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The Collatz Conjecture Challenge

Formalising the Collatz literature with proof assistants

Literature (350 entries)

2004

Why is the $3x+1$ Problem Hard?

Authors: Ethan Akin

Chapel Hill Ergodic Theory Workshops, Vol. 356, pp. 1--20

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Una breve introduzione a diffusioni su insiemi frattali e ad alcuni essempi di sistemi dinamici semplici

Authors: Sergio Albeverio and Danilo Merlini and Remiglio Tartini

Note di matematica e fisica, Vol. 3, pp. 1--39

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Sur la conjecture de ``Syracuse-Kakutani-Collatz''

Authors: Jean-Paul Allouche

Séminaire de Théorie des Nombres 1978--1979, Expose No. 9

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A linear algebra approach to the conjecture of Collatz

Authors: João F. Alves and Mário M. Graca and M. E. Sousa Dias and José Sousa Ramos

Lin. Alg. Appl., Vol. 394, pp. 277--289

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The $2$-adic valuation of a sequence arising from a rational integral

Authors: Tewodrus Amdeberhan and Dante Manna and Victor H. Moll

J. Combinatorial Theory, Series A, Vol. 115(8), pp. 1474--1486

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On some difference equations with eventually periodic solutions

Authors: Amal S. Amleh and Edward A. Grove and Candace M. Kent and Gerasimos Ladas

J. Math. Anal. Appl., Vol. 223, pp. 196--215

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On total stopping times under $3X+1$ iteration

Authors: Paul Andaloro

Fibonacci Quarterly, Vol. 38, pp. 73--78

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The $3X+1$ problem and directed graphs

Authors: Paul Andaloro

Fibonacci Quarterly, Vol. 40, pp. 43--54

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Struggling with the $3x + 1$ problem

Authors: S. Anderson

Math. Gazette, Vol. 71, pp. 271--274

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A Functional View over the Collatz's Problem

Authors: Stefan Andrei and Wei-Ngan Chin and Huu Hai Nguyen

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Some results on the Collatz problem

Authors: Stefan Andrei and Manfred Kudlek and Radu Stefan Niculescu

Acta Informatica, Vol. 37, pp. 145--160

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About the Collatz Conjecture

Authors: Stefan Andrei and Cristian Masalagiu

Acta Informatica, Vol. 35, pp. 167--179

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Density Bounds for the $3x+1$ Problem I. Tree-Search Method

Authors: David Applegate and Jeffrey C. Lagarias

Math. Comp., Vol. 64, pp. 411--426

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Density Bounds for the $3x+1$ Problem II. Krasikov Inequalities

Authors: David Applegate and Jeffrey C. Lagarias

Math. Comp., Vol. 64, pp. 427--438

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On the distribution of $3x+1$ trees

Authors: David Applegate and Jeffrey C. Lagarias

Experimental Mathematics, Vol. 4, pp. 101--117

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Lower bounds for the total stopping time of $3x+1$ iterates

Authors: David Applegate and Jeffrey C. Lagarias

Math. Comp., Vol. 72, pp. 1035--1049

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The $3x+1$ semigroup

Authors: David Applegate and Jeffrey C. Lagarias

J. Number Theory, Vol. 177, pp. 146--159

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1986

Algorithmes pour vérifier la conjecture de Syracuse

Authors: Jacques Arsac

C. R. Acad. Sci. Paris, Vol. 303, pp. 155--159

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Further Investigations of the Wondrous Numbers

Authors: Charles Ashbacher

J. Recreational Math., Vol. 24, pp. 1--15

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1966

Comment on Problem $63-13^{*}$

Authors: Arthur Oliver Lonsdale Atkin

SIAM Review, Vol. 8, pp. 234--236

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