       Re: Part specification... is neither an integer nor a list of integers

• To: mathgroup at smc.vnet.net
• Subject: [mg109710] Re: Part specification... is neither an integer nor a list of integers
• From: Chandler May <cjmay4754 at gmail.com>
• Date: Thu, 13 May 2010 07:23:53 -0400 (EDT)

```Thanks everyone, that clears it up.  I was neglecting that indices
start at one, not zero, but the g[n_] := g[n] = n - g[g[n-1]] form is
much nicer anyway.  Very cool!

Chandler

On Tue, May 11, 2010 at 11:55 PM, Patrick Scheibe
<pscheibe at trm.uni-leipzig.de> wrote:
> Hi,
>
> your first element in your list is 0. In the call s[[Last[s]]] you are
> taking
> the zero'th element of s which is the head "List". This is sure not what you
> want.
>
> Check this out:
>
> g = 0
> g[n_] := g[n] = n - g[g[n - 1]]
>
> but note that the \$RecursionLimit is set to 256 per default, so:
>
> \$RecursionLimit = 2000;
> g
>
> Cheers
> Patrick
>
>
> Am May 11, 2010 um 12:28 PM schrieb Chandler May:
>
>> Hi Mathematica sages,
>>
>> I want to implement a recursive function on the natural numbers:
>>
>> g(n) = n - g(g(n-1))
>> g(0) = 0
>>
>> First I tried the following in Mathematica.
>>
>> g := 0
>> g[n_] := n - g[g[n-1]]
>>
>> This worked, but it was much too slow.  In hopes of reducing the
>> number computations, I thought I would make a function gseq[n_] to
>> generate the sequence of successive values of g(n) like so:
>>
>> gseq := {0}
>> gseq[n_] := With[{s=gseq[n-1]}, Append[s, n - s[[Last[s]]]]]
>>
>> However, when I ask for gseq[n] for n > 1, Mathematica complains that
>> the "Part specification... is neither an integer nor a list of
>> integers", like the first line here
>> <http://reference.wolfram.com/mathematica/ref/message/General/pspec.html>
>> (sorry, I don't have Mathematica in front of me at the moment).
>> gseq gives me something like {0, 1 - List}.
>>
>> What exactly is going wrong, and how do I mend it?  Also, in the With
>> construct, will gseq[n-1] be evaluated once and stored in s, or will
>> every instance of s be replaced by a call to gseq[n-1] (so that
>> gseq[n-1] is wastefully evaluated three times per call to gseq[n])?
>> If gseq[n-1] will be evaluated more than once (per call to gseq[n]),
>> is there a way to change the code so that it won't be?  If there's a
>> better way to efficiently implement g(n) altogether, please share (but
>> function g(n)--don't spoil my fun).
>>
>> Thanks,
>> Chandler
>>
>
>

```

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