[seqfan] Re: A009994

[David Radcliffe]

The inequality holds when n is sufficiently large. The number of
nonnegative integers with at most k digits in non-decreasing order is (k+9
choose 9), which is less than k^10 for sufficiently large n. This means
that a(k^10) must have more than k digits, so a(k^10) > 10^k, hence a(n) >
10^(n^(1/10)).

On Sat, Jul 27, 2019 at 10:55 AM Fred Lunnon <fred.lunnon at gmail.com> wrote:

> On 7/27/19, Павел Калугин <paul.kalug at gmail.com> wrote:
> >
> > Hello!
> > Could you please explain me formula of http://oeis.org/A009994
> > (
> https://link.getmailspring.com/link/4B1E82F3-E7CD-4784-9AE7-42FA3B042F65@getmailspring.com/0?redirect=http%3A%2F%2Foeis.org%2FA009994&recipient=c2VxZmFuQGxpc3Quc2VxZmFuLmV1
> )
> > ? Because it seems wrong to me.
> > exp(1000^(1/10)) is almost equal to 7, but a(1000) is definetely more
> than
> > 500.
> >
>
>