A136720 Prime quadruples: 2nd term.

7, 13, 103, 193, 823, 1483, 1873, 2083, 3253, 3463, 5653, 9433, 13003, 15643, 15733, 16063, 18043, 18913, 19423, 21013, 22273, 25303, 31723, 34843, 43783, 51343, 55333, 62983, 67213, 69493, 72223, 77263, 79693, 81043, 82723, 88813, 97843

Offset

1,1

Comments

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

Links

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

Formula

a(n) = A007530(n)+2 = A136721(n)-4 = A090258(n)-6. - Robert Israel, Oct 11 2019

Example

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.

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, p2
  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, p2]]]], {n, 12^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)

Crossrefs

Cf. A007530, A090258, A136721.

Sequence in context: A039687 A001544 A202152 * A323468 A035030 A046519

Adjacent sequences: A136717 A136718 A136719 * A136721 A136722 A136723

Keyword

easy,nonn

Author

Enoch Haga, Jan 18 2008

Extensions

Edited by Charles R Greathouse IV, Oct 11 2009

Status

approved