"more" sequence,

[Robert G. Wilson v]

Everyone,

	I got:
0,1,7,15,19,31,37,61,63,65,91,127,169,175,211,217,255,271,331,369,397,469,511,547,631,665,671,721,781,817,919,1023,1027,1105,1141,1261,1387,1519,1657,1695,1801,1951,2047,2059,2101,2107,2269,2437,2465,2611,2791,
	and I used Mmca:
  t = {}; Do[a = (m + 1)^k - m^k; If[a < 3000, AppendTo[t, a]], {m, 3000}, {k, 23}]; t = Split@ Sort@ t; Union@ Flatten@ t[[Select[ Range at 1500, Length at t[[ # ]] > 1 &]]]

Bob.

Jim Nastos wrote:

> Hi all,
> 
> Sequence A115783 is named:
> 
>     Numbers n such that n can be presented in the form
>     (m+1)^k-m^k at least in two ways.
> 
> And the entry contains only the numbers 0, 1, 7, 15, 19, 127.
> 
> Why do the following not count for this sequence?
> 
> 31 = 2^5 - 1^5 = 16^2 - 15^2
> 37 = 4^3 - 3^3 = 19^2 - 18^2
> 61 = 5^3 - 4^3 = 31^2 - 30^2
> 63 = ...
> 65 = ...
> 91 = ...
> 127 = 2^7 - 1^7 = 7^3 - 6^3 = 64^2 - 63^2 (three ways)
> 169 = ...
> 175 = ...
> 211 = ...
> 
> J
> 
>