Describe and add

[Michele Dondi]

On Thu, 18 Aug 2005 hv at crypt.org wrote:

> Here's some perl code:
>  perl -Mbigint -wle '$n=$a=1; while (1) { print "$n: $a"; ++$n; $a = desc($a) + $a } sub desc { my %a; ++$a{$_} for split //, shift; join "", map +($a{$_}, $_), sort { $a <=> $b } keys %a }'

Oops! I hadn't noticed that you had already wrote a script for that. 
Obviously I'm reading these mails very late.

> Compute:
[cut]
> 9: 20314234480170281558
> 10: 20317265802504533296
> 11: 50431498946030705115
[cut...]

Hmmm, the outputs of our programs differ from some point on. Thus mine or 
yours is wrong - this is not exclusive or: they may both be wrong...

However looking at the rate of growth of your computed terms as estimated 
at first sight suggests me it may be far too slow. A naive estimate 
suggests that it should be at least as fast (or faster) than the aa 
sequence and that the first digits "until a certain point" should still be 
1,2 or 3.

Incidentally one nice feature of the aa seq is that it is basically 
base-independent provided that the base is greater than or equal to 3. Of 
course this modification makes it base dependent and thus much less 
attractive. Maybe it would be more interesting if restricted to base 3, or 
perhaps, say, base 4 and in the latter case one may look e.g. at the 
number of occurrencies of 4's, but then I would expect it to be 
approximately growing , but otherwise rather wild.


Michele
-- 
>What is the current status of chaos theory? A decade ago it was supposed 
>to be The Next Big Thing.
Yeah, well, that kind of thing is notoriously hard to predict, longterm.
- Lee Rudolph in sci.math, "Re: Chaos Theory?"