A111503 Numbers k such that k^3 - k^2 - 1 and k^3 - k^2 + 1 are twin primes.

2, 3, 6, 13, 21, 33, 48, 58, 90, 96, 99, 100, 111, 118, 120, 121, 133, 138, 195, 204, 279, 334, 348, 366, 393, 400, 465, 525, 541, 565, 594, 721, 736, 789, 855, 859, 925, 946, 1044, 1099, 1239, 1279, 1323, 1410, 1459, 1470, 1513, 1521, 1524, 1629, 1630, 1638

Offset: 1

Author

Pierre CAMI, Nov 16 2005

Keywords

• nonn

Comments

Intersection of A111501 and A162293. - Ivan Neretin, Aug 24 2016

Examples

			2^3 - 2^2 - 1 = 3, 2^3 - 2^2 + 1 = 5, 3 and 5 are twin primes, so 2 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A111501, A162293.

Programs

Magma

[n: n in [0..100000] |IsPrime(n^3-n^2-1) and IsPrime(n^3-n^2+1)]; // Vincenzo Librandi, Nov 13 2010

Mathematica

lst={}; Do[If[PrimeQ[n^3-n^2-1]&&PrimeQ[n^3-n^2+1], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)
tpQ[n_]:=Module[{c=n^3-n^2},And@@PrimeQ[{c+1,c-1}]]; Select[Range[ 1700],tpQ] (* Harvey P. Dale, Aug 27 2012 *)

PARI

isok(n) = isprime(n^3 - n^2 - 1) && isprime(n^3 - n^2 + 1); \\ Michel Marcus, Aug 24 2016