A124199 Primes of the form k(k+1)/2-2 (i.e., two less than triangular numbers).

13, 19, 43, 53, 89, 103, 151, 229, 251, 349, 433, 463, 593, 701, 739, 859, 1033, 1223, 1429, 1483, 1709, 1889, 1951, 2143, 2699, 3001, 3079, 3319, 3739, 4003, 4093, 4463, 4751, 5563, 5669, 6553, 7019, 7873, 8513, 9043, 10009, 10151, 10729, 11173, 11779

Offset: 1

Author

Peter Pein (petsie(AT)dordos.net), Dec 07 2006

Keywords

• easy
• nonn

Comments

Equal to primes of the form (k^2-17)/8. Also equal to primes p such that 8*p+17 is a square. - Chai Wah Wu, Jul 14 2014

Examples

			The (first five triangular numbers)-2 are: -1,1,4,8,13. So a(1)=13 is the first prime of this form.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2000.

Crossrefs

Cf. A055472.

Programs

Mathematica

Pick[ #1, PrimeQ[ #1]]&[((1/2)*#1*(#1 + 1) - 2 & ) /@ Range[180]]
Select[Accumulate[Range[250]]-2,PrimeQ] (* Harvey P. Dale, Jun 07 2020 *)

PARI

isok(p) = isprime(p) && ispolygonal(p+2, 3); \\ Michel Marcus, Sep 19 2022

Python

import sympy
[n*(n+1)/2-2 for n in range(10**6) if isprime(n*(n+1)/2-2)] # Chai Wah Wu, Jul 14 2014