Ethan Akin: Why is the 3x+1 problem so hard? Math. Magazine ... (ca. 1996), ... 24228 Ethan Akin: Why is the 3x+1 problem hard? Cont. Math 356 (2004), 1-20. 25469 J. Alves/M. Graca/M. Sousa Dias/J. Sousa Ramos: A linear algebra approach to the conjecture of Collatz. Lin. Alg. Appl. 394 (2005), 277-289. Paul Andaloro: The 3x+1 problem and directed graphs. Eichsta''t Conference 1999, 5p. 13469 Stefan Andrei/Manfred Kudlek/Radu Stefan Niculescu: Some results on the Collatz problem. Eichsta''t Conference 1999, 15p. Stefan Andrei/C. Masalagiu: About the Collatz conjecture. Acta Informatica 35 (1998), 167-179. 24553 David Applegate/Jeffrey Lagarias: The 3x+1 semigroup. J. Number Theory 117 (2006), 146-159. J. Arsac: Algorithmes pour verifier la conjecture de Syracuse. RAIRO Inform. Theor. Appl. 21 (1987), 3-9. Ranan Banerji: Some properties of the 3n+1 function using number representation. Eichsta''t Conference 1999, 4p. 25406 Edward Belaga: Reflecting on the 3x+1 mystery. Internet 2011, 11p. 22424 E. Belaga/M. Mignotte: Cyclic structure of dynamical systems associated with 3x+d extensions of Collatz' problem. Internet ca. 2002, 62p. Lothar Berg/G. Meinardus: Functional equations connected with the Collatz problem. Res. Math. 25 (1994), 1-12. Lothar Berg/G. Meinardus: The 3n+1 Collatz problem and functional equations. Rostocker Math. Koll. 48 (1995), 11-18. Daniel Bernstein: A non-iterative 2-adic statement of the 3x+1 conjecture. Proc. Am. Math. Soc. 121 (199.), 405-408. 9744 Daniel Bernstein/Jeffrey Lagarias: The 3x+1 conjugacy map. Can. J. Math. 48 (1996), 1154-1169. Corrado Boehm/Giovanna Santacchi: On the existence of cycles of given length in integer sequences like x_{n+1}=x_n/2 if x_n even, and x_{n+1}=3x_n+1 otherwise. Atti Acc. Naz. Lincei 64 (1978), 260-264. R. Buttsworth/Keith Matthews: On some Markov matrices arising from the generalized Collatz mapping. Acta Arithm. 55 (1990), 43-57. 25407 Benjamin Cawaling: Collatz 3x+1 conjecture proved! Internet ca. 2006, 29p. An attempt; wrong? Marc Chamberland: A dynamical systems approach to the 3x+1 problem. Eichsta''t Conference 1999, 1p. 25408 Marc Chamberland: An update of the 3x+1 problem. Internet ca. 2011, 32p. Similar to "A 3x+1 survey" in 25401 Lagarias, 57-78. John Horton Conway: Unpredictable iterations. Proc. Number Theory Conf. Boulder 1972, 49-55. 23727 John Horton Conway: On unsettleable arithmetical problems. Am. Math. Monthly 120/3 (2013), 192-198. R. Crandall: On the "3x+1" problem. Math. Comp. 32 (1978), 1281-1292. J. Dolan/A. Gilman/S. Manickam: A generalization of Everett's result on the Collatz 3x+1 problem. Adv. Appl. Math. 8 (1987), 405-409. 25502 Jeffrey Dumont/Clifford Reiter: Visualizing generalized 3x+1 function dynamics. Computers & Graphics 25/5 (2001), 883-898. S. Eliahou: The 3x+1 problem: new lower bounds on nontrivial cycle lengths. Discrete Math. 118 (1993), 45-56. C. Everett: Iteration of the number-theoretic function f(2n)=n, f(2n+1)=3n. Adv. Math. 25 (1977), 42-45. 27392 Craig Alan Feinstein: The Collatz 3n+1 conjecture is unprovable. Arxiv: 0312.309 (2003-2011), 2p. [math.GM, INQ 11309.] 25297 Zachary Franco/Carl Pomerance: On a conjecture of Crandall concerning the qx+1 problem. Math. Comp. 64/211 (1995), 1333-1336. L. Garner: On the Collatz 3n+1 algorithm. Proc. AMS 82 (1981), 19-22. F. Gruenberger: 3x+1 revisited. Popular Computing 7 (October 1979), 3-12. 