A173627 - OEIS

%I #29 Sep 08 2022 08:45:50

%S 5,19,61,971,1451,2711,3061,3449,6011,15139,15241,21821,27851,39839,

%T 51749,62459,75679,76081,82591,97001,121039,121441,122299,135581,

%U 161569,162671,196681,196831,200881,214741,217271,222931,242069,243119,254161

%N Primes p such that p^2 + 6, p^2 + 12 and p^2 + 18 are all prime.

%C For p > 2,  p^2 + 24 is composite (divisible by 5). - _Zak Seidov_, Sep 07 2018

%H Zak Seidov, <a href="/A173627/b173627.txt">Table of n, a(n) for n = 1..1800</a>

%t okQ[n_]:=Module[{p2=n^2},And@@PrimeQ[{p2+6,p2+12,p2+18}]]; Select[Prime[Range[30000]],okQ] (* _Harvey P. Dale_, Dec 18 2010 *)

%o (Magma)[p: p in PrimesUpTo(600000)|IsPrime(p^2+6) and IsPrime(p^2+12) and IsPrime(p^2+18)] // _Vincenzo Librandi_, Dec 13 2010

%o (PARI) isok(p) = isprime(p) && isprime(p^2+6) && isprime(p^2+12) && isprime(p^2+18); \\ _Michel Marcus_, Sep 08 2018

%Y Cf. A062718 (p and p^2 + 6 are both prime).

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 09 2010