Fred>On 11/17/13, Bill Gosper <billgosper@gmail.com> wrote: On Thu, Nov 14, 2013 at 3:39 AM, Bill Gosper <billgosper@gmail.com> wrote: This must have been found by Newman himself but I only just noticed. ... Hypothesis: the thread topic is (distantly related to) Calkin-Wilf and Stern-Brocot trees --- see eg. http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree Adam>Here's one I prepared earlier: http://cp4space.wordpress.com/2013/10/24/enumerating-the-rationals/ Sincerely, Adam P. Goucher Eye gotcha: Plotting renders both functions newm[x_] := 1/(1 - x + 2 Floor[x]) oldm[x_] := 2*Ceiling[#] - 1 - # &[1/x] Plot[{newm[r], oldm[r]}, {r,-π,π}, AspectRatio -> Automatic] visually indistinguishable from odd ones, although the same could be said of Floor[x+1/2]. Plot[oldm[oldm[oldm[x]]], {x,-π,π}] reminds me of graphs in Gödel, Escher, Bach. Strangely, the minor change Clear[newm]; newm[x_?NumericQ] := 1/(1 - x + 2 Floor[x]) Plot[newm[newm[x]], {x,-π,π}] ruins the effect by trying to draw a continuous function connected by bogus "verticals". --rwg