A136721 Prime quadruples: 3rd term.

11, 17, 107, 197, 827, 1487, 1877, 2087, 3257, 3467, 5657, 9437, 13007, 15647, 15737, 16067, 18047, 18917, 19427, 21017, 22277, 25307, 31727, 34847, 43787, 51347, 55337, 62987, 67217, 69497, 72227, 77267, 79697, 81047, 82727, 88817, 97847

Offset: 1

Author

Enoch Haga, Jan 18 2008

Keywords

• easy
• nonn

Comments

Primes p such that p-6, p-4, and p+2 are prime. Apart from the first term, a(n) = 17 (mod 30).

The members of each quadruple are twin primes when they are 1st and 2nd terms and when 3rd and 4th terms. When they are 2nd and 3rd terms they differ by 4.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007530, A090258, A136720.

Programs

Maple

p2:= 0: p3:= 0: p4:= 0:
Res:= NULL: count:= 0:
while count < 100 do
  p1:= p2; p2:= p3; p3:= p4;
  p4:= nextprime(p4);
  if [p2-p1, p3-p2, p4-p3] = [2, 4, 2] then
     count:= count+1; Res:= Res, p3
  fi
od:
Res; # Robert Israel, Oct 11 2019

Mathematica

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

Formula

a(n) = A007530(n)+6 = A136720(n)+4 = A090258(n)-2. - Robert Israel, Oct 11 2019

Extensions

Edited by Charles R Greathouse IV, Oct 11 2009