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] = 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[1900] > > 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] := 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] := {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[1] 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 >> please don't reveal any mathematical properties about the particular >> function g(n)--don't spoil my fun). >> >> Thanks, >> Chandler >> > >