A055472 Primes of the form k(k+1)/2+2 (i.e., two more than a triangular number).

2, 3, 5, 17, 23, 47, 107, 173, 233, 353, 467, 563, 743, 863, 1277, 1433, 1487, 2213, 2417, 2777, 3083, 3323, 4007, 4373, 5153, 7877, 8387, 10733, 11177, 11783, 13043, 13697, 14537, 15053, 15227, 17207, 17393, 17957, 18917, 21323, 22157, 23873

Offset: 1

Author

Henry Bottomley, Jun 27 2000

Keywords

• nonn

Comments

Equal to primes of the form (k^2+15)/8. Also equal to primes p such that 8*p-15 is a square. - Chai Wah Wu, Jul 14 2014

Primes of A152948. - Klaus Purath, Jan 03 2021

Links

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

Crossrefs

Cf. A000040, A000217, A022856, A152948.

Programs

Mathematica

Select[Table[(n^2-n+4)/2,{n,3000}],PrimeQ] (* Vincenzo Librandi, Jul 14 2012 *)
Select[Accumulate[Range[0,300]]+2,PrimeQ] (* Harvey P. Dale, Feb 05 2019 *)

Python

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