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A145994 Last prime in a run of at least 2 consecutive primes of the form 4k+3. 8

%I

%S 11,23,47,71,83,107,131,167,227,311,367,383,443,503,631,647,691,727,

%T 751,827,863,919,971,991,1091,1171,1283,1319,1427,1451,1471,1487,1543,

%U 1583,1667,1787,1847,1871,1987,2011,2087,2111,2207,2267,2351,2411,2467,2543,2591,2671,2687

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

%D Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6

%e 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 := proc()

%p local m,p,r,i,lp ;

%p m := 3 ;

%p p := 2 ;

%p r := 0 ;

%p for i from 2 to 1000 do

%p if modp(p,4) = m then

%p r := r+1 ;

%p else

%p if r > 1 then

%p printf("%d,",prevprime(p)) ;

%p end if;

%p r := 0;

%p end if;

%p p := nextprime(p) ;

%p end do:

%p end proc:

%p A145994() ; # _R. J. Mathar_, Aug 29 2018

%t Last /@ Select[Split[Select[4Range[1000]+3, PrimeQ], #2 == NextPrime[#1]&], Length[#]>1&] (* _Jean-Fran├žois Alcover_, Mar 26 2020 *)

%o (UBASIC) 10 'cluster primes

%o 20 C=1

%o 30 input "end #";L

%o 40 for N=3 to L step 2

%o 50 S=int(sqrt(N))

%o 60 for A=3 to S step 2

%o 70 B=N/A

%o 80 if int(B)*A=N then cancel for:goto 170

%o 90 next A

%o 100 C=C+1

%o 110 E=N/4:E=int(E):R=N-(4*E)

%o 120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1

%o 130 if R=3 then T1=0

%o 140 if R=3 then print " ";N;:C3=C3+1:T2=T2+1:print T2

%o 150 if R=1 then T2=0

%o 160 if T1>10 or T2>10 then stop

%o 170 next

%o 180 print "Total primes=";C;:print "Type A";C1;"Type B";C3

%Y Cf. A039702, A055623, A145986, A145988, A145990, A145991, A145992 (run lengths), A145993 (first prime in run)

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Oct 26 2008

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Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)