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A145993 Primes that start a run of at least 2 consecutive primes of the form 4k+3. 5
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 (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

Table of n, a(n) for n=1..55.

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A192755 A141193 A104163 * A265676 A054690 A259486

Adjacent sequences:  A145990 A145991 A145992 * A145994 A145995 A145996

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Oct 26 2008

EXTENSIONS

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

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)