%I #13 May 31 2019 20:10:51

%S 1,3,28,217,1570,12515,102942,867677,7541800,66571277,595524791

%N Number of consecutive prime runs of 1 prime congruent to 3 mod 4 below 10^n.

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

%e a(3)=28 because 28 single primes occur below 10^3, each interrupted in the run by a prime congruent to 1 mod 4.

%t A002144 = Join[{0}, Select[4 Range[0, 10^4] + 1, PrimeQ[#] &]];

%t A002145 = Select[4 Range[0, 10^4] + 3, PrimeQ[#] &];

%t lst = {}; Do[If[Length[s = Select[A002145, Between[{A002144[[i]], A002144[[i + 1]]}]]] == 1, AppendTo[lst, Last[s]]], {i, Length[A002144] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}] (* _Robert Price_, May 31 2019 *)

%Y Cf. A091318, A092636 - A092665.

%K more,nonn

%O 1,2

%A _Enoch Haga_, Mar 02 2004

%E a(9)-a(11) from _Chai Wah Wu_, Mar 18 2018