OK. My original proposal was for the plain vanilla Farey series. It looks like you've settled the Max-depth question, since 1/N and (N-1)/N are laggards. Min-depth looks loggish; I wonder if the earliest is near .618 & .382? The depth must be closely related to the continued fraction for K/N, probably the sum of the partial quotients. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of James Propp [jpropp@cs.uml.edu] Sent: Wednesday, December 15, 2010 11:27 AM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] q. re Farey-ish fractions with weighted mediants
I don't see where the restriction to odd denominators comes from. --Rich
Maybe I missed the drift of the conversation, but I thought the topic was my weighted-mediants version of the Stern-Brocot tree, starting with 0/1 and 1/1. If a/b and c/d have odd denominators, so must (2a+c)/(2b+d) and (a+2c)/(b+2d). (This doesn't apply to the numerators, since we start with 0/1 which has even numerator.) Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun