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

1,2

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 (all terms up to 20000)

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 *)

Prog

(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

Crossrefs

Intersection of A089001 and A168550.

Sequence in context: A355484 A358222 A165717 * A043103 A242756 A268665

Adjacent sequences: A239871 A239872 A239873 * A239875 A239876 A239877

Keyword

nonn

Author

Zak Seidov, Mar 28 2014

Status

approved