A092663 Number of consecutive prime runs of 10 primes congruent to 1 mod 4 below 10^n.

0, 0, 0, 0, 0, 5, 19, 323, 3653, 37544, 381413, 3799344, 37591054

Offset: 1

Author

Enoch Haga, Mar 02 2004

Keywords

• more
• nonn
• hard

Examples

			a(6)=5 because 5 sets of 10 primes occur below 10^6, each run interrupted by a prime congruent to 3 mod 4. These runs start at prime(31798)=373649, prime(41181)=495377, at prime(42241)=509389, at prime(50017)=612109, *not* at prime(61457) which has a larger run length, and at prime(63146)=789097.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A092664, A092665, A039702, A100672, A145990.

Formula

Generate the prime sequence with primes labeled 1 mod 4 or 3 mod 4. Add count of primes to sequence if just 10 primes occur before interruption by a prime congruent to 3 mod 4

Extensions

a(9) and a(10) from Sean A. Irvine, Oct 06 2011

a(11) from Chai Wah Wu, Mar 18 2018

a(12) and a(13) from Lucas A. Brown, Oct 15 2024