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

1,1

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

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 *)

Prog

(Magma) [a: n in [0..200] | IsPrime(a) where a is  (3*n^2 - 3*n + 2) div 2]; // Vincenzo Librandi, Mar 22 2013
(PARI) is(n)=n%6==1 && ispolygonal((n-1)/3, 3) && isprime(n) \\ Charles R Greathouse IV, Nov 03 2015

Crossrefs

Cf. A005448, A125603.

Sequence in context: A243450 A237418 A240126 * A139847 A087764 A146691

Adjacent sequences: A125599 A125600 A125601 * A125603 A125604 A125605

Keyword

nonn,easy

Author

Zak Seidov, Nov 27 2006

Status

approved