covering all N with squares (2nd degree polynomials with integer coeffs.).

[Brendan McKay]

> How to cover all N (natural numbers) with simple
> poynomials of the second degree even with some overlaps.
> 
> n^2 =   1, 4, 9, 16, 25, ...
> n^2+1 = 2, 5, 10, 17, 26, ...
> n^2+2 = 3, 6, 11, 18, 27, ...
> etc
> 
> does cover many integers but I do not think it does work.
> It does not matter if there are some overlaps.
> 
> of course, in the above example, n^2+k at n=1 will eventually
> reach any number but let's say : can it be done non-trivially?

The problem needs to be more precise!   But anyway, here's a
problem which is raised by your example.  Let's use n^2+k
for exactly those k which are not included already:

 1, 4, 9,16,25,...
 2, 5,10,17,26,...
 3, 6,11,18,27,...
 7,10,15,22,...
 8,11,16,23,...
12,15,20,27,...
13,16,21,28,...
14,17,22,29,...
19,22,27,...
24,27,...
30,...

The first column 1,2,3,7,8,12,13,14,19,24,30... is not in OEIS.
What is it?

Brendan.