a remarkable coincidence showing that numerical data can be misleading!

[Jonathan Post]

Should there be something equivalent for a(n) = 3/(3^(1/n)-1 with n =
1, 2, 3, ...

2, 5, 7, 10, 13, 15, 18, 21, 24, 26, 29, 32, 35, 37, 40, ...?

or, corrected parenthesization:

3/(3^((1/15)-1)) for n = 1, 2, 3, ...

3, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9,
convergent to 9.

It's not an exact analogue, as b(n) = floor((3*n/(log 3))) begins with
n = 0, 1, 2, 3, ...:

0, 6, 12, 18, 25, 31, 37, 44, 50, 56, 62, 81, 88, 94, ...

and I don't see an obvious correlation between a(n) and b(n).

So it's not trivially living in the integer formulae, but
intrinsically telling us something about hypercube tic-tac-toe and the
Law of Small Numbers?  Or Beatty sequences floor( 2*n/(log 2) )?  Or
what?  I should have read Max Alekseyev's discussion, or Golomb's
paper first, but I guess that I'm syaing that the comment in the
revised sequence is still not entirely clear.

I hesitate to point out to the usual suspects that 77451915729368 uses
every digit but 0 (that is base and irrelevant), or that
77451915729368 = 2^3 * 3^4 * 11 * 7151 * 15252431 as that
factorization sheds no light whatsoever.

But where do the A129935 and A078608 really come from, at a structural
level? And how can it be parametrized and generalized, as I've failed
to do in going naively from 2 to 3?