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{{Short description|Centered figurate number representing a dodecahedron}} ..., a '''centered dodecahedral number''' is a [[Centered number|centered]] [[figurate number]] that represents a [[dodecahedron]]. The centered dodecahedral numb ...

{{Short description|Figurate number representing an icosahedron}} In [[mathematics]], an '''icosahedral number''' is a [[figurate number]] that represents an [[icosahedron]]. The ''n''th icosahedral number ...

{{Short description|Three-dimensional figurate centered icosahedral numbers}} ...oints arranged in the shape of a [[regular icosahedron]]. As cuboctahedral numbers, they represent points arranged in the shape of a [[cuboctahedron]], and ar ...

{{Short description|Centered figurate number representing a tetrahedron}} ...for a single dot, is:{{r|oeis}}<ref>Deza numbers the centered tetrahedral numbers at <math>n=1</math> for a single dot, leading to a different formula.</ref> ...

{{Short description|Figurate number representing a dodecahedron}} In [[mathematics]], a '''dodecahedral number''' is a [[figurate number]] that represents a [[dodecahedron]]. The ''n''th dodecahedral numbe ...

{{Short description|Centered figurate number representing an octahedron}} ...rtain two-dimensional lattice paths.<ref name="s03" /> The Haüy octahedral numbers are named after [[René Just Haüy]]. ...

{{Short description|Figurate number based on the stella octangula}} ...numbers: n*(2*n^2 - 1)|mode=cs2}}.</ref><ref>{{citation|title=The Book of Numbers|page=51|url=https://books.google.com/books?id=0--3rcO7dMYC&pg=PA51|first1=J ...

...thematics of [[figurate number]]s, the '''cannonball problem''' asks which numbers are both [[Square number|square]] and [[square pyramidal number|square pyra ...ite OEIS|sequencenumber=A000292|name=Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6}}</ref> ...

...o possible to derive [[Euler's formula]] <math>V-E+F=2</math> relating the numbers of vertices, edges, and faces of a convex polyhedron from Descartes' theore ...s from polyhedra, generalizing the classical Greek definitions of figurate numbers such as the [[square number]]s and [[triangular number]]s from two-dimensio ...

...uthor1-link=Elena Deza | last2 = Deza | first2 = Michel | title = Figurate Numbers | publisher = World Scientific Publishing | year = 2012 | location = Singap {{Classes of natural numbers}} ...

They include the significant [[decimal]] numbers 10⁶ (a [[million]]), 100⁶ (a [[Trillion (short scale) The sixth powers of integers can be characterized as the numbers that are simultaneously squares and cubes.<ref>{{citation|magazine=Mechanic ...

...=PA136 | volume = 9 | year = 2001}}</ref> one of the first four Carmichael numbers identified by [[Robert Daniel Carmichael|R. D. Carmichael]] in his 1910 pap ...01101 are both [[Palindromic number|palindromes]],<ref>{{cite OEIS|A097856|Numbers that are palindromic in bases 2 and 4}}</ref> and (because the binary repre ...

{{Classes of natural numbers}} [[Category:Figurate numbers]] ...

{{Classes of natural numbers}} [[Category:Figurate numbers]] ...

The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as <math>n = 4^a(8b + 7)</math>) are ...p.&nbsp;314 [https://books.google.com/books?id=cDxYdstLPz4C&dq=%22figurate+numbers%22+incomplete+legendre+gauss++-wikipedia&pg=PA314]</ref> ...

...natural number greater than 1 that is not a product of two smaller natural numbers. | The partition numbers, number of additive breakdowns of n. ...

'''''From Zero to Infinity: What Makes Numbers Interesting''''' is a book in [[popular mathematics]] and [[number theory]] ...s book soon afterward.{{r|singmaster}} Her intended title was ''What Makes Numbers Interesting''; the title ''From Zero to Infinity'' was a change made by the ...

* '''Rule 4.''' Given <math>n</math> arbitrary numbers <math>k_1, k_2, \dots, k_n</math>,<ref name=k497/> ...ions, [[integer partitions]], binomial coefficients, generalized Fibonacci numbers.<ref name=mii25/> ...

...sum]] of [[8 (number)|8]], within an [[aliquot sequence]] of two composite numbers (14, [[8 (number)|8]], [[7 (number)|7]], [[1 (number)|1]], 0) in the prime ...f>{{Cite web|url=https://oeis.org/A000108|title=Sloane's A000108 : Catalan numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Founda ...

...values of <math>g_n(m) </math> (these values are also called the "figurate numbers for the n-dimensional cross polytopes" in the OEIS<ref>{{citation | title=s ...