The nonprimes n!+2 ... n!+n are the a(n)-th string of n-1 prime-free consecutive terms, the first such one being the string of composite numbers A000230(k)+1 through A001632(k)-1 when n=2k, or through A001632(k)-2 when n=2k-1.

A060977

The nonprimes n!+2 ... n!+n are the a(n)-th string of n-1 prime-free consecutive terms, the first such one being the string of composite numbers A000230(k)+1 through A001632(k)-1 when n=2k, or through A001632(k)-2 when n=2k-1.