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%I #21 Sep 08 2022 08:45:51
%S 3,5,59,269,1949,2999,6359,11489,11549,14549,18539,19889,21839,31079,
%T 32909,32969,33329,33599,42569,42839,50459,53549,58109,68879,70199,
%U 74609,79229,80909,93809,96329,98909,104309,109139,114599,121019,125789
%N List of primes p1 such that (p1,p2) are twin primes where both 2*p1+p2 and p1+2*p2 are primes.
%C Terms >5 are congruent to 29 mod 30. - _Zak Seidov_, May 10 2012
%C Also 2*p1+p2 and p1+2*p2 are twin primes. - _Zak Seidov_, May 10 2012
%H Zak Seidov, <a href="/A174920/b174920.txt">Table of n, a(n) for n = 1..1000</a>
%F From _Wesley Ivan Hurt_, May 03 2022: (Start)
%F a(n) = A132929(n) - 1.
%F a(n) = A177336(n) - 2. (End)
%e a(1)=3 because 3, 5 are twin primes and 2*3+5=11, 3+2*5=13 are also primes.
%p select(q -> isprime(q) and isprime(q+2) and isprime(3*q+2) and isprime(3*q+4), [3,5,seq(i,i=29..200000,30)]); # _Robert Israel_, May 06 2019
%t lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[2*p1+p2]&&PrimeQ[p1+2*p2],AppendTo[lst,p1]],{n,8!}];lst
%o (Magma) [NthPrime(n): n in [1..12000] | forall{p: p in [NthPrime(n)+2,3*NthPrime(n)+2,3*NthPrime(n)+4] | IsPrime(p)}]; // _Bruno Berselli_, May 10 2012
%Y Cf. A001359, A174913, A174915, A174916, A174917, A177335.
%Y Cf. A132929, A177336.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 02 2010
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