a puxxle

[cino hilliard]

Hi,

1, 3, 8, 18, ? 89, 189

Some observations.
If this was on a civil service exam then

1. the solution has to be simple and doable with basic math

2. since an internal term is asked for, it follows that the 89 and the 189 
are needed to
   find a parttern.

3. we have to think outside of the box

4. there may be a range of solutions allowed.

or

it could be a hoax.

Considering point 2., we have this possibility skipping every 2 terms
18*10 + 9 = 189
  8*10 + 9 = 89
?
  1*10 + 8 = 18

This implies if a(n) is even multiply by 10 and add 9. If it is odd multiply 
by 10 and add 8.

this will give us ? as 3*10 + 8 = 38. so the term after 189 is 38*10 + 9 = 
389

1,3,8,18,38,89,189,389,898,...

In any event we have found yet another sequence :-)

Cino


>From: Lei Zhou <lzhou5 at emory.edu>
>To: seqfan at ext.jussieu.fr
>Subject: Re: a puxxle
>Date: Fri, 14 Apr 2006 18:19:49 -0400
>
>A weird solution.  It might not make sense.
>
>>
>>Differences: 2 5 10 a b 100 , but a+b = 71, which is ugly.
>>
>>Neil
>
>