A145988 Ending prime: n-th prime in the first occurrence of n consecutive primes of the form 4k + 3.

3, 11, 223, 227, 491, 499, 503, 36607, 39703, 183283, 241727, 241739, 241771, 9177607, 9177611, 95949631, 105639463, 341118731, 727335359, 727335379, 1786054619, 1786054631, 22964264759, 54870713999, 79263248759

Offset: 1

Author

Enoch Haga, Oct 26 2008

Keywords

• nonn

Comments

a(1)=3 is the same as A055624(1) because 3 is a single-digit number.

Examples

			a(2)=11 because this is the 2nd prime in the first run of 2 primes where p == 3 mod 4.
		

References

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

Crossrefs

Cf. A055623, A054624, A145986, A145989, A145990, A145991, A145992, A145993, A145994.

Programs

Mathematica

Prime[#]&/@Flatten[Table[SequencePosition[If[Mod[#,4]==3,1,0]&/@Prime[ Range[ 615000]],PadRight[{},n,1],1],{n,15}],1][[All,2]] (* The program generates the first 15 terms of the sequence. *) (* Harvey P. Dale, Jun 17 2022 *)

PARI

r=0; c=0; forprime(p=2, 4e9, if(p%4==3, if(c++>r, r=c; print1(p", ")), c=0)) \\ Charles R Greathouse IV, Mar 22 2011

UBASIC

10 'cluster primes 20 C=1 30 input "end #";L 40 for N=3 to L step 2 50 S=int(sqrt(N)) 60 for A=3 to S step 2 70 B=N/A 80 if int(B)*A=N then cancel for:goto 170 90 next A 100 C=C+1 110 E=N/4:E=int(E):R=N-(4*E) 120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1 130 if R=3 then T1=0 140 if R=3 then print " ";N;:C3=C3+1:T2=T2+1:print T2 150 if R=1 then T2=0 160 if T1>10 or T2>10 then stop 170 next 180 print "Total primes=";C;:print "Type A";C1;"Type B";C3

Extensions

Entry rewritten by, and a(14)-a(25) from, Charles R Greathouse IV, Mar 22 2011