sums of mods

[Chuck Seggelin]

Here's a little sequence I put together the other day, but I doubt it is 
interesting enough for inclusion in the OEIS, and even if it were I don't 
know how I would describe it in one sentence.  Here's how I compute the 
terms:

To compute a(n), take the first n primes and find the first value M (>0) 
which is not divisible by any of these primes, but which *is* divisible by 
the remainders for each of these primes summed together, or zero if there is 
no such M.  In other words:

a(1) = first value M which is not divisible by 2, but is divisible by (M mod 
2).  a(1) = 1.
a(2) = 0.
a(3) = first value M which is not divisible by 2, 3, or 5, but is divisible 
by (M mod 2) + (M mod 3) + (M mod 5).  a(3) = 119.
a(4) = first value M which is not divisible by 2, 3, 5, or 7, but is 
divisible by  (M mod 2) + (M mod 3) + (M mod 5) + (M mod 7).  a(4) = 649.

The first 21 terms:

1, 0, 119, 649, 13, 493, 989, 667, 4399, 67, 3763, 4819, 4717, 9943, 179, 
20437, 15677, 193, 26797, 27977, 21251, 37267, ...

The sequence generally trends upward, but occasionally dips very low when 
the sum of the remainders happens to exactly equal a prime (as in 13, 67, 
179, 193, ...).

Is such a sequence worth including?  If so, what would be the best way to 
describe it?

            -- Chuck Seggelin