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%I #24 Sep 08 2022 08:46:12
%S 37,521,881,1619,2053,2213,2341,3527,3637,3727,4157,5147,7019,10009,
%T 10891,12277,14741,15913,16273,17747,18757,24499,25307,25577,26209,
%U 27073,31481,31517,32833,35083,36739,36791,39079,40231,40949,41039,42013,42461,42767,47917
%N Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.
%H K. D. Bajpai, <a href="/A256811/b256811.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 37; (37^2 + 2)/3 = 457; (37^4 + 2)/3 = 624721; all three are prime.
%t Select[Prime[Range[10^4]], PrimeQ[(#^2 + 2)/3] && PrimeQ[(#^4 + 2)/3] &]
%o (PARI) forprime(p=1,10^5,if(!((p^2+2)%3)&&!((p^4+2)%3)&&isprime((p^2+2)/3)&&isprime((p^4+2)/3),print1(p,", "))) \\ _Derek Orr_, Apr 16 2015
%o (Magma) [p: p in PrimesUpTo(5*10^4) | IsPrime((p^2+2) div 3) and IsPrime((p^4+2) div 3 )]; // _Vincenzo Librandi_, Apr 20 2015
%Y Cf. A241120, A253941, A253976, A253940.
%K nonn,easy
%O 1,1
%A _K. D. Bajpai_, Apr 15 2015