[seqfan] Re: [math-fun] Mathematical hell, sequence and the sequence A007699

[Marc LeBrun]

It might be good for sequences like these to also submit (for instance)

  a(n) := A007698(n) - A007699(n),

which would have offset 1403.

This makes me wonder: what are the largest offsets in the OEIS?

Further, it would seem that this difference sequence must obey a recurrence
relation that somehow combines those of its "parents"--can we write it down?