The 3x + 1 Problem: an Annotated Bibliography

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[1]  Bryan Thwaites.  Two Conjectures or how to win £1100 , 1996 .

[2]  Daniel J. Bernstein,et al.  The 3x+1 conjugacy map , 1996 .

[3]  Lynn E. Garner.  On the Collatz $3n+1$ algorithm , 1981 .

[4]  Richard K. Guy,et al.  Conway's Prime Producing Machine , 1983 .

[5]  Tanguy Urvoy.  Regularity of Congruential Graphs , 2000, MFCS.

[6]  S. Brocco.  A Note On Mignosi′s Generalization of the (3X+1)-Problem , 1995 .

[7]  Some Borel measures associated with the generalized Collatz mapping , 1992 .

[8]  R. Terras.  On the existence of a density , 1979 .

[9]  Jeffrey C. Lagarias,et al.  The 3x + 1 Problem and its Generalizations , 1985 .

[10]  Daniel A. Rawsthorne.  Imitation of an Iteration , 1985 .

[11]  G. Venturini.  Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x + 1 Problem) , 1992 .

[12]  Ivan Korec.  A density estimate for the $3x+1$ problem , 1994 .

[13]  G. Wirsching.  An improved estimate concerning 3n+1 predecessor sets , 1993 .

[14]  Michael Avidon.  On Primitive 3-smooth Partitions of n , 1997, Electron. J. Comb..

[15]  Guo-Gang Gao.  On consecutive numbers of the same height in the Collatz problem , 1993, Discret. Math..

[16]  G. Wirsching.  A functional differential equation and 3n+1 dynamics , 2001 .

[17]  J. Sander.  On the (3N+1)-conjecture , 1990 .

[18]  L. Halbeisen,et al.  Optimal bounds for the length of rational Collatz cycles , 1997 .

[19]  T. Brox.  Collatz cycles with few descents , 2000 .

[20]  Serge Burckel.  Functional Equations Associated with Congruential Functions , 1994, Theor. Comput. Sci..

[21]  Y. Sinai.  A Theorem About Uniform Distribution , 2004 .

[22]  G. Wirsching.  On the problem of positive predecessor density in $3n+1$ dynamics , 2003 .

[23]  K. Mahler,et al.  An unsolved problem on the powers of 3/2 , 1968, Journal of the Australian Mathematical Society.

[24]  H. Möller.  Über Hasses Verallgemeinerung des Syracuse-Algorithmus (Kakutanis Problem) , 1978 .

[25]  S. Znám,et al.  A Note on the 3x + 1 Problem , 1987 .

[26]  K. Stolarsky.  A prelude to the 3x+1 problem , 1998 .

[27]  Yakov G. Sinai,et al.  Structure Theorem for (d, g, h)-Maps , 2002 .

[28]  Lynn E. Garner.  On heights in the Collatz 3n + 1 problem , 1985, Discret. Math..

[29]  R. Terras,et al.  A stopping time problem on the positive integers , 1976 .

[30]  M. Feix,et al.  Statistical properties of an iterated arithmetic mapping , 1994 .

[31]  R. Guy.  Unsolved Problems in Number Theory , 1981 .

[32]  Philippe Devienne,et al.  Halting Problem of One Binary Horn Clause is Undecidable , 1993, STACS.

[33]  D. Boyd.  Which Rationals are Ratios of Pisot Sequences? , 1985, Canadian Mathematical Bulletin.

[34]  E. Heppner.  Eine Bemerkung zum Hasse-Syracuse-Algorithmus , 1978 .

[35]  G. Venturini.  On a Generalization of the 3 x+1 Problem , 1997 .

[36]  Clifford A. Reiter,et al.  Visualizing generalized 3x+1 function dynamics , 2001, Comput. Graph..

[37]  Maurice Margenstern,et al.  Frontier between decidability and undecidability: a survey , 2000, Theor. Comput. Sci..

[38]  Kenneth G. Monks,et al.  The autoconjugacy of the 3x+1 function , 2004, Discret. Math..

[39]  R. Guy.  John Isbell's Game of Beanstalk and John Conway's Game of Beans-Don't-Talk , 1986 .

[40]  Y. Sinai.  Uniform Distribution in the (3x+1)-Problem , 2003 .

[41]  I. Krasikov.  HOW MANY NUMBERS SATISFY THE 3X + 1 CONJECTURE? , 1989 .

[42]  G. Wirsching.  Über das 3n + 1 Problem , 2000 .

[43]  Günther Wirsching,et al.  The Dynamical System Generated by the 3n+1 Function , 1998 .

[44]  K. Matthews,et al.  A Markov approach to the generalized Syracuse algorithm , 1985 .

[45]  Jeffrey C. Lagarias,et al.  THE 3x + 1 PROBLEM: TWO STOCHASTIC MODELS , 1992 .

[46]  Carl Pomerance,et al.  On a conjecture of Crandall concerning the qx + 1 problem , 1995 .

[47]  I. Korec.  The $3x+1$ problem, generalized Pascal triangles and cellular automata , 1992 .

[48]  Richard K. Guy,et al.  Don't Try to Solve These Problems! , 1983 .

[49]  Y. Matiyasevich,et al.  A binomial representation of the 3x + 1 problem , 1999 .

[50]  Games of cards, dynamical systems, and a characterization of the floor and ceiling functions , 1990 .

[51]  A. Gilman,et al.  A generalization of Everett's result on the Collatz 3x + 1 problem , 1987 .

[52]  H. Müller.  Über eine klasse 2-adischer funktionen im zusammenhang mit dem „3X + 1“-problem , 1994 .

[53]  Jeffrey C. Lagarias,et al.  Lower bounds for the total stopping time of 3x + 1 iterates , 2001, Math. Comput..

[54]  Steven J. Miller,et al.  Benford's law, values of L-functions and the 3x+1 problem , 2004, math/0412003.