

A117048


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


7



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
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OFFSET

1,1


COMMENTS

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


LINKS



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(nk*(k+1)/2, 3), return(n>3 && isprime(n)))); n==2 \\ Charles R Greathouse IV, Nov 07 2014


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



