A153974 Numbers n such that n^3 - 3 is prime.

2, 4, 8, 10, 14, 16, 26, 34, 38, 40, 74, 80, 106, 110, 116, 124, 136, 158, 178, 184, 190, 206, 224, 230, 238, 256, 274, 280, 316, 320, 338, 340, 386, 410, 428, 446, 458, 464, 470, 484, 496, 530, 544, 550, 556, 590, 626, 634, 644, 646, 674, 710, 718, 728, 730

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

• nonn

Comments

2^3 - 3 = 5 is prime, 4^3 - 3 = 61 is prime, ...

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A028870, A028873, A038599, A108701, A153975.

Programs

Magma

[n: n in [2..500] | IsPrime(n^3-3)]; // Vincenzo Librandi, Nov 26 2010

Mathematica

a[n_]:=n^x-y;lst={};x=3;y=3;Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,0,6!}];lst
Select[Range[2, 1000], PrimeQ[#^3 - 3] &] (* G. C. Greubel, Sep 01 2016 *)

PARI

is(n)=isprime(n^3-3) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

First two terms 0,1, removed by Zak Seidov, Mar 14 2009