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A145990
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Primes which start a run of at least length 2 of consecutive primes == 1 (mod 4).
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6
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13, 37, 89, 109, 193, 229, 277, 313, 349, 389, 449, 509, 613, 661, 701, 757, 797, 853, 887, 929, 997, 1093, 1109, 1193, 1237, 1297, 1373, 1429, 1489, 1549, 1597, 1609, 1637, 1669, 1709, 1733, 1789, 1873, 1889, 1933, 1993, 2069, 2113, 2137, 2153, 2213
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6
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LINKS
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Table of n, a(n) for n=1..46.
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EXAMPLE
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a(1)=13 because this sequence includes consecutive runs of any length and this first term > 1 in a run of 2 is 13.
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MAPLE
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for i from 2 to 300 do
if (ithprime(i) mod 4) = 1 and ithprime(i-1) mod 4 <> 1 and ithprime(i+1) mod 4 = 1 then
printf("%d, ", ithprime(i)) ;
end if;
end do: # R. J. Mathar, Sep 30 2011
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PROG
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(Other) UBASIC:
10 'cluster primes
20 C=1
30 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
110 E=N/4:E=int(E):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
140 if R=3 then 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
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CROSSREFS
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Cf. A039702, A055623, A054624, A145986, A145988 - A145994.
Sequence in context: A039367 A139697 A124706 * A089528 A043190 A043970
Adjacent sequences: A145987 A145988 A145989 * A145991 A145992 A145993
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KEYWORD
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easy,nonn
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AUTHOR
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Enoch Haga, Oct 26 2008
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STATUS
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approved
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