3285 R. Guy: Don't try to solve these problems. Am. Math. Monthly (1981), 33-41. R. Guy: Conway's prime producing machine. Math. Mag. 56 (1983), 26-33. 9832 Lorenz Halbeisen/Norbert Hungerbu''hler: Optimal bounds for the length of rational Collatz cycles. Acta Arithm. 78 (1997), 227-239. E. Heppner: Einige Bemerkungen zum Hasse-Syracuse Algorithmus. Arch. Math. 31 (1977/79), 317-320. 25416 Stefan Kohl: Wildness of iteration of certain residue-class-wise affine mappings. Internet ca. 2008, 8p. I. Korec/S. Znam: A note on the 3x+1 problem. Am. Math. Monthly 94 (1987), 771-772. I. Krasikov: How many numbers satisfy the 3x+1 conjecture? Int. J. Math. Sci. 12 (1989), 761-796. 1992 Jeffrey Lagarias: The 3x+1 problem and its generalizations. Am. Math. Monthly 92 (1985), 3-23. 1973 Jeffrey Lagarias: The set of rational cycles for the 3x+1 problem. Acta Arithm. 46 (1990), 33-53. 25405 Jeffrey Lagarias: Benford's law for the 3x+1 function. Internet 2006, 16p. 25401 Jeffrey Lagarias: The ultimate challenge - the 3x+1 problem. AMS 2010, 340p. Eur 59. G. Leigh: A Markov process underlying the generalized Syracuse algorithm. Acta Arithm. 46 (1985), 125-143. Simon Letherman/Dierk Schleicher/Reg Wood: The 3n+1 problem and holomorphic dynamics. Eichsta''t Conference 1999, 11p. 25413 Dan Levy: Injectivity and surjectiviy of Collatz functions. Discrete Math. 285 (2004), 191-199. Keith Matthews: A Markov approach to the generalized Syracuse algorithm. Acta Arithm. 45 (1985), 29-42. Keith Matthews: Some Borel measures associated with the generalized Collatz mapping. Colloquium Math. 63 (1992), 191-202. 7209 Keith Matthews: The generalized 3x+1 mapping. Internet 1995, 19p. (on http://www.maths.uq.oz.au/~krm/home.html). 25414 Keith Matthews: Generalized 3x+1 mappings - Markov chains and ergodic theory. In 24501 Lagarias, 79-103. Keith Matthews/G. Leigh: A generalization of the Syracuse algorithm in F_q[x]. J. Number Theory 25 (1987), 274-278. 25404 Keith Matthews/A. Watts: A generalization of Hasse's generalization of the Syracuse algorithm. Acta Arithmetica 43 (1984), 167-175. Keith Matthews/A. Watts: A Markov approach to the generalized Syracuse algorithm. Acta Arithm. 45 (1985), 29-42. H. Moeller: Ueber Hasse's Verallgemeinerungen des Syracuse-Algorithmus. Acta Arithm. 34 (1978), 219-226. 25474 Liesbeth de Mol: Tag systems and Collatz-like functions. Theor. Comp. Sci. 390 (2008), 92-101. Ken Monks: A category of topological spaces encoding acyclic set-theoretic dynamics. Eichsta''t Conference 1999, 26p. 27396 Ken Monks: The sufficiency of arithmetic progressions for the 3x+1 problem. Proc. AMS 134/10 (2006), 2861-2872. 27397 Keenan Monks/Kenneth G. Monks/Kenneth M. Monks/Maria Monks: Strongly sufficient sets and the distribution of arithmetic sequences in the 3x+1 graph. Arxiv: 1204.3904 (2012), 35p. 25409 Francis Charles Motta/Henrique Roscoe de Oliveira/Thiago Aparecido Catalan: An analysis of the Collatz conjecture. Internet ca. 1997, 16p. 3471 Helmut Mu''ller: Das (3n+1)-Problem. Mitt. Math. Ges. Hamburg 12 (1991), 231-251. Helmut Mu''ller: U''ber eine Klasse 2-adischer Funktionen im Zusammenhang mit dem "3x+1"-Problem. Abh. Math. Sem. Univ. Hamburg 64 (1994), 293-302. J. Nievergelt/J. Farrar/E. Reingold: Computer approaches to mathematical problems. Prentice-Hall 1974, 211-217. 