Fwd: Re: a puzzle sequence that is going around

[cino hilliard]

>From: "Paul C. Leopardi" <leopardi at bigpond.net.au>
>To: seqfan at ext.jussieu.fr
>Subject: Fwd: Re: a puzzle sequence that is going around
>Date: Sun, 16 Jan 2005 22:17:40 +1100

>Hi all,
>See http://neopets.com/newnt/index.phtml?section=4080&week=26
>The page states that the answers to conundrum Rounds 9, 16 and 25 were
>2616, 3, 11, respectively. Was there a conundrum Round with 10850 as an
>answer? Indeed!
>http://petpages.neopets.com/newnt/index.phtml?section=9589&week=78
>has 10850 as the answer to Round 36.
>
>So, maybe there have been at least 100 Rounds, with answers:
>
>   9:  2616
>  16:     3
>  25:    11
>  36: 10850
>  49: ?
>  64:    25
>100:  2038
>
>If this is the case, then the answer to the puzzle is not a number at all,
>  but "Abracadabra", which is listed at

It could be a number if we take the traditional mapping of base conversion 
to base 36 to include
0123456789ABC..Z in the transformatiom as I have in my pari base(b1,b2,str) 
function.
For upper case only
gp > base(28,10,ABRACADABRA)
%14 = "3088672228688686"
gp > base(10,28,3088672228688686)
%15 = "ABRACADABRA"

For mixed case we need to go further
0123456789ABC..Zabc..z
gp > base(54,10,AbraCadabra)
%1 = "2256665031069608214"
gp > base(10,54,2256665031069608214)
%2 = "AbraCadabra"

So we have Many solutions  (How many?) :-)  for numbers base 54 to base 10 
of
mixedcase(ABRACADABRA).

If it wasn't for the R, we could do it in base 16 for upper case
gp > base(16,10,ABABACADABABA)
%3 = "3020061197122234"
gp > base(10,16,3020061197122234)
%4 = "ABABACADABABA"

Should this the Neopets entry be a sequence? I don't think so as it is too 
esoteric and too contrived. If it is dubmitted it belongs in dumb.

Cino