A117112 Primes expressible as the sum of two triangular numbers (including zero).

2, 3, 7, 11, 13, 29, 31, 37, 43, 61, 67, 73, 79, 83, 97, 101, 127, 137, 139, 151, 157, 163, 181, 191, 193, 199, 211, 227, 241, 263, 277, 281, 307, 331, 353, 367, 373, 379, 389, 409, 421, 433, 443, 461, 463, 487, 499, 541, 571, 577, 587, 601, 619, 631, 659, 661

Offset: 1

Author

Greg Huber, Apr 18 2006

Keywords

• easy
• nonn

Comments

See A117048 for the primes that are the sum of two positive triangular numbers. The only difference is that the prime 3 occurs here.

Examples

			2 = 1 + 1
3 = 0 + 3
7 = 1 + 6
and so on.
		

Crossrefs

Cf. A000217, A117048.

Programs

Mathematica

tri = Table[n (n + 1)/2, {n, 0, 40}]; Select[Union[Flatten[Outer[Plus, tri, tri]]], # <= tri[[-1]]+1 && PrimeQ[#] &] (* T. D. Noe, Apr 07 2011 *)
Select[Total/@Tuples[Accumulate[Range[0,40]],2],PrimeQ]//Union (* Harvey P. Dale, Apr 21 2019 *)

Formula

A000040 intersect A020756. - Jonathan Vos Post, Apr 17 2006