cp's OEIS Frontend

A145994 Last prime in a run of at least 2 consecutive primes of the form 4k+3.

%I A145994 #13 Mar 26 2020 06:40:10
%S A145994 11,23,47,71,83,107,131,167,227,311,367,383,443,503,631,647,691,727,
%T A145994 751,827,863,919,971,991,1091,1171,1283,1319,1427,1451,1471,1487,1543,
%U A145994 1583,1667,1787,1847,1871,1987,2011,2087,2111,2207,2267,2351,2411,2467,2543,2591,2671,2687
%N A145994 Last prime in a run of at least 2 consecutive primes of the form 4k+3.
%D A145994 Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6
%e A145994 a(1)=11 because this sequence includes consecutive runs of any length >1 and this ending term in a run of 2 is 11.
%p A145994 A145994 := proc()
%p A145994     local m,p,r,i,lp ;
%p A145994     m := 3 ;
%p A145994     p := 2 ;
%p A145994     r := 0 ;
%p A145994     for i from 2 to 1000 do
%p A145994         if modp(p,4) = m then
%p A145994             r := r+1 ;
%p A145994         else
%p A145994             if r > 1 then
%p A145994                 printf("%d,",prevprime(p)) ;
%p A145994             end if;
%p A145994             r := 0;
%p A145994         end if;
%p A145994         p := nextprime(p) ;
%p A145994     end do:
%p A145994 end proc:
%p A145994 A145994() ; # _R. J. Mathar_, Aug 29 2018
%t A145994 Last /@ Select[Split[Select[4Range[1000]+3, PrimeQ], #2 == NextPrime[#1]&], Length[#]>1&] (* _Jean-François Alcover_, Mar 26 2020 *)
%o A145994 (UBASIC) 10 'cluster primes
%o A145994 20 C=1
%o A145994 30 input "end #";L
%o A145994 40 for N=3 to L step 2
%o A145994 50 S=int(sqrt(N))
%o A145994 60 for A=3 to S step 2
%o A145994 70 B=N/A
%o A145994 80 if int(B)*A=N then cancel for:goto 170
%o A145994 90 next A
%o A145994 100 C=C+1
%o A145994 110 E=N/4:E=int(E):R=N-(4*E)
%o A145994 120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1
%o A145994 130 if R=3 then T1=0
%o A145994 140 if R=3 then print " ";N;:C3=C3+1:T2=T2+1:print T2
%o A145994 150 if R=1 then T2=0
%o A145994 160 if T1>10 or T2>10 then stop
%o A145994 170 next
%o A145994 180 print "Total primes=";C;:print "Type A";C1;"Type B";C3
%Y A145994 Cf. A039702, A055623, A145986, A145988, A145990, A145991, A145992 (run lengths), A145993 (first prime in run)
%K A145994 easy,nonn
%O A145994 1,1
%A A145994 _Enoch Haga_, Oct 26 2008