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A145993 Primes that start a run of at least 2 consecutive primes of the form 4k+3.

%I A145993 #11 Aug 29 2018 06:32:41
%S A145993 7,19,43,67,79,103,127,163,199,307,359,379,439,463,619,643,683,719,
%T A145993 739,823,859,883,967,983,1087,1163,1279,1303,1423,1439,1459,1483,1499,
%U A145993 1559,1663,1783,1811,1867,1979,1999,2083,2099,2179,2239,2347,2399,2447,2531,2579,2659,2683,2699,2803,2843,2879
%N A145993 Primes that start a run of at least 2 consecutive primes of the form 4k+3.
%D A145993 Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6
%e A145993 a(1)=7 because this sequence includes consecutive runs of any length and this first term >1 in a run of 2 is 7.
%p A145993 A145993 := proc()
%p A145993     local m,p,r,i,sp ;
%p A145993     m := 3 ;
%p A145993     p := 2 ;
%p A145993     r := 0 ;
%p A145993     sp := -1 ;
%p A145993     for i from 2 to 1000 do
%p A145993         if modp(p,4) = m then
%p A145993             r := r+1 ;
%p A145993             if r = 1 then
%p A145993                 sp := p ;
%p A145993             end if;
%p A145993         else
%p A145993             if r > 1 then
%p A145993                 printf("%d,",sp) ;
%p A145993             end if;
%p A145993             r := 0;
%p A145993             sp := -1 ;
%p A145993         end if;
%p A145993         p := nextprime(p) ;
%p A145993     end do:
%p A145993 end proc:
%p A145993 A145993() ; # _R. J. Mathar_, Aug 29 2018
%t A145993 Most[First /@ Select[ SplitBy[ Prime@ Range@ 425, Mod[#, 4] &], Mod[#[[1]], 4] == 3 && Length[#] > 1 &]] (* _Giovanni Resta_, Aug 29 2018 *)
%Y A145993 Cf. A039702, A055623, A145986, A145988, A145989, A145990, A145991, A145992 (run lengths) A145994.
%K A145993 easy,nonn
%O A145993 1,1
%A A145993 _Enoch Haga_, Oct 26 2008
%E A145993 619 inserted by _R. J. Mathar_, Aug 29 2018