%I #25 Nov 03 2024 18:53:45

%S 1,6,9,21,27,30,72,96,99,162,186,204,237,264,297,321,357,360,375,492,

%T 537,621,759,819,834,897,936,1065,1242,1326,1329,1359,1419,1494,1506,

%U 1596,1662,1704,1740,1749,1761,1842,1869,2157,2175,2250,2274,2451,2547

%N Integers k such that 2*k^2 + 1 and 2*k^3 + 1 are prime.

%C All terms > 1 are multiples of 3. Also, no term is congruent to 3 modulo 5.

%H Zak Seidov, <a href="/A239874/b239874.txt">Table of n, a(n) for n = 1..1367</a> [Duplicate terms removed by _Georg Fischer_, Nov 03 2024]

%p select(t -> isprime(2*t^2+1) and isprime(2*t^3+1), [$1..6000]); # _Robert Israel_, Nov 03 2024

%t s={1};Do[If[PrimeQ [2k^2+1]&&PrimeQ[2k^3+1],AppendTo[s,k]],{k,3,10^3,3}];s

%t Select[Range[3500], PrimeQ[2 #^2 + 1] && PrimeQ[2 #^3 + 1]&] (* _Vincenzo Librandi_, Mar 29 2014 *)

%o (PARI) s=[]; for(n=1, 4000, if(isprime(2*n^2+1) && isprime(2*n^3+1), s=concat(s, n))); s \\ _Colin Barker_, Mar 28 2014

%Y Intersection of A089001 and A168550.

%K nonn

%O 1,2

%A _Zak Seidov_, Mar 28 2014