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

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

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