A134204.out2 gives:
1) n such that a(n) < n
2) a(n)
3) # primes p <= n such that p not in a(0)...a(n-1)
4) # primes n < p <= n log n such that p not in a(0)...a(n-1)
5) # primes p > n log n such that p in a(0)...a(n-1)

Letting m(n) = # primes p < n such that p not in a(0)...a(n), m(n)
appears to grow roughly like n/log(n)**3.25 (slower than n/log(n)**3,
faster than n/log(n)**4).

Some relevant gnuplot commands:

A fit to the data:
gnuplot> fit f*x/log(x)**g 'A134204.out2' using 1:3 via f,g

A plot of m(n), along with some fits:
gnuplot> plot 'A134204.out2' using 1:3, 8.30439e-5*x with lines, 0.00153532*x/log(x) with lines, 0.0283556*x/log(x)**2 with lines, 0.522982*x/log(x)**3 with lines, 9.63096*x/log(x)**4 with lines

Another plot, showing n/m(n) along with the same fits:
gnuplot> plot 'A134204.out2' using 1:($1/$3), 1/8.30439e-5 with lines, log(x)/0.00153532 with lines, log(x)**2/0.0283556 with lines, log(x)**3/0.522982 with lines, log(x)**4/9.63096 with lines