Article View: fj.sci.math
Article #14106Collatz problem (was: Re: [Q]koratt)
From: Yuzuru Hiraga
Date: Fri, 08 Dec 1995 00:00
Date: Fri, 08 Dec 1995 00:00
55 lines
2761 bytes
2761 bytes
$BJ?2l!w?^=q4[>pJsBg3X$G$9!#(J In article <4a4c3l$7se@news.tech.gakken.co.jp> yamada@tech.gakken.co.jp writes: >$B;3ED(J@$B3X=,8&5f<R$G$9!#(J "Collatz$B$NLdBj(J"$B$K$D$$$F$O(J > >"Unsolved Problems in Number Theory" Richard K.Guy >1981 Springer-Verlag $B!JBh#2HG$,$"$k!)!K(J > >$B$N(JP120$B$K=q$$$F$"$j$^$9!#(J7x10^11$B$^$G$O3NG'$5$l$F$$$k$h$&$G$9!#(J >$B$3$NCf$KJ88%%j%9%H$b=q$$$F$"$j$^$9!#(J sci.math $B$N(J FAQ $B$K$b0J2<$N$h$&$KF1$8;XE&$,$"$j$^$9!'(J >From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) >Subject: sci.math FAQ: Unsolved Problems >Summary: Part 20 of 32, New version >Message-ID: <DID14t.20C@undergrad.math.uwaterloo.ca> >Date: Mon, 20 Nov 1995 21:02:53 GMT > > UNSOLVED PROBLEMS ... >Collatz Problem > Take any natural number m > 0. > n : = m; > repeat > if (n is odd) then n : = 3*n + 1; else n : = n/2; > until (n==1) > > Conjecture 1 For all positive integers m, the program above > terminates. > The conjecture has been verified for all numbers up to 7 * 10^(11). >References > Unsolved Problems in Number Theory. Richard K Guy. Springer, Problem E16. > Elementary Number Theory. Underwood Dudley. 2nd ed. $B$?$@(J 7*10^11 $B$H$$$&>e8B$O$@$$$V8E$$$h$&$G!"(J $B!!!!FqGH40<$!'!V3QC+!J$+$/$?$K!K$NLdBj!W(J $B!!!!!J?t3X%;%_%J!<A}4)!"!V?t3X(J 100 $B$NLdBj!W(Jp.117-119$B!"F|K\I>O@<R(J, 1984$B!K(J $B$H$$$#0G/0J>eA0$N5-;v$G$b!"(J3*10^12 $B$^$G$O2r$,$J$$!JJFED?.IW;a$i$K$h$k!K(J $B$H$J$C$F$$$^$9!#$b$A$m$s:#$G$O$b$C$H@h$^$G8!>Z$5$l$F$$$k$N$G$7$g$&!#(J In article <WAKAMATU.95Dec7180030@parsley.kurims.kyoto-u.ac.jp> wakamatu@kurims.kyoto-u.ac.jp (Wakamatsu Kazuhiro) writes: >$B<c>>$G$9!#(J >$BA0H>$NA`:n$N8e$OI,$:4q?t$G$9$+$iBg;(GD$K!"(J >$B3NN(E*$K$$$&$H#1!?#2$N3NN($GLs#3!?#2G\!"(J >$B#1!?#2$N3NN($G#1!?#2G\$K$J$k$o$1$G!"(J >$B#22s$G4|BTCM!J!)!K$,Ls#3!?#4G\$K$J$k$o$1$G(J >$BD9$$L\$G8+$l$P>.$5$/$J$C$F$$$/$7!"$^$"!"@5$7$$$@$m$&$H$$$&(J >$B5$3Z$JOC$,$"$j$^$9!#(J $B>e$NFqGH@h@8$N5-;v$K$b$3$l$HF1MM$NI>2A!J$?$@$7>pJsNL$G=q$+$l$F$$$k!K(J $B$,9T$o$l$F$$$^$9!#$3$N5-;v$OC;$$$J$,$i!"B>$K$b$*$b$7$m$$OC$,=P$F$$$^$9!#(J $B!JJ?2l!K(J
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X-Google-Language: Japanese,JIS X-Google-Thread: f4956,9b8699e8e6da9a25 X-Google-Attributes: gidf4956,public From: hiraga@ulis.ac.jp (Yuzuru Hiraga) Subject: Collatz problem (was: Re: [Q]koratt) Date: 1995/12/08 Message-ID: <DJABML.DBq@ulis.ac.jp> X-Deja-AN: 121281352 distribution: fj sender: news@ulis.ac.jp (bach Usenet News System) references: <TAKERU.95Dec4213830@metis.cse.kyutech.ac.jp> <4a4c3l$7se@news.tech.gakken.co.jp> organization: Univ. of Lib. & Info. Sci., Tsukuba Japan newsgroups: fj.sci.math