[seqfan] Re: permutation of nonnegative integers

[M. F. Hasler]

On Thu, Apr 12, 2018 at 12:09 AM, jnthn stdhr wrote:
>
> > BTW, could you elaborate on "Increment a and b".  What exactly does that
> > mean?
> >
> Add one to a and b, then repeat:
>

Then actually we always have b=a+1, so
 [ a, a+b, a*b, b] = [ a, 2a+1, a*(a+1), a+1]

and one can omit the trailing b = a+1
since it is equal to the next a' = a+1
which will come immediately after (if not yet there).

Unless I'm wrong, the a*(a+1) = a²+a will always be "new" (except for
initial terms) ,
since (much) larger than all that came earlier;
idem for the 2a+1 because it is odd while a(a+1) is always even.
So only the first term "a" will occur in a somewhat "irregular" fashion
(namely, when  a  is even but not in the set of  oblong numbers a(a+1))
to fill in the missing even numbers.

-- 
Maximilian