Path: csiph.com!eternal-september.org!feeder.eternal-september.org!nntp.eternal-september.org!.POSTED!not-for-mail From: Tim Rentsch Newsgroups: comp.arch Subject: Re: A useless machine Date: Thu, 12 Mar 2026 21:11:50 -0700 Organization: A noiseless patient Spider Lines: 34 Message-ID: <86ldfw74hl.fsf@linuxsc.com> References: <10mpgtp$32h0n$1@dont-email.me> <1771094919-5857@newsgrouper.org> <10mqhq2$3dejk$1@dont-email.me> <1771104135-5857@newsgrouper.org> <10msbv2$3vgrg$1@dont-email.me> <10nd2e6$1gl20$1@dont-email.me> <10nf15f$256q4$1@dont-email.me> <10nfinr$2ao8l$1@dont-email.me> <10nh7uh$2sbtq$1@dont-email.me> <1772069274-5857@newsgrouper.org> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Injection-Date: Fri, 13 Mar 2026 04:11:53 +0000 (UTC) Injection-Info: dont-email.me; posting-host="cb1c5db134e2203ca5fd5b23b9ffc3a7"; logging-data="2855307"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19tZODqCeKD3cgL6aTZY41YKfdA7OV50zw=" User-Agent: Gnus/5.11 (Gnus v5.11) Emacs/22.4 (gnu/linux) Cancel-Lock: sha1:XFl4yDOzoC0t2V5xiOhINdLVgIY= sha1:bz7YGXeYPXoXhEalD1VJuaDohL8= Xref: csiph.com comp.arch:115310 MitchAlsup writes: > David Brown posted: > >> On 22/02/2026 19:38, BGB wrote: >> >>> I was initially seeing it more like a very large hash table. >>> But, I have since realized it is not a hash table, it is a more >>> organized pattern. >> >> As far as we know, the result of apply the Collatz function >> (calculating the number of steps to reach 1, if it ever does) >> follows a pattern statistically but not any clear pattern for >> individual values. There are a lot of mathematical functions like >> that - a good example being the number of prime factors in a >> number. You can draw graphs and visually see nice patterns - some >> of which can be proven, others are still unproven and may not apply >> over a big enough scale. Sometimes there are tricks or hints to >> ways to improve your chances when guessing which values might be >> outliers. > > Given by definition: even: n = n/2 > odd: n = 3xn+1 {which is even} > > The most one can get out of an iteration is nx1.5 {for large n} > while the most one can loose from an iteration is n/2 > > So, there will be vanishingly small numbers of n which see the odd > iteration enough times to out weight the even iterations. Thus one > would expect the conjecture is true. Unfortunately this kind of reasoning isn't very compelling. It's easy to find examples of propositions, even just on integers, that are true almost everywhere and yet are not true everywhere.