[seqfan] Re: is A055493 finite?

Max Alekseyev maxale at gmail.com
Mon Feb 9 09:36:07 CET 2009

On Mon, Feb 9, 2009 at 3:14 AM, Dmitry Kamenetsky
<Dmitry.Kamenetsky at nicta.com.au> wrote:

> It seems that there are no more terms in A055493, because for larger n
> (say above 500) the value (sum_{k=1..n} k!) - 2 is always divisible by
> 467. Can someone confirm this?

You are correct.
Actually, it's enough to check whether (sum_{k=1..466} k!) - 2 is
divisible by 467 - and it is! - to conclude that (sum_{k=1..n} k!) - 2
is divisible by 467 for all n>=466. The reason is that all term k! in
the sum are divisible by 467 as soon as k>=467.


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