A162307 Primes of the form k*(k+2)/3 - 2, k > 0.

3, 19, 31, 83, 131, 223, 383, 479, 643, 1279, 1823, 2131, 2239, 2579, 2819, 3331, 4483, 4639, 6163, 6719, 7103, 7699, 8963, 9631, 9859, 10559, 11779, 13331, 14143, 14419, 15263, 17939, 19843, 21503, 22531, 24659, 25759, 28031, 29599, 30803, 35423

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

• nonn
• easy

Comments

Or: primes of the form k*(k+1)*(k+2)/(k+(k+1)+(k+2))-2.

Generated by k=3, 7, 9, 15, 19, 25, 33, 37, 43, ....

Primes p such that 3*p+7 is a square. - Vincenzo Librandi, Dec 05 2015

Primes of the forms 3*k^2 + 2*k - 2 and 3*k^2 + 4*k - 1. - Robert Israel, Nov 27 2017

Examples

			k=3 contributes a term because 3*(3+2)/3 - 2 = 3 = a(1) is prime.
		

Links

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

Programs

Magma

[p: p in PrimesUpTo(45000) | IsSquare(3*p+7)]; // Vincenzo Librandi, Dec 05 2015

Maple

select(isprime, [seq(seq((3*j+i)*(3*j+i+2)/3-2, i=0..1),j=1..1000)]); # Robert Israel, Nov 27 2017

Mathematica

f[n_]:=(n*(n+1)*(n+2))/(n+(n+1)+(n+2))-2; lst={};Do[p=f[n];If[PrimeQ[p], AppendTo[lst,p]],{n,6!}];lst
Select[Table[(k(k+2))/3-2,{k,350}],PrimeQ] (* Harvey P. Dale, May 10 2014 *)

PARI

forprime(p=2, 1e5, if(issquare(3*p+7), print1(p , ", "))) \\ Altug Alkan, Dec 05 2015

Extensions

Definition simplified by R. J. Mathar, Jul 02 2009