[seqfan] Re: Numbers n such that (n+n+1) divides the concatenation [n, n+1]

[Maximilian Hasler]

On Tue, Sep 21, 2010 at 10:51 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> I think this seq (not in the OEIS) starts like this:
>
> C = 1,4,16,49,166,...
>

(10:46) gp > last=0;for(n=1,99999, eval(Str(n,n+1))%(1+2*n)  | print1(n,","))
1,4,16,49,166,499,1666,4999,16666,49999,

> We have:
> 1+2 divides 12          ->       12/3=4
> 4+5 divides 45          ->       45/9=5
> 16+17 divides 1617      ->    1617/33=49
> 49+50 divides 4950      ->    4950/99=50
> 166+167 divides 166167  -> 166167/333=499
> ...
> Pattern?

Yes!  ;-)
Proof : left as exercise.

M.
%F :
a(2n)=5*10^(n-1)-1
a(2n+1)=(10^n*5-2)/3