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

*To*: mathgroup at smc.vnet.net*Subject*: [mg109672] Part specification... is neither an integer nor a list of integers*From*: Chandler May <cjmay4754 at gmail.com>*Date*: Tue, 11 May 2010 06:28:11 -0400 (EDT)

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