22069 Gerhard Opfer: An analytic approach to the Collatz 3n+1 problem. Hamburger Beiträge zur Angew. Math. ... (2011), 34p. Contains perhaps (a function theoretic) proof of the 3n+1 conjecture. D. Rawsthorne: Imitation of an iteration. Preprint, ca. 1985. C. Rometsch: Das (3n+1)-Problem. Diplomarbeit Tu''bingen 1988. J. Rouet/M. Feix: The (3x+1)/2 problem and its generalisation - a stochastic approach. Eichsta''t Conference 1999, 18p. 27394 Olivier Rozier: The 3x+1 problem - a lower bound hypothesis. Arxiv: 1510.01610 (2016), 18p. 1971 J. Sander: On the (3N+1)-conjecture. Acta Arithmetica 55 (1990), 241-248. B. Schuppar: Kettenbrueche und der (3a+1) Algorithmus. Preprint, ca. 1985. 3283 Benedict Seifert: On the arithmetic of cycles for the Collatz-Hasse ('Syracuse') conjectures. Discrete Math. 68 (1988), 293-298. J. Shallit/D. Wilson: The 3x+1 problem and finite automata. EATCS Bull. 46 (1992), 182-185. Ray Steiner: A theorem on the Syracuse problem. Proc. 7th Manitoba Conf. Numerical Math. Winnipeg 1977, 553-559. Ray Steiner: On the Qx+1 problem, Q odd. I-II. Fibonacci Quart. 19 (1981), 285-296. 27398 David Stroup: Collatz's problem and encoding vectors. MSc. thesis Univ. Akron 2006, 55p. 27393 Riho Terras: A stopping time problem on the positive integers. Acta Arithm. 30 (1976), 241-252. Riho Terras: On the existence of a density. Acta Arithm. 35 (1979), 101-102. B. Thwaites: My conjecture. Bull. Inst. Math. Appl. 21 (1985), 35-41. R. Tijdeman: On the Fermat-Catalan equation. Jahresbericht DMV 87 (1985), 1-18. G. Venturini: Sul comportamento delle iterazioni di alcune funzioni numeriche. Ist. Lombardo Acc. Sci. A 116 (1982), 1-16. 2538 G. Venturini: On the 3x+1 problem. Adv. Appl. Math. 10 (1989), 344-347. 3817 G. Venturini: Iterates of number theoretic functions with periodic rational coefficients (generalization of the 3x+1 problem). Studies Appl. Math. 86 (1992), 185-218. 10732 G. Venturini: On a generalization of the 3x+1 problem. Adv. Appl. Math. 19 (1997), 295-305. 25501 Xingyan Wang/Xuejing Yu: Dynamics of the generalized 3x+1 function determined by its fractal images. Progress Nat. Sci. 18 (2008), 217-223. 25418 Patrick Wiltrout/Eric Landquist: The Collatz conjecture and integers of the form 2^kb-m and 3^kb-1. Electr. J. Undergr. Math. 17 (2013), 5p. Günther Wirsching: An improved estimate concerning 3x+1 predecessor sets. Acta Arithm. 63 (1993), 205-210. Günther Wirsching: A Markov chain underlying the backwards Syracuse algorithm. Rev. Roum. Math. pures appl. 39 (1994), 915-926. Günther Wirsching: The dynamical system on the natural numbers generated by the 3n+1 function. Habilitationsschrift, ca. 1994. 11518 Günther Wirsching: The dynamical system generated by the 3n+1 function. Springer LN Math. 1681 (1998), 160p. 3-540-63970-5. Günther Wirsching: Über das (3n+1)-Problem. Elem. Math. 55 (2000), 142-155. 18225 Günther Wirsching: On the problem of positive predecessor density in 3n+1 dynamics. Discrete Cont. Dyn. Syst. 9/3 (2003), 771-787. 27395 Roger Zarnowski: The congruence structure of the 3x+1 map. Internet 2009, 18p.