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%I #10 Sep 08 2022 08:45:48
%S 2,3,5,7,11,29,31,43,53,59,67,89,109,137,157,173,197,239,313,347,353,
%T 389,449,521,547,557,571,577,599,613,647,677,733,743,787,857,907,941,
%U 977,1051,1069,1093,1153,1193,1223,1229,1237,1303,1433,1453,1459,1481,1571
%N Primes p such that 3*p*(p-1)+1 is also prime.
%H Vincenzo Librandi, <a href="/A165682/b165682.txt">Table of n, a(n) for n = 1..1000</a>
%F 3*a(n)*(a(n)-1)+1 = A165683(n).
%e For p=5 = a(3), 3*p^2-3*p+1=61 = A165683(3). For a(4)=p=7: 3*p^2-3*p+1=127 = A165684(4).
%t Select[Prime[Range[800]], PrimeQ[3 # (# - 1) + 1]&] (* _Vincenzo Librandi_, Apr 15 2013 *)
%o (Magma) [p: p in PrimesUpTo(1600) | IsPrime(3*p*(p-1)+1)]; // _Vincenzo Librandi_, Apr 15 2013
%Y Cf. A165681, A165683.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Sep 24 2009
%E 2 and 3 inserted by _R. J. Mathar_, Sep 26 2009
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