A145993 Primes that start a run of at least 2 consecutive primes of the form 4k+3.

7, 19, 43, 67, 79, 103, 127, 163, 199, 307, 359, 379, 439, 463, 619, 643, 683, 719, 739, 823, 859, 883, 967, 983, 1087, 1163, 1279, 1303, 1423, 1439, 1459, 1483, 1499, 1559, 1663, 1783, 1811, 1867, 1979, 1999, 2083, 2099, 2179, 2239, 2347, 2399, 2447, 2531, 2579, 2659, 2683, 2699, 2803, 2843, 2879

Offset: 1

Author

Enoch Haga, Oct 26 2008

Keywords

• easy
• nonn

Examples

			a(1)=7 because this sequence includes consecutive runs of any length and this first term >1 in a run of 2 is 7.
		

References

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

Crossrefs

Cf. A039702, A055623, A145986, A145988, A145989, A145990, A145991, A145992 (run lengths) A145994.

Programs

Maple

A145993 := proc()
    local m,p,r,i,sp ;
    m := 3 ;
    p := 2 ;
    r := 0 ;
    sp := -1 ;
    for i from 2 to 1000 do
        if modp(p,4) = m then
            r := r+1 ;
            if r = 1 then
                sp := p ;
            end if;
        else
            if r > 1 then
                printf("%d,",sp) ;
            end if;
            r := 0;
            sp := -1 ;
        end if;
        p := nextprime(p) ;
    end do:
end proc:
A145993() ; # R. J. Mathar, Aug 29 2018

Mathematica

Most[First /@ Select[ SplitBy[ Prime@ Range@ 425, Mod[#, 4] &], Mod[#[[1]], 4] == 3 && Length[#] > 1 &]] (* Giovanni Resta, Aug 29 2018 *)

Extensions

619 inserted by R. J. Mathar, Aug 29 2018