A145992 Run lengths of 2 or more consecutive primes of the form 4k+3.

2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 7, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 5, 5, 2, 2, 4, 2, 2, 3, 2, 2, 3, 4, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 3, 2, 3, 3, 2, 3, 4, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3

Offset: 1

Author

Enoch Haga, Oct 26 2008

Keywords

• easy
• nonn

Examples

			a(1) = 2 counts the two 3's from A039702(4) to A039702(5).
a(9) = 4 counts the four 3's from A039702(46) to A039702(49).
a(14)= 7 counts the seven 4's from A039702(90) to A039702(96).
		

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

Crossrefs

Cf. A039702, A055623, A145986, A145988, A145989, A145990, A145991, A145993, A145994.

Programs

Maple

A145992 := proc()
    local m,p,r,i ;
    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,",r) ;
            end if;
            r := 0;
        end if;
        p := nextprime(p) ;
    end do:
end proc:
A145992() ; # R. J. Mathar, Aug 29 2018

Mathematica

Most[Length /@ Select[ SplitBy[ Prime@ Range@ 780, Mod[#, 4] &], Mod[#[[1]], 4] == 3 && Length[#] > 1 &]] (* Giovanni Resta, Aug 29 2018 *)
Length/@Select[Split[Table[If[Mod[n,4]==3,1,0],{n,Prime[Range[ 1000]]}]], FreeQ[ #,0]&]/.(1->Nothing) (* Harvey P. Dale, Jul 27 2020 *)

Extensions

Corrected by R. J. Mathar, Aug 29 2018