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%I #13 Jun 09 2019 21:16:28
%S 0,0,4,38,305,2450,20939,182955,1618599,14491882,131026137
%N Number of consecutive prime runs of 3 primes congruent to 1 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 3 primes occur before interruption by a prime congruent to 3 mod 4.
%e a(5)=305 because 305 sets of 3 primes occur below 10^5, each run interrupted by a prime congruent to 3 mod 4.
%t A002145 = Join[{0}, Select[4 Range[0, 10^4] + 3, PrimeQ[#] &]];
%t A002144 = Select[4 Range[0, 10^4] + 1, PrimeQ[#] &];
%t lst = {}; Do[If[Length[s = Select[A002144, Between[{A002145[[i]], A002145[[i + 1]]}]]] == 3, AppendTo[lst, Last[s]]], {i, Length[A002145] - 1}]; Table[Count[lst, x_ /; x < 10^n], {n, 4}] (* _Robert Price_, Jun 09 2019 *)
%Y Cf. A092643, A092644.
%K more,nonn
%O 1,3
%A _Enoch Haga_, Mar 02 2004
%E a(9)-a(11) from _Chai Wah Wu_, Mar 18 2018