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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A157975 A339862 A045370 * A040128 A209630 A235266

Adjacent sequences: A117045 A117046 A117047 * A117049 A117050 A117051

Keyword

easy,nonn

Author

Andrew S. Plewe, Apr 15 2006

Status

approved