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A145992 Run lengths of 2 or more consecutive primes of the form 4k+3.

%I A145992 #19 Jul 25 2024 02:40:21
%S A145992 2,2,2,2,2,2,2,2,4,2,2,2,2,7,2,2,2,2,3,2,2,5,2,2,2,2,2,3,2,3,2,2,5,5,
%T A145992 2,2,4,2,2,3,2,2,3,4,2,2,3,3,2,3,2,3,2,2,2,2,2,3,3,2,3,3,2,4,2,2,3,2,
%U A145992 2,3,2,2,2,2,4,2,2,3,2,3,3,2,3,4,2,2,2,4,2,2,3,2,2,2,2,2,3,2,3,2,3,3
%N A145992 Run lengths of 2 or more consecutive primes of the form 4k+3.
%D A145992 Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6
%H A145992 Harvey P. Dale, <a href="/A145992/b145992.txt">Table of n, a(n) for n = 1..1000</a>
%e A145992 a(1) = 2 counts the two 3's from A039702(4) to A039702(5).
%e A145992 a(9) = 4 counts the four 3's from A039702(46) to A039702(49).
%e A145992 a(14)= 7 counts the seven 4's from A039702(90) to A039702(96).
%p A145992 A145992 := proc()
%p A145992     local m,p,r,i ;
%p A145992     m := 3 ;
%p A145992     p := 2 ;
%p A145992     r := 0 ;
%p A145992     for i from 2 to 1000 do
%p A145992         if modp(p,4) = m then
%p A145992             r := r+1 ;
%p A145992         else
%p A145992             if r > 1 then
%p A145992                 printf("%d,",r) ;
%p A145992             end if;
%p A145992             r := 0;
%p A145992         end if;
%p A145992         p := nextprime(p) ;
%p A145992     end do:
%p A145992 end proc:
%p A145992 A145992() ; # _R. J. Mathar_, Aug 29 2018
%t A145992 Most[Length /@ Select[ SplitBy[ Prime@ Range@ 780, Mod[#, 4] &], Mod[#[[1]], 4] == 3 && Length[#] > 1 &]] (* _Giovanni Resta_, Aug 29 2018 *)
%t A145992 Length/@Select[Split[Table[If[Mod[n,4]==3,1,0],{n,Prime[Range[ 1000]]}]], FreeQ[ #,0]&]/.(1->Nothing) (* _Harvey P. Dale_, Jul 27 2020 *)
%Y A145992 Cf. A039702, A055623, A145986, A145988, A145989, A145990, A145991, A145993, A145994.
%K A145992 easy,nonn
%O A145992 1,1
%A A145992 _Enoch Haga_, Oct 26 2008
%E A145992 Corrected by _R. J. Mathar_, Aug 29 2018