[seqfan] Re: "integers >4 which cannot be written as the sum of a nontrivial triangular number (>1) and a prime"

[franktaw at netscape.net]

1 should also be in that list.

And any description of this sequence should say "triangular greater 
than 1" or some such language.  "Nontrivial triangular" is not good 
enough; I would expect that to exclude only 0, not both 0 and 1.  (I 
wouldn't use it as a description for that concept, either, because it 
is ambiguous.)

Franklin T. Adams-Watters

-----Original Message-----
From: Jim Nastos <nastos at gmail.com>

On Sun, Dec 20, 2009 at 3:33 PM, Jonathan Post <jvospost3 at gmail.com> 
wrote:
> Playing on paper with pencil I think that
> 7, 16, 36, 42, 61, ...
> is "integers >4 which cannot be written as the sum of a nontrivial
> triangular number (>1) and a prime"

Hi, here is my output:

Numbers of form prime+triangular in exactly 0 ways:
2 3 4 7 36 42 54 61 90 105 171 210 211 216 325 351 406 528 561 630 741
780 990 1081 1176 1275 1596 1711 1830 1953 2016 2145 2346 2628 2775
3003 3081 3240 3321 3655 3741 3916 4278 4371 4465 4560 4851

(Note that 16 is not in this list... 16 = 13(prime) + 3(nontrivial 
triangular)
...