Editing Mathematical coincidence (section)

=== Decimal coincidences ===
* <math>3^3+4^4+3^3+5^5=3435 </math>, making 3435 the only non-trivial [[Perfect digit-to-digit invariant|Münchhausen number]] in base 10 (excluding 0 and 1). If one adopts the convention that <math>0^0=0</math>, however, then 438579088 is another Münchhausen number.<ref>{{Cite web|url=http://mathworld.wolfram.com/MuenchhausenNumber.html|title=Münchhausen Number|first=Eric|last=Weisstein|website=mathworld.wolfram.com|language=en|access-date=2017-12-04}}</ref>
* <math>\,1!+4!+5!=145</math> and <math>\,4!+0!+5!+8!+5!=40585</math> are the only non-trivial [[factorion]]s in base 10 (excluding 1 and 2).<ref>{{OEIS|A014080}}</ref>
* <math>\frac{16}{64}=\frac{1\!\!\!\not6}{\not64}=\frac{1}{4}</math>, &nbsp;&nbsp;&nbsp;<math>\frac{26}{65}=\frac{2\!\!\!\not6}{\not65}=\frac {2}{5}</math>, &nbsp;&nbsp;&nbsp;<math>\frac{19}{95}=\frac{1\!\!\!\not9}{\not95}=\frac{1}{5}</math>, &nbsp;and&nbsp;&nbsp;<math>\frac{49}{98}=\frac{4\!\!\!\not9}{\not98}=\frac{4}{8}</math>. If the end result of these four [[anomalous cancellation]]s<ref>{{Mathworld|title=Anomalous Cancellation|urlname=AnomalousCancellation}}</ref> are multiplied, their product reduces to exactly 1/100.
* <math>\,(4+9+1+3)^3=4913</math>, <math>\,(5+8+3+2)^3=5832</math>, and <math>\,(1+9+6+8+3)^3=19683</math>.<ref>{{OEIS|A061209}}</ref> (In a similar vein, <math>\,(3+4)^3=343</math>.)<ref>[http://primes.utm.edu/curios/page.php/343.html Prime Curios!: 343].</ref>
* <math>\,-1+2^7=127</math>, making 127 the smallest nice [[Friedman number]]. A similar example is <math>2^5\cdot9^2=2592</math>.<ref name="Friedman">Erich Friedman, [http://www.stetson.edu/~efriedma/mathmagic/0800.html Problem of the Month (August 2000)] {{Webarchive|url=https://web.archive.org/web/20191107050027/https://www2.stetson.edu/~efriedma/mathmagic/0800.html |date=2019-11-07 }}.</ref>
* <math>\,1^3+5^3+3^3=153</math>, <math>\,3^3+7^3+0^3=370</math>, <math>\,3^3+7^3+1^3=371</math>, and <math>\,4^3+0^3+7^3=407</math> are all [[narcissistic number]]s.<ref>{{OEIS|A005188}}</ref>
* <math>\,588^2+2353^2=5882353 </math>,<ref>{{OEIS|A064942}}</ref> a prime number. The fraction 1/17 also produces 0.05882353 when rounded to 8 digits.
* <math>\,2^1+6^2+4^3+6^4+7^5+9^6+8^7=2646798</math>. The largest number with this pattern is <math>\,12157692622039623539=1^1+2^2+1^3+\ldots+9^{20}</math>.<ref>{{OEIS|A032799}}</ref>
*<math>13532385396179=13\times53^{2}\times3853\times96179</math>. This number, found in 2017, answers a question by [[John Horton Conway|John Conway]] whether the digits of a composite number could be the same as its prime factorization.<ref>{{cite web|url=https://oeis.org/A248380/a248380.pdf|title=Five $1,000 Problems (Update 2017)|first=John H.|last=Conway|publisher=[[Online Encyclopedia of Integer Sequences]]|access-date=2024-04-15}}</ref>