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

1,1

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.

Links

Table of n, a(n) for n=1..56.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000217, A117048.

Sequence in context: A357713 A038963 A167609 * A145032 A233414 A233863

Adjacent sequences: A117109 A117110 A117111 * A117113 A117114 A117115

Keyword

easy,nonn

Author

Greg Huber, Apr 18 2006

Status

approved