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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A055472.

Sequence in context: A252021 A216101 A096455 * A119869 A272200 A106904

Adjacent sequences: A124196 A124197 A124198 * A124200 A124201 A124202

Keyword

easy,nonn

Author

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

Status

approved