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*The sum of the [[Multiplicative inverse|reciprocals]] of all non-zero [[triangular number]]s converges to 2.<ref>{{Cite journal |last=Grabowski |first=Adam |title=Polygonal numbers |journal=Formalized Mathematics |year=2013 |volume=21 |number=2 |pages=103–113 |publisher=Sciendo ([[De Gruyter]])|doi=10.2478/forma-2013-0012 |doi-access=free |s2cid=15643540 |zbl=1298.11029 }}</ref>
*Numbers also cannot be laid out in a <math>2\times2</math> [[magic square]] that yields a [[magic constant]], and as such they are the only [[null set|null]] <math>n</math> by <math>n</math> magic square set.<ref>{{Cite OEIS |A006052|Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections. |access-date=2022-07-21 }}</ref>{{efn|1=Meanwhile, the [[magic constant]] of an <math>n</math>-pointed normal [[magic star]] is <math>M = 4n + 2</math>. }}
*Every number <math>n</math> is [[Polygonal number|polygonal]] by being <math>2</math>-gonal (i.e., a [[natural number]]), as well as the root of some type of <math>n</math>-gonal number. For <math>n = 2</math>, being <math>2</math>-gonal and <math>n</math>-gonal is the same, which make two the only number that is polygonal in only one way.▼
*In [[John Horton Conway|John Conway's]] [[look-and-say sequence|look-and-say function]], which can be represented faithfully with a [[quaternary numeral system]], two consecutive twos (as in "22" for "two twos"), or equivalently "2 - 2", is the only [[fixed point (mathematics)|fixed point]].<ref>{{cite journal |title=Look-and-Say Biochemistry: Exponential RNA and Multistranded DNA |first=Oscar |last=Martin |journal=American Mathematical Monthly |year=2006 |volume=113 |issue=4 |pages=289–307 |publisher=Mathematical association of America |issn=0002-9890 |url=http://www.uam.es/personal_pdi/ciencias/omartin/Biochem.PDF |archive-url=https://web.archive.org/web/20061224154744/http://www.uam.es/personal_pdi/ciencias/omartin/Biochem.PDF |archive-date=2006-12-24 |access-date=2022-07-21 |doi=10.2307/27641915 |jstor=27641915 }}</ref>
Regarding [[Bernouilli number]]s <math>B_{2k}</math>, by convention <math>2</math> has an [[Regular prime#Irregular index|irregularity]] of <math>-1.</math><ref>{{Cite OEIS |A061576 |Smallest prime of irregularity index n. |access-date=2024-03-25 }}</ref> Two is also the first number to return zero for the [[Mertens function]].<ref>{{Cite OEIS |A028442 |Numbers k such that Mertens's function M(k) (A002321) is zero. |access-date=2023-09-02 }}</ref>
▲*Every number <math>n</math> is [[Polygonal number|polygonal]] by being <math>2</math>-gonal (i.e., a [[natural number]]), as well as the root of some type of <math>n</math>-gonal number. For <math>n = 2</math>, being <math>2</math>-gonal and <math>n</math>-gonal is the same, which make two the only number that is polygonal in only one way.
== Binary numbers ==
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