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%I #11 Jun 21 2021 11:52:24
%S 3,5,11,41,107,311,461,599,641,1277,1619,1997,2309,2381,2789,3671,
%T 4787,5099,6659,6701,6827,7457,7487,8219,8537,8597,9929,10709,11117,
%U 12071,12107,12251,13709,17747,18047,18251,18521,22091,22637,23027
%N Primes p with q = p + 2 and prime(q) + 2 both prime.
%C According to the conjecture in A236456, this sequence should have infinitely many terms.
%C See A236458 for a similar sequence.
%H Zhi-Wei Sun, <a href="/A236457/b236457.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 since 3 + 2 = 5 and prime(5) + 2 = 13 are both prime, but 2 + 2 = 4 is not.
%t p[n_]:=PrimeQ[n+2]&&PrimeQ[Prime[n+2]+2]
%t In[2]:= n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
%t Select[Prime[Range[2600]],AllTrue[{#+2,Prime[#+2]+2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 21 2021 *)
%o (PARI) s=[]; forprime(p=2, 24000, q=p+2; if(isprime(q) && isprime(prime(q)+2), s=concat(s, p))); s \\ _Colin Barker_, Jan 26 2014
%Y Cf. A000040, A001359, A006512, A236119, A236456, A236458.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 26 2014
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