A145994 Last prime in a run of at least 2 consecutive primes of the form 4k+3.

11, 23, 47, 71, 83, 107, 131, 167, 227, 311, 367, 383, 443, 503, 631, 647, 691, 727, 751, 827, 863, 919, 971, 991, 1091, 1171, 1283, 1319, 1427, 1451, 1471, 1487, 1543, 1583, 1667, 1787, 1847, 1871, 1987, 2011, 2087, 2111, 2207, 2267, 2351, 2411, 2467, 2543, 2591, 2671, 2687

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

Table of n, a(n) for n=1..51.

Example

a(1)=11 because this sequence includes consecutive runs of any length >1 and this ending term in a run of 2 is 11.

Maple

A145994 := proc()
    local m, p, r, i, lp ;
    m := 3 ;
    p := 2 ;
    r := 0 ;
    for i from 2 to 1000 do
        if modp(p, 4) = m then
            r := r+1 ;
        else
            if r > 1 then
                printf("%d, ", prevprime(p)) ;
            end if;
            r := 0;
        end if;
        p := nextprime(p) ;
    end do:
end proc:
A145994() ; # R. J. Mathar, Aug 29 2018

Mathematica

Last /@ Select[Split[Select[4Range[1000]+3, PrimeQ], #2 == NextPrime[#1]&], Length[#]>1&] (* Jean-François Alcover, Mar 26 2020 *)

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, A145986, A145988, A145990, A145991, A145992 (run lengths), A145993 (first prime in run)

Sequence in context: A161897 A282531 A309851 * A217047 A139834 A100558

Adjacent sequences: A145991 A145992 A145993 * A145995 A145996 A145997

Keyword

easy,nonn

Author

Enoch Haga, Oct 26 2008

Status

approved