- Sequence one
Number which is equal to the product of the factorials of its digits.
- Sequence two
Factorial of a number is equal to the product of factorials of its digits.
2026-03-26 20:36:39.1774557399
Is these sequence present on OEIS?
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Sequence two is all the single digits and no others. $10$ is too large and all other factorials will have a factor $11$ while the product of digit factorials will not. I suspect sequence one is just $1,2$ but cannot prove it. Note that you want the average base $10$ log of the digit factorials to be about $1$, so the number has to consist mostly of digits $0,1,2,3$.