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A145986 Ending prime: n-th prime in the first occurrence of n consecutive primes of the form 4k + 1. 7


%S 5,17,101,409,2633,11657,11677,11681,11689,373777,766373,3358373,

%T 12205121,12270281,12270301,12270317,297388097,297779509,297779513,

%U 1113443473,1113443521,1113443533,1113443549,1113443561,84676453373,84676453429

%N Ending prime: n-th prime in the first occurrence of n consecutive primes of the form 4k + 1.

%C a(1)=5 is same as A055623(1) because 5 is a single-digit number.

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

%e a(2)=17 because this is the 2nd prime in the first run of 2 primes where p == 1 mod 4.

%o (UBASIC) 10 'cluster primes

%o 20 C=1: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: E=int(N/4):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: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

%o (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 Cf. A055623, A054624, A145988, A145989, A145990, A145991, A145992, A145993, A145994.

%K nonn

%O 1,1

%A _Enoch Haga_, Oct 26 2008

%E Entry rewritten and a(13)-a(26) added by _Charles R Greathouse IV_, Mar 22 2011

%E Edited by _M. F. Hasler_, May 02 2015

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)