[seqfan] Re: permutation of nonnegative integers
M. F. Hasler
seqfan at hasler.fr
Thu Apr 12 15:10:33 CEST 2018
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
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