A145986 n-th prime in the first occurrence of at least n consecutive primes of the form 4k + 1.
5, 17, 101, 409, 2633, 11657, 11677, 11681, 11689, 373777, 766373, 3358373, 12205121, 12270281, 12270301, 12270317, 297388097, 297779509, 297779513, 1113443473, 1113443521, 1113443533, 1113443549, 1113443561, 84676453373, 84676453429
Offset: 1
Keywords
Examples
a(2)=17 because this is the 2nd prime in the first run of 2 primes where p == 1 mod 4.
References
- Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007, pp. 30-31. ISBN 978-1-885794-24-6
Programs
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Mathematica
Flatten[Table[SequencePosition[Table[If[Mod[p-1,4]==0,1,0],{p,Prime[Range[250000]]}],PadRight[ {},n,1],1],{n,12}],1][[;;,-1]]//Prime (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jul 14 2024 *) -
PARI
r=0;c=0;forprime(p=2,4e9,if(p%4==1,if(c++>r,r=c;print1(p", ")),c=0)) \\ Charles R Greathouse IV, Mar 22 2011
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UBASIC
10 'cluster primes 20 C=1: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: E=int(N/4):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: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 and a(13)-a(26) added by Charles R Greathouse IV, Mar 22 2011
Edited by M. F. Hasler, May 02 2015
Definition clarified by N. J. A. Sloane, Dec 18 2022
Comments