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

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Keywords

• nonn
• easy

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111503, A154731.

Programs

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

Maple

select(k -> andmap(isprime,[k^3+k^2-1,k^3+k^2+1]), [$1..10000]); # Robert Israel, Jan 07 2025

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 *)

PARI

isok(n) = isprime(n^3+n^2+1) && isprime(n^3+n^2-1); \\ Michel Marcus, Dec 27 2015