I believe it's only a coincidence. There is an upper bound on the number of "factorions" and these are the only two below that bound. It's a coincidence since you can see it's purely a fact of the base one chooses.
These are the only two numbers (besides 1 & 2) that can be written as the sum of the factorials of their digits (in base 10).pic.twitter.com/CHzrPjAhWt
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Anything when you extend it to the gamma function?
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good question! not sure
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This sounds like it should have a nice proof. Do share.
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Proof is not elegant,, you find an upper bound then test all cases
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only 2? sounds like a challenge
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They are odd numbers.
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