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Prime quadruples: 2nd term.
3

%I #15 Oct 11 2019 15:54:55

%S 7,13,103,193,823,1483,1873,2083,3253,3463,5653,9433,13003,15643,

%T 15733,16063,18043,18913,19423,21013,22273,25303,31723,34843,43783,

%U 51343,55333,62983,67213,69493,72223,77263,79693,81043,82723,88813,97843

%N Prime quadruples: 2nd term.

%C Primes p such that p-2, p+4, and p+6 are prime. Apart from the first term, a(n) = 13 (mod 30).

%H Robert Israel, <a href="/A136720/b136720.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007530(n)+2 = A136721(n)-4 = A090258(n)-6. - _Robert Israel_, Oct 11 2019

%e The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.

%p p2:= 0: p3:= 0: p4:= 0:

%p Res:= NULL: count:= 0:

%p while count < 100 do

%p p1:= p2; p2:= p3; p3:= p4;

%p p4:= nextprime(p4);

%p if [p2-p1, p3-p2, p4-p3] = [2,4,2] then

%p count:= count+1; Res:= Res, p2

%p fi

%p od:

%p Res; # _Robert Israel_, Oct 11 2019

%t lst={};Do[p0=Prime[n];If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p2]]]], {n, 12^4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 22 2008 *)

%Y Cf. A007530, A090258, A136721.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Jan 18 2008

%E Edited by _Charles R Greathouse IV_, Oct 11 2009