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A145986 n-th prime in the first occurrence of at least n consecutive primes of the form 4k + 1.

%I A145986 #18 Jul 14 2024 12:31:42
%S A145986 5,17,101,409,2633,11657,11677,11681,11689,373777,766373,3358373,
%T A145986 12205121,12270281,12270301,12270317,297388097,297779509,297779513,
%U A145986 1113443473,1113443521,1113443533,1113443549,1113443561,84676453373,84676453429
%N A145986 n-th prime in the first occurrence of at least n consecutive primes of the form 4k + 1.
%C A145986 a(1)=5 is same as A055623(1) because 5 is a single-digit number.
%D A145986 Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007, pp. 30-31. ISBN 978-1-885794-24-6
%e A145986 a(2)=17 because this is the 2nd prime in the first run of 2 primes where p == 1 mod 4.
%t A145986 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 *)
%o A145986 (UBASIC) 10 'cluster primes
%o A145986 20 C=1:input "end #";L
%o A145986 40 for N=3 to L step 2
%o A145986 50 S=int(sqrt(N))
%o A145986 60 for A=3 to S step 2
%o A145986 70 B=N/A
%o A145986 80 if int(B)*A=N then cancel for:goto 170
%o A145986 90 next A
%o A145986 100 C=C+1: E=int(N/4):R=N-(4*E)
%o A145986 120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1
%o A145986 130 if R=3 then T1=0:print " ";N;:C3=C3+1:T2=T2+1:print T2
%o A145986 150 if R=1 then T2=0
%o A145986 160 if T1>10 or T2>10 then stop
%o A145986 170 next
%o A145986 180 print "Total primes=";C;:print "Type A:";C1;" Type B:";C3
%o A145986 (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
%Y A145986 Cf. A055623, A054624, A145988, A145989, A145990, A145991, A145992,  A145993, A145994.
%K A145986 nonn
%O A145986 1,1
%A A145986 _Enoch Haga_, Oct 26 2008
%E A145986 Entry rewritten and a(13)-a(26) added by _Charles R Greathouse IV_, Mar 22 2011
%E A145986 Edited by _M. F. Hasler_, May 02 2015
%E A145986 Definition clarified by _N. J. A. Sloane_, Dec 18 2022