No - this one has no biggies until the one I mention. There is no apparent connection with class number 1 however there is a class number of 11 deriving from a prime factor of the discriminant. John McKay From: IN%"math-fun@mailman.xmission.com" "math-fun" 27-APR-2004 21:31:30.21 To: IN%"math-fun@mailman.xmission.com" CC: Subj: [math-fun] continued fraction of root of cubic Return-path: <math-fun-bounces+mckay=vax2.concordia.ca@mailman.xmission.com> Received: from bonnie.concordia.ca (bonnie.Concordia.CA [132.205.7.81]) by vax2.concordia.ca (PMDF V6.2 #30759) with ESMTP id <01L9FTU4LH9W005JEU@vax2.concordia.ca> for mckay@vax2.concordia.ca (ORCPT mckay@vax2.concordia.ca); Tue, 27 Apr 2004 21:31:29 -0400 (EDT) Received: from mailman.xmission.com (mailman.xmission.com [198.60.22.29]) by bonnie.concordia.ca (8.12.10/8.12.10) with ESMTP id i3S1VJA0013479 for <mckay@vax2.concordia.ca>; Tue, 27 Apr 2004 21:31:19 -0400 Received: from localhost ([127.0.0.1] helo=mailman.xmission.com) by mailman.xmission.com with esmtp (Exim 3.36 #1 (Debian)) id 1BIduw-0001Ey-05 for <mckay@vax2.concordia.ca>; Tue, 27 Apr 2004 19:31:18 -0600 Received: from mgr8.xmission.com ([198.60.22.208] ident=mail) by mailman.xmission.com with esmtp (Exim 3.36 #1 (Debian)) id 1BIduo-0001En-00 for <math-fun@mailman.xmission.com>; Tue, 27 Apr 2004 19:31:10 -0600 Received: from [192.12.69.5] (helo=optima.cs.arizona.edu) by mgr8.xmission.com with esmtp (Exim 4.30) id 1BIdun-0000bh-Q6 for math-fun@mailman.xmission.com; Tue, 27 Apr 2004 19:31:09 -0600 Received: from baskerville.CS.Arizona.EDU (baskerville.cs.arizona.edu [192.12.69.35]) by optima.cs.arizona.edu (8.12.9p2/8.12.8) with ESMTP id i3S1V8G7037718 for <math-fun@mailman.xmission.com>; Tue, 27 Apr 2004 18:31:08 -0700 Received: (from rcs@localhost) by baskerville.CS.Arizona.EDU (8.8.8p2+Sun/8.8.8) id SAA19959; Tue, 27 Apr 2004 18:31:08 -0700 (MST) Date: Tue, 27 Apr 2004 18:31:08 -0700 (MST) From: Richard Schroeppel <rcs@CS.Arizona.EDU> Subject: [math-fun] continued fraction of root of cubic Sender: math-fun-bounces+mckay=vax2.concordia.ca@mailman.xmission.com To: math-fun@mailman.xmission.com Errors-to: math-fun-bounces+mckay=vax2.concordia.ca@mailman.xmission.com Reply-to: math-fun <math-fun@mailman.xmission.com> Message-id: <200404280131.SAA19959@baskerville.CS.Arizona.EDU> Precedence: list X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on mgr8.xmission.com X-Spam-Level: X-Spam-Status: No, hits=0.0 required=8.0 tests=none autolearn=no version=2.63 X-SA-Exim-Mail-From: rcs@CS.Arizona.EDU X-SA-Exim-Version: 3.1 (built Mon Jan 26 13:00:24 MST 2004) X-SA-Exim-Scanned: Yes X-BeenThere: math-fun@mailman.xmission.com X-Mailman-Version: 2.1.4 X-Scanned-By: MIMEDefang 2.35 List-Post: <mailto:math-fun@mailman.xmission.com> List-Subscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=subscribe> List-Unsubscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=unsubscribe> List-Archive: <http://mailman.xmission.com/cgi-bin/mailman/private/math-fun> List-Help: <mailto:math-fun-request@mailman.xmission.com?subject=help> List-Id: math-fun <math-fun.mailman.xmission.com> Original-recipient: rfc822;mckay@vax2.concordia.ca

The real root of x*x*x - 156*x + 817 has a very large term round about the 800th position. Is there any explanation for this? It is of the order of 10**7.

I think that seeing occasional terms that are O(N^2) is to be expected, so this is somewhat unusual. If there's an analogy with the Brillhart/Stark situation, which I think <fade, fade> was for X^3 = aX+b with a,b in {6,8,10}, then one of (X+-c)^2 for small c (< 10 or 20) should have a much larger term, and it should appear earlier. Rich rcs@cs.arizona.edu _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun