
| state = {{{state|<includeonly>collapsed</includeonly>}}} | | state = {{{state|<includeonly>collapsed</includeonly>}}} | ||
| − | |group1 = [[Exponentiation|Powers]] and | + | |group1 = [[Exponentiation|Powers]] and related numbers |
|list1 = | |list1 = | ||
* [[Achilles number|Achilles]] | * [[Achilles number|Achilles]] | ||
* [[Power of two|Power of 2]] | * [[Power of two|Power of 2]] | ||
| + | * [[Power of three|Power of 3]] | ||
* [[Power of 10]] | * [[Power of 10]] | ||
* [[Square number|Square]] | * [[Square number|Square]] | ||
| Line 16: | Line 17: | ||
* [[Sixth power]] | * [[Sixth power]] | ||
* [[Seventh power]] | * [[Seventh power]] | ||
| + | * [[Eighth power]] | ||
* [[Perfect power]] | * [[Perfect power]] | ||
* [[Powerful number|Powerful]] | * [[Powerful number|Powerful]] | ||
* [[Prime power]] | * [[Prime power]] | ||
| − | |group2 = Of the form | + | |group2 = Of the form ''a'' × 2<sup>''b''</sup> ± 1 |
|list2 = | |list2 = | ||
* [[Cullen number|Cullen]] | * [[Cullen number|Cullen]] | ||
| Line 30: | Line 32: | ||
* [[Woodall number|Woodall]] | * [[Woodall number|Woodall]] | ||
| − | |group3 = Other polynomial | + | |group3 = Other polynomial numbers |
|list3 = | |list3 = | ||
* [[Carol number|Carol]] | * [[Carol number|Carol]] | ||
| Line 39: | Line 41: | ||
* [[Loeschian number|Loeschian]] | * [[Loeschian number|Loeschian]] | ||
* [[Lucky numbers of Euler]] | * [[Lucky numbers of Euler]] | ||
| − | |||
| − | |group4 = [[Recursion|Recursively]] defined | + | |group4 = [[Recursion|Recursively]] defined numbers |
|list4 = | |list4 = | ||
* [[Fibonacci number|Fibonacci]] | * [[Fibonacci number|Fibonacci]] | ||
| Line 50: | Line 51: | ||
* [[Pell number|Pell]] | * [[Pell number|Pell]] | ||
* [[Perrin number|Perrin]] | * [[Perrin number|Perrin]] | ||
| − | |group5 = Possessing a | + | |group5 = Possessing a specific set of other numbers |
|list5 = | |list5 = | ||
* [[Knödel number|Knödel]] | * [[Knödel number|Knödel]] | ||
* [[Riesel number|Riesel]] | * [[Riesel number|Riesel]] | ||
| − | * [[ | + | * [[Sierpiński number|Sierpiński]] |
| − | |group6 = Expressible via | + | |group6 = Expressible via specific sums |
|list6 = | |list6 = | ||
* [[Nonhypotenuse number|Nonhypotenuse]] | * [[Nonhypotenuse number|Nonhypotenuse]] | ||
| Line 65: | Line 66: | ||
* [[Wolstenholme number|Wolstenholme]] | * [[Wolstenholme number|Wolstenholme]] | ||
| − | |group7 | + | |group7 = [[Figurate number]]s |
| − | + | |list7 = {{Navbox|subgroup | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | | | ||
| group1 = [[Two-dimensional space|2-dimensional]] | | group1 = [[Two-dimensional space|2-dimensional]] | ||
| list1 = {{Navbox|subgroup | | list1 = {{Navbox|subgroup | ||
| Line 93: | Line 86: | ||
* [[Triangular number|Triangular]] | * [[Triangular number|Triangular]] | ||
* [[Square number|Square]] | * [[Square number|Square]] | ||
| − | |||
* [[Square triangular number|Square triangular]] | * [[Square triangular number|Square triangular]] | ||
* [[Pentagonal number|Pentagonal]] | * [[Pentagonal number|Pentagonal]] | ||
| Line 117: | Line 109: | ||
| list2 = | | list2 = | ||
* [[Tetrahedral number|Tetrahedral]] | * [[Tetrahedral number|Tetrahedral]] | ||
| + | * [[Cube (algebra)|Cubic]] | ||
* [[Octahedral number|Octahedral]] | * [[Octahedral number|Octahedral]] | ||
* [[Dodecahedral number|Dodecahedral]] | * [[Dodecahedral number|Dodecahedral]] | ||
| Line 134: | Line 127: | ||
|group1 = centered | |group1 = centered | ||
|list1 = | |list1 = | ||
| − | |||
| − | |||
| − | |||
|group2 = non-centered | |group2 = non-centered | ||
|list2 = | |list2 = | ||
* [[Pentatope number|Pentatope]] | * [[Pentatope number|Pentatope]] | ||
| + | * [[Squared triangular number|Squared triangular]] | ||
| + | * [[Fourth power|Tesseractic]] | ||
}} | }} | ||
}} | }} | ||
| − | | | + | |group8 = Combinatorial numbers |
| − | + | |list8 = | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | | | ||
* [[Bell number|Bell]] | * [[Bell number|Bell]] | ||
* [[Cake number|Cake]] | * [[Cake number|Cake]] | ||
| Line 173: | Line 152: | ||
* [[Schröder–Hipparchus number|Schröder–Hipparchus]] | * [[Schröder–Hipparchus number|Schröder–Hipparchus]] | ||
| − | | | + | |group9 = [[Prime number|Primes]] |
| − | | | + | |list9 = |
| − | |group1 = | + | * [[Wieferich prime#Wieferich numbers|Wieferich]] |
| + | * [[Wall–Sun–Sun prime|Wall–Sun–Sun]] | ||
| + | * [[Wolstenholme prime]] | ||
| + | * [[Wilson prime#Wilson numbers|Wilson]] | ||
| + | |||
| + | |group10 = [[Pseudoprime]]s | ||
| + | |list10 = | ||
| + | * [[Carmichael number]] | ||
| + | * [[Catalan pseudoprime]] | ||
| + | * [[Elliptic pseudoprime]] | ||
| + | * [[Euler pseudoprime]] | ||
| + | * [[Euler–Jacobi pseudoprime]] | ||
| + | * [[Fermat pseudoprime]] | ||
| + | * [[Frobenius pseudoprime]] | ||
| + | * [[Lucas pseudoprime]] | ||
| + | * [[Lucas–Carmichael number]] | ||
| + | * [[Somer–Lucas pseudoprime]] | ||
| + | * [[Strong pseudoprime]] | ||
| + | |||
| + | |group11 = [[Arithmetic function]]s and [[Arithmetic dynamics|dynamics]] | ||
| + | |list11 = {{Navbox|subgroup | ||
| + | |group1 = [[Divisor function]]s | ||
|list1 = | |list1 = | ||
* [[Abundant number|Abundant]] | * [[Abundant number|Abundant]] | ||
* [[Almost perfect number|Almost perfect]] | * [[Almost perfect number|Almost perfect]] | ||
* [[Arithmetic number|Arithmetic]] | * [[Arithmetic number|Arithmetic]] | ||
| + | * [[Betrothed numbers|Betrothed]] | ||
* [[Colossally abundant number|Colossally abundant]] | * [[Colossally abundant number|Colossally abundant]] | ||
| + | * [[Deficient number|Deficient]] | ||
* [[Descartes number|Descartes]] | * [[Descartes number|Descartes]] | ||
* [[Hemiperfect number|Hemiperfect]] | * [[Hemiperfect number|Hemiperfect]] | ||
| Line 188: | Line 190: | ||
* [[Multiply perfect number|Multiply perfect]] | * [[Multiply perfect number|Multiply perfect]] | ||
* [[Perfect number|Perfect]] | * [[Perfect number|Perfect]] | ||
| − | * [[Practical number]] | + | * [[Practical number|Practical]] |
* [[Primitive abundant number|Primitive abundant]] | * [[Primitive abundant number|Primitive abundant]] | ||
* [[Quasiperfect number|Quasiperfect]] | * [[Quasiperfect number|Quasiperfect]] | ||
* [[Refactorable number|Refactorable]] | * [[Refactorable number|Refactorable]] | ||
| + | * [[Semiperfect number|Semiperfect]] | ||
* [[Sublime number|Sublime]] | * [[Sublime number|Sublime]] | ||
* [[Superabundant number|Superabundant]] | * [[Superabundant number|Superabundant]] | ||
| Line 197: | Line 200: | ||
* [[Superperfect number|Superperfect]] | * [[Superperfect number|Superperfect]] | ||
| − | + | |group3 = [[Euler's totient function]] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |group3 = | ||
|list3 = | |list3 = | ||
* [[Highly cototient number|Highly cototient]] | * [[Highly cototient number|Highly cototient]] | ||
| Line 213: | Line 209: | ||
* [[Sparsely totient number|Sparsely totient]] | * [[Sparsely totient number|Sparsely totient]] | ||
| − | | | + | |group2 = [[Prime omega function]]s |
| − | | | + | |list2 = |
| + | * [[Almost prime]] | ||
| + | * [[Semiprime]] | ||
| + | |||
| + | |group5 = [[Aliquot sequence]]s | ||
| + | |list5 = | ||
* [[Amicable numbers|Amicable]] | * [[Amicable numbers|Amicable]] | ||
| − | * [[ | + | * [[Perfect number|Perfect]] |
| − | + | * [[Sociable numbers|Sociable]] | |
| − | * [[ | ||
* [[Untouchable number|Untouchable]] | * [[Untouchable number|Untouchable]] | ||
| − | + | ||
| − | + | |group6 = [[Primorial]] | |
| + | |list6 = | ||
* [[Euclid number|Euclid]] | * [[Euclid number|Euclid]] | ||
* [[Fortunate number|Fortunate]] | * [[Fortunate number|Fortunate]] | ||
| + | }} | ||
| − | | | + | |group12 = Other [[prime factor]] or [[divisor]] related numbers |
| − | + | |list12 = | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | | | ||
* [[Blum integer|Blum]] | * [[Blum integer|Blum]] | ||
* [[Erdős–Nicolas number|Erdős–Nicolas]] | * [[Erdős–Nicolas number|Erdős–Nicolas]] | ||
* [[Erdős–Woods number|Erdős–Woods]] | * [[Erdős–Woods number|Erdős–Woods]] | ||
* [[Friendly number|Friendly]] | * [[Friendly number|Friendly]] | ||
| − | |||
* [[Giuga number|Giuga]] | * [[Giuga number|Giuga]] | ||
* [[Harmonic divisor number|Harmonic divisor]] | * [[Harmonic divisor number|Harmonic divisor]] | ||
* [[Lucas–Carmichael number|Lucas–Carmichael]] | * [[Lucas–Carmichael number|Lucas–Carmichael]] | ||
| + | * [[Pronic number|Pronic]] | ||
* [[Regular number|Regular]] | * [[Regular number|Regular]] | ||
* [[Rough number|Rough]] | * [[Rough number|Rough]] | ||
* [[Smooth number|Smooth]] | * [[Smooth number|Smooth]] | ||
| − | |||
* [[Sphenic number|Sphenic]] | * [[Sphenic number|Sphenic]] | ||
* [[Størmer number|Størmer]] | * [[Størmer number|Størmer]] | ||
| Line 251: | Line 245: | ||
* [[Zeisel number|Zeisel]] | * [[Zeisel number|Zeisel]] | ||
| − | | | + | |group13 = [[Numeral system]]-dependent numbers |
| − | | | + | |list13 = {{Navbox|subgroup |
| − | |group1 = | + | |group1 = [[Arithmetic function]]s and [[Arithmetic dynamics|dynamics]] |
|list1 = | |list1 = | ||
| − | * [[ | + | * [[Persistence of a number|Persistence]] |
| − | * [[ | + | ** [[Additive persistence|Additive]] |
| − | * [[Digit- | + | ** [[Multiplicative persistence|Multiplicative]] |
| + | {{Navbox|subgroup | ||
| + | |group1 = [[Digit sum]] | ||
| + | |list1 = | ||
| + | * [[Digit sum]] | ||
| + | * [[Digital root]] | ||
| + | * [[Self number|Self]] | ||
| + | * [[Sum-product number|Sum-product]] | ||
| + | |||
| + | |group2 = Digit product | ||
| + | |list2 = | ||
| + | * [[Multiplicative digital root]] | ||
| + | * [[Sum-product number|Sum-product]] | ||
| + | |||
| + | |group3 = Coding-related | ||
| + | |list3 = | ||
| + | * [[Meertens number|Meertens]] | ||
| + | |||
| + | |group4 = Other | ||
| + | |list4 = | ||
* [[Dudeney number|Dudeney]] | * [[Dudeney number|Dudeney]] | ||
| − | |||
| − | |||
* [[Factorion]] | * [[Factorion]] | ||
| − | |||
| − | |||
| − | |||
* [[Kaprekar number|Kaprekar]] | * [[Kaprekar number|Kaprekar]] | ||
| + | * [[Kaprekar's routine|Kaprekar's constant]] | ||
* [[Keith number|Keith]] | * [[Keith number|Keith]] | ||
* [[Lychrel number|Lychrel]] | * [[Lychrel number|Lychrel]] | ||
| − | |||
* [[Narcissistic number|Narcissistic]] | * [[Narcissistic number|Narcissistic]] | ||
| + | * [[Perfect digit-to-digit invariant]] | ||
| + | * [[Perfect digital invariant]] | ||
| + | ** [[Happy number|Happy]] | ||
| + | }} | ||
| + | |group2 = [[P-adic numbers]]-related | ||
| + | |list2 = | ||
| + | * [[Automorphic number|Automorphic]] | ||
| + | ** [[Trimorphic number|Trimorphic]] | ||
| + | |||
| + | |group3 = [[Numerical digit|Digit]]-composition related | ||
| + | |list3 = | ||
* [[Palindromic number|Palindromic]] | * [[Palindromic number|Palindromic]] | ||
* [[Pandigital number|Pandigital]] | * [[Pandigital number|Pandigital]] | ||
| − | |||
| − | |||
| − | |||
| − | |||
* [[Repdigit]] | * [[Repdigit]] | ||
* [[Repunit]] | * [[Repunit]] | ||
| − | |||
* [[Self-descriptive number|Self-descriptive]] | * [[Self-descriptive number|Self-descriptive]] | ||
* [[Smarandache–Wellin number|Smarandache–Wellin]] | * [[Smarandache–Wellin number|Smarandache–Wellin]] | ||
| − | |||
* [[Strictly non-palindromic number|Strictly non-palindromic]] | * [[Strictly non-palindromic number|Strictly non-palindromic]] | ||
| − | * [[ | + | * [[Undulating number|Undulating]] |
| − | * [[ | + | |
| + | |group4 = Digit-[[permutation]] related | ||
| + | |list4 = | ||
| + | * [[Cyclic number|Cyclic]] | ||
| + | * [[Digit-reassembly number|Digit-reassembly]] | ||
| + | * [[Parasitic number|Parasitic]] | ||
| + | * [[Primeval number|Primeval]] | ||
* [[Transposable integer|Transposable]] | * [[Transposable integer|Transposable]] | ||
| − | * [[ | + | |
| − | * [[ | + | |group5 = Divisor-related |
| − | * [[Vampire number|Vampire]] | + | |list5 = |
| + | * [[Equidigital number|Equidigital]] | ||
| + | * [[Extravagant number|Extravagant]] | ||
| + | * [[Frugal number|Frugal]] | ||
| + | * [[Harshad number|Harshad]] | ||
| + | * [[Polydivisible number|Polydivisible]] | ||
| + | * [[Smith number|Smith]] | ||
| + | * [[Vampire number|Vampire]] | ||
| + | |||
| + | |group6 = Other | ||
| + | |list6 = | ||
| + | * [[Friedman number|Friedman]] | ||
}} | }} | ||
| + | |||
| + | |group14 = [[Binary number]]s | ||
| + | |list14 = | ||
| + | * [[Evil number|Evil]] | ||
| + | * [[Odious number|Odious]] | ||
| + | * [[Pernicious number|Pernicious]] | ||
| + | |||
| + | |group15 = Generated via a [[Sieve theory|sieve]] | ||
| + | |list15 = | ||
| + | * [[Lucky number|Lucky]] | ||
| + | * [[Generation of primes|Prime]] | ||
| + | |||
| + | |group16 = [[Sorting algorithm|Sorting]] related | ||
| + | |list16 = | ||
| + | * [[Pancake sorting|Pancake number]] | ||
| + | * [[Sorting number]] | ||
| + | |||
| + | |group17 = [[Natural language]] related | ||
| + | |list17 = | ||
* [[Aronson's sequence]] | * [[Aronson's sequence]] | ||
* [[Ban number|Ban]] | * [[Ban number|Ban]] | ||
| − | * [[ | + | |
| + | |group18 = [[Graphemics]] related | ||
| + | |list18 = | ||
| + | * [[Strobogrammatic number|Strobogrammatic]] | ||
| belowclass = hlist | | belowclass = hlist | ||
| Line 305: | Line 357: | ||
==See also== | ==See also== | ||
*{{tl|Divisor classes}} | *{{tl|Divisor classes}} | ||
| + | *{{tl|Figurate numbers}} | ||
*{{tl|Prime number classes}} | *{{tl|Prime number classes}} | ||
*{{tl|Series (mathematics)}} | *{{tl|Series (mathematics)}} | ||
Latest revision as of 15:52, 8 September 2020
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}}
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
- {{Divisor classes}}
- {{Figurate numbers}}
- {{Prime number classes}}
- {{Series (mathematics)}}
| Editors can experiment in this template's sandbox (edit | diff) and testcases (create) pages. Subpages of this template. |