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A145990 Primes which start a run of at least length 2 of consecutive primes == 1 (mod 4). 7
13, 37, 89, 109, 193, 229, 277, 313, 349, 389, 449, 509, 613, 661, 701, 757, 797, 853, 877, 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, 2269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1)=13 because this sequence includes consecutive runs of any length and this first term > 1 in a run of 2 is 13.

MAPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A039702, A055623, A054624, A145986, A145988 - A145994.

Sequence in context: A039367 A139697 A124706 * A089528 A317986 A043190

Adjacent sequences:  A145987 A145988 A145989 * A145991 A145992 A145993

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Oct 26 2008

EXTENSIONS

Corrected and extended by Harvey P. Dale, Aug 02 2017

STATUS

approved

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Last modified May 22 05:03 EDT 2019. Contains 323473 sequences. (Running on oeis4.)