A154732 - OEIS

%I #14 Sep 08 2022 08:45:40

%S 2,5,9,11,12,26,44,47,62,69,71,89,125,140,147,179,219,254,264,285,294,

%T 312,317,326,341,344,384,407,461,495,659,680,714,740,837,845,861,866,

%U 867,957,989,1071,1079,1152,1215,1310,1437,1481,1499,1511,1530,1577

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

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

%t lst={};Do[k=n^3+n^2;If[PrimeQ[k-1]&&PrimeQ[k+1],AppendTo[lst,n]],{n,8!}];lst

%t Select[Range[3000], PrimeQ[#^3 + #^2 - 1] && PrimeQ[#^3 + #^2 + 1] &] (* _Vincenzo Librandi_, Dec 26 2015 *)

%o (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

%o (PARI) isok(n) = isprime(n^3+n^2+1) && isprime(n^3+n^2-1); \\ _Michel Marcus_, Dec 27 2015

%Y Cf. A111503, A154731.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 14 2009