A092646 Number of consecutive prime runs of just 4 primes congruent to 3 mod 4 below 10^n.

0, 0, 1, 15, 111, 1013, 8963, 78496, 703783, 6388533, 58446494

Offset

1,4

Links

Table of n, a(n) for n=1..11.

Formula

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

Example

a(5)=111 because 111 sets of 4 primes occur below 10^5, each run interrupted by a prime congruent to 1 mod 4.

Mathematica

p1 = p3 = 0; p = 15; s = Mod[{2, 3, 5, 7, 11, 13}, 4]; Do[ While[p < 10^n, If[s == {3, 1, 1, 1, 1, 3}, p1++]; If[s == {1, 3, 3, 3, 3, 1}, p3++]; p = NextPrime@ p; s = Join[ Take[s, -5], {Mod[p, 4]}]]; Print[{p1, p3}], {n, 2, 9}] (* Robert G. Wilson v, Sep 30 2011 *)

Crossrefs

Cf. A092645, A092647.

Sequence in context: A290361 A254869 A034184 * A222117 A105051 A105040

Adjacent sequences: A092643 A092644 A092645 * A092647 A092648 A092649

Keyword

more,nonn

Author

Enoch Haga, Mar 02 2004

Extensions

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

Status

approved