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A145990 Primes which start a run of at least length 2 of consecutive primes == 1 (mod 4).

%I A145990 #15 May 04 2019 00:36:57
%S A145990 13,37,89,109,193,229,277,313,349,389,449,509,613,661,701,757,797,853,
%T A145990 877,929,997,1093,1109,1193,1237,1297,1373,1429,1489,1549,1597,1609,
%U A145990 1637,1669,1709,1733,1789,1873,1889,1933,1993,2069,2113,2137,2153,2213,2269
%N A145990 Primes which start a run of at least length 2 of consecutive primes == 1 (mod 4).
%D A145990 Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007, pp. 30-31. ISBN 978-1-885794-24-6
%H A145990 Harvey P. Dale, <a href="/A145990/b145990.txt">Table of n, a(n) for n = 1..1000</a>
%e A145990 a(1)=13 because this sequence includes consecutive runs of any length and this first term > 1 in a run of 2 is 13.
%p A145990 for i from 2 to 300 do
%p A145990         if (ithprime(i) mod 4) = 1  and ithprime(i-1) mod 4 <> 1 and ithprime(i+1) mod 4 = 1 then
%p A145990                 printf("%d,",ithprime(i)) ;
%p A145990         end if;
%p A145990 end do: # _R. J. Mathar_, Sep 30 2011
%t A145990 Prime[#+1]&/@(SequencePosition[Table[If[Mod[n,4]==1,1,0],{n,Prime[ Range[ 350]]}],{0,1,1},Overlaps->False][[All,1]]) (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 02 2017 *)
%o A145990 (UBASIC)
%o A145990 10 'cluster primes
%o A145990 20 C=1
%o A145990 30 input "end #";L
%o A145990 40 for N=3 to L step 2
%o A145990 50 S=int(sqrt(N))
%o A145990 60 for A=3 to S step 2
%o A145990 70 B=N/A
%o A145990 80 if int(B)*A=N then cancel for:goto 170
%o A145990 90 next A
%o A145990 100 C=C+1
%o A145990 110 E=N/4:E=int(E):R=N-(4*E)
%o A145990 120 if R=1 then print N;:C1=C1+1:T1=T1+1:print T1
%o A145990 130 if R=3 then T1=0
%o A145990 140 if R=3 then print " ";N;:C3=C3+1:T2=T2+1:print T2
%o A145990 150 if R=1 then T2=0
%o A145990 160 if T1>10 or T2>10 then stop
%o A145990 170 next
%o A145990 180 print "Total primes=";C;:print "Type A";C1;"Type B";C3
%Y A145990 Cf. A039702, A055623, A054624, A145986, A145988 - A145994.
%K A145990 easy,nonn
%O A145990 1,1
%A A145990 _Enoch Haga_, Oct 26 2008
%E A145990 Corrected and extended by _Harvey P. Dale_, Aug 02 2017