A174915 Numbers p such that p, q=p+2 and p+2*q are all primes.

3, 5, 11, 41, 59, 101, 179, 191, 269, 311, 431, 521, 599, 821, 881, 1019, 1061, 1151, 1229, 1301, 1451, 1481, 1619, 1721, 1949, 2081, 2111, 2141, 2729, 2999, 3299, 3821, 4001, 4091, 4259, 4421, 4799, 4931, 5009, 5519, 5639, 5849, 6131, 6359, 6689, 6701

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

• nonn

Comments

Subsequence of A175914.

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A174913, A175914.

Programs

Magma

[p: p in PrimesUpTo(7000) | IsPrime(p+2) and IsPrime(3*p+4)]; // Vincenzo Librandi, Jan 29 2015

Mathematica

lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1+2*p2],AppendTo[lst,p1]],{n,7!}];lst
Reap[Do[p = Prime[m]; If[PrimeQ[p + 2 ] && PrimeQ[3 p + 4], Sow[p]], {m, 10^3}]][[2, 1]](* Zak Seidov, Oct 14 2012 *)
Transpose[Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]]==2 && PrimeQ[ #[[1]]+2#[[2]]]&]][[1]] (* Harvey P. Dale, Jan 28 2015 *)

PARI

forprime(p=2,7000,q=p+2;if(isprime(q)&& isprime(p+2*q),print1(p,", ")))

Extensions

Definition and comment corrected by Zak Seidov, Dec 06 2010