[seqfan] smallest odd prime that divides n + sum of all smaller primes

[Neil Fernandez]

Hello,

A sequence I've just submitted (A274649):

a(n) is the smallest odd prime that divides n + the sum of all smaller
primes, or 0 if unknown

Starting with a(0), the sequence runs

5, 3, 0, 0, 3, 5, 859, 3, 41, 233, 3, 7, 0, 3, 307, 5, 3, 1459, 7, 3, 5,
9907, 3, 13, 3, 31, 11

Does a(n) exist for all n?
If a(2) or a(3) exists, it is greater than 600000.

Neil