A154732 Integers k such that (k^3 + k^2) -+ 1 are primes.

2, 5, 9, 11, 12, 26, 44, 47, 62, 69, 71, 89, 125, 140, 147, 179, 219, 254, 264, 285, 294, 312, 317, 326, 341, 344, 384, 407, 461, 495, 659, 680, 714, 740, 837, 845, 861, 866, 867, 957, 989, 1071, 1079, 1152, 1215, 1310, 1437, 1481, 1499, 1511, 1530, 1577

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

2^3 + 2^2 = 12 -+ 1 = 11 and 13 (both prime).

Mathematica

lst={}; Do[k=n^3+n^2; If[PrimeQ[k-1]&&PrimeQ[k+1], AppendTo[lst, n]], {n, 8!}]; lst
Select[Range[3000], PrimeQ[#^3 + #^2 - 1] && PrimeQ[#^3 + #^2 + 1] &] (* Vincenzo Librandi, Dec 26 2015 *)

Prog

(Magma) [n: n in [1..5*10^3] |IsPrime(n^3+n^2-1) and IsPrime(n^3+n^2+1)]; // Vincenzo Librandi, Dec 26 2015
(PARI) isok(n) = isprime(n^3+n^2+1) && isprime(n^3+n^2-1); \\ Michel Marcus, Dec 27 2015

Crossrefs

Cf. A111503, A154731.

Sequence in context: A332821 A283481 A284875 * A242936 A080154 A069829

Adjacent sequences: A154729 A154730 A154731 * A154733 A154734 A154735

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Status

approved