Quote:
Originally Posted by Dubslow
Is there an OEIS entry for this sequence (starting with f(0)=3)?

Yes:
oeis.org/A146556
Quote:
Or, as a corollary, the secondary sequence g(n) where g(n) is the first index of f(n) which is divisible by the nth Mersenne prime?
Such that we know at least the first 873 terms of f(n); meanwhile g(1) = 0, g(2) = 2, g(3) = 29, with g(5) unknown as evidenced by this thread?

Seems not  actually g(3) = 30, and g(4) = 492. The only OEIS match for these terms is
oeis.org/A143414 which is clearly unrelated.