A330438 Numbers k such that k^2-2 and k^3-2 are prime.

9, 15, 19, 27, 37, 121, 135, 145, 211, 217, 259, 265, 267, 279, 355, 357, 387, 391, 435, 489, 525, 561, 615, 621, 727, 951, 987, 1029, 1119, 1141, 1177, 1251, 1287, 1357, 1435, 1491, 1561, 1617, 1717, 1785, 1819, 1839, 1875, 1909, 1989, 2001, 2077, 2107, 2211

Offset: 1

Author

K. D. Bajpai, Dec 14 2019

Keywords

• nonn

Comments

Intersection of A028870 and A038599.

Examples

			a(1) = 9: 9^2 - 2 = 79; 9^3 - 2 = 727; both results are prime.
a(2) = 15: 15^2 - 2 = 223; 15^3 - 2 = 3373; both results are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A028870, A028873, A038599, A038600, A108701.

Programs

Magma

[n : n in [1 .. 100] | IsPrime (n^2 - 2) and IsPrime (n^3 - 2)];

Maple

filter:= k -> isprime(k^2-2) and isprime(k^3-2):
select(filter, [$2..10000]); # Robert Israel, Dec 24 2019

Mathematica

Select[Range[10000], PrimeQ[#^3 - 2] && PrimeQ[#^2 - 2] &]