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

1,6

Links

Table of n, a(n) for n=1..13.

Lucas A. Brown, Python program.

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

Example

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.

Crossrefs

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

Sequence in context: A357363 A122150 A368888 * A072526 A095218 A119964

Adjacent sequences: A092660 A092661 A092662 * A092664 A092665 A092666

Keyword

more,nonn,hard

Author

Enoch Haga, Mar 02 2004

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

Status

approved