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Primes p such that 3(p-3)-1 and 3(p-3)+1 are twin primes.
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%I #14 Jan 16 2017 08:13:24

%S 5,7,13,17,23,37,53,67,79,83,97,107,157,193,223,277,347,353,367,433,

%T 443,479,487,499,569,577,599,647,653,773,797,853,907,937,1087,1103,

%U 1123,1259,1277,1367,1409,1423,1427,1549,1553,1747,1889,2069,2153,2237,2267

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

%C In other words, primes p such that 3*(p-3) is a term of A014574. - _Omar E. Pol_, Aug 05 2009

%H Robert Israel, <a href="/A163385/b163385.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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

%t 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

%t 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 *)

%Y Cf. A163386, A163387, A163388. - _Omar E. Pol_, Aug 05 2009

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 25 2009

%E Definition clarified and edited by _Omar E. Pol_, Aug 05 2009