2 questions: kth +integer which is coprime to j

[Stefan Steinerberger]

> Is the sequence of positive integers infinite, where m is included in the
> sequence if and only if: the mth integer from among those positive
> integers which are coprime to (m+1) = the (m+1)th integer from
> among those positive integers which are coprime to m ?
> This sequence begins 3, 15,...

Assuming my programming isn't faulty the sequence should
go like this: 3, 15, 104, 164, 255, 2625, 2834,...
So far every number also appears in A001274 although there
are some numbers (like 194) in A001274 which aren't in the
sequence.

If it could be shown that this sequence is a subset of A001274,
then its infinitude will be hard to prove since it is an open problem
whether A001274 is indeed infinite.

Best wishes,
Stefan