Primefree sequences in the OEIS

[Alonso Del Arte]

Here's an interesting new sequence in PrimeFan's Listing of Esoteric
Integer Sequences which would be self-referential if included in the
OEIS:

4, 7, 12, 35, ..., 290, ..., 384, ..., 566, 567, ..., 578, 580, 581,
582, 583, 584, ..., 1014, 1015, ..., 1106, 1107, ..., 2808, ...,
18252, ..., 97785, ..., 100766, 100767, ..., 105416

Sequence An in Sloane's Online Encyclopedia of Integer Sequences
contains no primes.

The ellipses presumably stand for ranges PrimeFan has not yet checked.

The first four terms given correspond neatly to M0001 through M0004 in
the 1995 Sloane et Plouffe EIS. Thus it follows that M0005 through
M3182 all contain at least one prime, but I don't know if there is a
neat relation between the M numbers and the A numbers (for example,
M5487 is no longer A000015).

Though certainly finite, how close might this sequence to being
displayable in full in four lines?

Alonso