A239874 Integers k such that 2*k^2 + 1 and 2*k^3 + 1 are prime.

1, 6, 9, 21, 27, 30, 72, 96, 99, 162, 186, 204, 237, 264, 297, 321, 357, 360, 375, 492, 537, 621, 759, 819, 834, 897, 936, 1065, 1242, 1326, 1329, 1359, 1419, 1494, 1506, 1596, 1662, 1704, 1740, 1749, 1761, 1842, 1869, 2157, 2175, 2250, 2274, 2451, 2547

Offset: 1

Author

Zak Seidov, Mar 28 2014

Keywords

• nonn

Comments

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

Links

• Zak Seidov, Table of n, a(n) for n = 1..1367 [Duplicate terms removed by _Georg Fischer_, Nov 03 2024]

Crossrefs

Intersection of A089001 and A168550.

Programs

Maple

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

Mathematica

s={1};Do[If[PrimeQ [2k^2+1]&&PrimeQ[2k^3+1],AppendTo[s,k]],{k,3,10^3,3}];s
Select[Range[3500], PrimeQ[2 #^2 + 1] && PrimeQ[2 #^3 + 1]&] (* Vincenzo Librandi, Mar 29 2014 *)

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