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%I #30 Sep 08 2022 08:45:05
%S 3,5,23,29,83,89,173,233,239,293,419,659,953,1013,1223,1409,1559,1583,
%T 1889,2003,2129,2339,2549,2693,2939,3359,3389,3593,3803,4349,4373,
%U 4409,4919,4943,5333,6113,6173,8093,8273,8513,9059,9479,9539,10163,10313
%N Numbers n such that n, 2n+1, 3n+2 are primes.
%C a(n)*(2a(n)+1)*(3a(n)+2) are Lucas-Carmichael numbers for n > 1. Analogous to A174734 as A006972 (Lucas-Carmichael numbers) is analogous to A002997 (Carmichael numbers). - _Amiram Eldar_, Aug 11 2017
%H Charles R Greathouse IV, <a href="/A067256/b067256.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Prime[Range[10^4]],PrimeQ[2*#+1]&&PrimeQ[3*#+2] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 27 2008 *)
%o (Magma) [n: n in [1..15000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2)]; // _Vincenzo Librandi_, Oct 31 2014
%o (PARI) is(n)=isprime(3*n+2) && isprime(2*n+1) && isprime(n) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A000040, A005384, A006972, A067257, A067258, A101767, A101768, A101769, A101770, A174734, A216925.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Feb 20 2002
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