A123396: prime case

[zak seidov]

Dear SeqFans,

Inspired by:
A123396 a(0)=0. a(n) = number of earlier terms each of
which, when added to n, give a triangular number

A1 (not submitted yet, pending gurus' Op):

a(0)=2, at n>0 a(n) = number of earlier terms each of
which, when added to n, give a prime number.

See attached graph 
(sorry to bother people not interested in primes).

Qs to gurus:
Is a(n)=0 at some large n?
Is it OK for OEIS?
Thanks, Zak
  

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