A078405

[David Wilson]

----- Original Message ----- 
From: "Max" <relf at unn.ac.ru>
To: <ham>; "David Wilson" <davidwwilson at comcast.net>
Cc: "Sequence Fans" <seqfan at ext.jussieu.fr>
Sent: Sunday, April 17, 2005 4:18 AM
Subject: Re: A078405


> David Wilson wrote:
>>
>> 2.  Is this sequence finite?
>
> It cannot be finite. There is a finite number of expressions including n 
> copies of n and various arithmetic operations.
> Hence, A078405(n) is defined for any n.

My concern was that the original problem as posed at
http://www.stetson.edu/~efriedma/mathmagic/1299.html, clearly implied that
n should be a digit, which would make a(9) the last element of this sequence
so that it is finite and full as it stands.  Of course, there generalization 
to
a(n) (n >= 10) is fairly straightforward.

> There is a trivial upper bound, btw:
> A078405(n) < (n-1)! * 6^(n-1).

Wow, this bears elucidation.

> Max