Two primes sum to a factorial

[Leroy Quet]

I want to submit this sequence, but I am unsure
if it isn't already in the EIS. There are too
many hits, but nothing that OBVIOUSLY matches,
unless I missed something while I was skimming
the results of the search. (I didn't check using
the zeroes in the list of terms I have
calculated.)

a(n) = number of primes p such that n!-p is
prime.

I get that the sequence begins:  (offset 1)
0,0,1,6,24,...

(a(n), for all n >= 4, is even.)

Maybe the sequence with each "prime" in the
definition is replaced with "noncomposite" (1 and
primes) is indeed in the EIS, if the prime
sequence isn't.

Thanks,
Leroy Quet




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