A125602 Centered triangular numbers that are prime.

19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589

Offset: 1

Author

Zak Seidov, Nov 27 2006

Keywords

• nonn
• easy

Comments

Prime terms in A005448, or primes of the form 3n(n-1)/2 + 1.

Primes that are the sum of 3 consecutive triangular numbers. - Vicente Izquierdo Gomez, Nov 03 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005448, A125603.

Programs

Magma

[a: n in [0..200] | IsPrime(a) where a is  (3*n^2 - 3*n + 2) div 2]; // Vincenzo Librandi, Mar 22 2013

Maple

select(isprime, [seq(3*n*(n-1)/2+1, n=1..1000)]); # Robert Israel, Nov 03 2015

Mathematica

lst={};Do[If[PrimeQ[p=3n(n-1)/2+1], (*Print[p];*)AppendTo[lst, p]], {n, 10^3}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
Select[Total/@Partition[Accumulate[Range[200]],3,1],PrimeQ] (* Harvey P. Dale, Dec 29 2020 *)

PARI

is(n)=n%6==1 && ispolygonal((n-1)/3,3) && isprime(n) \\ Charles R Greathouse IV, Nov 03 2015