06-21-2026, 12:12 PM
Summary
The OEIS sequence A014080 lists the factorions: numbers that are equal to the sum of the factorials of their decimal digits. The sequence contains only four numbers: $1, 2, 145, and 40585$. For example, $145 = 1! + 4! + 5! = 1 + 24 + 120$, and $40585 = 4! + 0! + 5! + 8! + 5!$. Mathematicians have shown that there are no other factorions in base 10, making this a finite and rare sequence. Factorions are interesting examples of how digit-based properties can create surprising fixed points in number theory.
ARTICLE
The OEIS sequence A014080 lists the factorions: numbers that are equal to the sum of the factorials of their decimal digits. The sequence contains only four numbers: $1, 2, 145, and 40585$. For example, $145 = 1! + 4! + 5! = 1 + 24 + 120$, and $40585 = 4! + 0! + 5! + 8! + 5!$. Mathematicians have shown that there are no other factorions in base 10, making this a finite and rare sequence. Factorions are interesting examples of how digit-based properties can create surprising fixed points in number theory.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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