A111503 Numbers n such that n^3 - n^2 - 1 and n^3 - n^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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(Magma) [n: n in [0..100000] |IsPrime(n^3-n^2-1) and IsPrime(n^3-n^2+1)] // Vincenzo Librandi, Nov 13 2010
(PARI) isok(n) = isprime(n^3 - n^2 - 1) && isprime(n^3 - n^2 + 1); \\ Michel Marcus, Aug 24 2016

Crossrefs

Sequence in context: A175281 A364606 A244790 * A239326 A075530 A032061

Adjacent sequences: A111500 A111501 A111502 * A111504 A111505 A111506

Keyword

nonn

Author

Pierre CAMI, Nov 16 2005

Status

approved