LEADER 02743nam 22006495 450 001 9910146298303321 005 20250731082225.0 010 $a3-540-69677-6 024 7 $a10.1007/BFb0095985 035 $a(CKB)1000000000437332 035 $a(SSID)ssj0000322751 035 $a(PQKBManifestationID)12099110 035 $a(PQKBTitleCode)TC0000322751 035 $a(PQKBWorkID)10289903 035 $a(PQKB)10004845 035 $a(DE-He213)978-3-540-69677-3 035 $a(MiAaPQ)EBC5595389 035 $a(Au-PeEL)EBL5595389 035 $a(OCoLC)1076258602 035 $a(MiAaPQ)EBC6842781 035 $a(Au-PeEL)EBL6842781 035 $a(OCoLC)1113609871 035 $a(PPN)15521764X 035 $a(EXLCZ)991000000000437332 100 $a20121227d1998 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Dynamical System Generated by the 3n+1 Function /$fby Günther J. Wirsching 205 $a1st ed. 1998. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1998. 215 $a1 online resource (VIII, 164 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1681 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-63970-5 327 $aSome ideas around 3n+1 iterations -- Analysis of the Collatz graph -- 3-adic averages of counting functions -- An asymptotically homogeneous Markov chain -- Mixing and predecessor density. 330 $aThe 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1681 606 $aNumber theory 606 $aComputer science 606 $aNumber Theory 606 $aTheory of Computation 615 0$aNumber theory. 615 0$aComputer science. 615 14$aNumber Theory. 615 24$aTheory of Computation. 676 $a519.2 700 $aWirsching$b Gu?nther J.$f1960-$0351066 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146298303321 996 $aThe Dynamical System Generated by the 3n+1 Function$94412835 997 $aUNINA