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%I #11 Sep 08 2022 08:45:08
%S 7,29,83,181,197,337,601,631,1303,1847,2029,3023,3109,3359,4591,4649,
%T 4831,6397,6791,7489,7559,7573,7951,8609,8933,9857,10151,10457,10501,
%U 10709,11467,11633,12011,12377,12641,12739,13469,14197,14449,14519
%N Primes p such that (3*p)^2 + p^2 + 3^2 and (3*p)^2 - p^2 - 3^2 are both prime.
%C Also called nonomatic primes. There is probably an infinity of them. There seems to be no prime number with a similar property using 5 or a larger factor in the polynomials.
%H Vincenzo Librandi and Charles R Greathouse IV, <a href="/A079796/b079796.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Librandi)
%e a(2) = 29 since (3*29)^2 + 29^2 + 3^2 = 8419 and (3*29)^2 - 29^2 - 3^2 = 6719 are both primes.
%t Select[Prime@Range[1, 2000], PrimeQ[9 #^2 + #^2 + 9] && PrimeQ[9 #^2 - #^2 - 9] &] (* _Vincenzo Librandi_, Oct 18 2012 *)
%o (Magma) [p: p in PrimesUpTo(15000)| IsPrime( (3*p)^2 + p^2 + 3^2) and IsPrime((3*p)^2 - p^2 - 3^2)]; // _Vincenzo Librandi_, Oct 18 2012
%o (PARI) is(n)=isprime(10*n^2+9) && isprime(8*n^2-9) && isprime(n) \\ _Charles R Greathouse IV_, Jun 10 2015
%K easy,nonn
%O 1,1
%A _Olivier Gérard_, Feb 19 2003