A163385 Primes p such that 3(p-3)-1 and 3(p-3)+1 are twin primes.

5, 7, 13, 17, 23, 37, 53, 67, 79, 83, 97, 107, 157, 193, 223, 277, 347, 353, 367, 433, 443, 479, 487, 499, 569, 577, 599, 647, 653, 773, 797, 853, 907, 937, 1087, 1103, 1123, 1259, 1277, 1367, 1409, 1423, 1427, 1549, 1553, 1747, 1889, 2069, 2153, 2237, 2267

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 25 2009

Keywords

• nonn
• easy

Comments

In other words, primes p such that 3*(p-3) is a term of A014574. - Omar E. Pol, Aug 05 2009

Examples

			3*(5-3) = 6, 3*(7-3) = 12, 3*(13-3) = 30, ...
		

Links

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

Crossrefs

Cf. A163386, A163387, A163388. - Omar E. Pol, Aug 05 2009

Programs

Maple

select(p -> isprime(p) and isprime(3*p-10) and isprime(3*p-8), [seq(i,i=3..10000,2)]); # Robert Israel, Nov 13 2016

Mathematica

f1[n_]:=If[PrimeQ[n-1]&&PrimeQ[n+1],True,False]; f2[n_]:=If[f1[n]&&PrimeQ[n/3+3],True,False]; lst={};Do[If[f2[n],AppendTo[lst,n/3+3]],{n,8!}];lst
Select[Prime[Range[400]],AllTrue[3(#-3)+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 16 2017 *)

Extensions

Definition clarified and edited by Omar E. Pol, Aug 05 2009