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Final prime in a run of more than 1 consecutive primes == 1 (mod 4).
5

%I #8 Jul 03 2016 00:17:34

%S 17,41,101,113,197,233,281,317,353,409,461,521,617,677,709,773,809,

%T 857,881,941,1013,1097,1117,1217,1249,1301,1381,1433,1493,1553,1601,

%U 1613,1657,1697,1721,1741,1801,1877,1901,1949,1997,2081,2129,2141,2161,2237

%N Final prime in a run of more than 1 consecutive primes == 1 (mod 4).

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

%e a(1)=17 because this sequence includes consecutive runs of any length and this ending term > 1 in a run of 2 (comprising 13 and 17) is 17.

%o (UBASIC)

%o 10 'cluster primes

%o 20 C=1

%o 30 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

%o 110 E=N/4:E=int(E):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

%o 140 if R=3 then 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

%Y Cf. A055623, A054624, A145986, A145988- A145994

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Oct 26 2008