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A111503 Numbers n such that n^3 - n^2 - 1 and n^3 - n^2 + 1 are twin primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A276690 A175281 A244790 * A239326 A075530 A032061

Adjacent sequences:  A111500 A111501 A111502 * A111504 A111505 A111506

KEYWORD

nonn

AUTHOR

Pierre CAMI, Nov 16 2005

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)