[seqfan] What is notable about A268390?

[Peter Munn]

Dear seqfans,

Working on a new sequence, I refer to some "notable sequences", and one
that I list is A268390. Now, _I_ think it is notable, but my comment in
the sequence is phrased in terms of its transversals in a group defined by
A059897, and not everyone might gain the same appreciation of the sequence
from this description. So, I sought a consequential property that can be
explained in terms you might find more familiar...

Write the terms of A268390 in any prime base, and every positive integer m
can be formed in that base by adding or removing trailing zeros from a
unique term.

Would anyone like to do an independent check on this, either theoretical
or empirical? It may help to know that the number of trailing zeros in the
term corresponding to m is bounded by its number of prime factors (counted
with multiplicity).

I believe A268390 is only the lexicographically earliest sequence with
this property, as its cosets in the A059897 group also qualify. We should
probably add the coset that includes the primes to OEIS - this might be
the lexicographically earliest qualifying sequence that doesn't start with
1.

Best Regards,

Peter