A067200 Numbers m such that m^3 + 2 is prime.

0, 1, 3, 5, 29, 45, 63, 65, 69, 71, 83, 105, 113, 123, 129, 143, 153, 171, 173, 189, 209, 215, 219, 231, 243, 245, 249, 263, 291, 299, 305, 311, 341, 363, 369, 395, 419, 425, 431, 435, 473, 483, 491, 495, 501, 503, 509, 515, 533, 549, 555, 561, 575, 579, 639

Offset: 1

Author

Benoit Cloitre, Feb 19 2002

Keywords

• nonn

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A144953.

Other sequences of the type "Numbers m such that m^k + k - 1 is prime": A000040 (k=1), A005574 (k=2), this sequence (k=3), A125259 (k=4), A125260 (k=5), A125261 (k=6), A125262 (k=7), A125263 (k=8), A125264 (k=10), A125265 (k=11).

Programs

Mathematica

lst={}; Do[If[PrimeQ[n^3+2], AppendTo[lst, n]], {n, 0, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
Select[Range[0,700],PrimeQ[#^3+2]&] (* Harvey P. Dale, Jul 27 2025 *)

PARI

is(n)=isprime(n^3 + 2) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = (A144953(n) - 2)^(1/3). - Zak Seidov, Sep 16 2013