Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 5 primes occur before interruption by a prime congruent to 3 mod 4.

EXAMPLE

a(6)=344 because 344 sets of 5 primes occur below 10^6, each run interrupted by a prime congruent to 3 mod 4.