Greg Egan on Nostr: These are the only bases in which I know it’s possible for the reciprocal of an ...

These are the only bases in which I know it’s possible for the reciprocal of an integer to have a repeating block of digits with every digit exactly once.

I proved this is never true for odd bases, but it’s not clear to me if there’s a simple way to rule out any other bases.

My web page on this: https://www.gregegan.net/SCIENCE/Reptends/Reptends.html

There’s an OEIS page that answers a different question: if we don’t care if some of the digits appear more than once in the reptend, what is the smallest integer that has a pandigital reptend in each base?

https://oeis.org/A382498