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

1,1

Comments

Intersection of A028870 and A038599.

Links

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

Example

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.

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] &]

Prog

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

Crossrefs

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

Sequence in context: A161163 A058211 A038599 * A321342 A338599 A333312

Adjacent sequences: A330435 A330436 A330437 * A330439 A330440 A330441

Keyword

nonn

Author

K. D. Bajpai, Dec 14 2019

Status

approved