A117048 Prime numbers that are expressible as the sum of two positive triangular numbers.

2, 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

Andrew S. Plewe, Apr 15 2006

Keywords

• easy
• nonn

Comments

If the triangular number 0 is allowed, only one additional prime occurs: 3. In that case, the sequence becomes A117112.

A subsequence of A051533. - Wolfdieter Lang, Jan 11 2017

Examples

			2 = 1 + 1
7 = 1 + 6
11 = 1 + 10
13 = 10 + 3, etc.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A002243, A002244, A020756, A051533, A053614, A060773, A002636.

Programs

Mathematica

tri = Table[n (n + 1)/2, {n, 40}]; Select[Union[Flatten[Outer[Plus, tri, tri]]], # <= tri[[-1]]+1 && PrimeQ[#] &] (* T. D. Noe, Apr 07 2011 *)

PARI

is(n)=for(k=sqrtint(4*n+1)\2+1,(sqrtint(8*n+1)-1)\2, if(ispolygonal(n-k*(k+1)/2,3), return(n>3 && isprime(n)))); n==2 \\ Charles R Greathouse IV, Nov 07 2014