The 3n+1 Problem: Scope, History and Results

Martiny, Theodore (2015) The 3n+1 Problem: Scope, History and Results. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

The 3n+1 problem can be stated in terms of a function on the positive integers: C(n) = n=2
if n is even, and C(n) = 3n + 1 if n is odd. The problem examines the iterations of this
function and asks how these iterations behave. Specifically it asks if the starting point is
important or if every starting point eventually reaches the number one.
We discuss the history of this problem and focus on how well rounded it is. This problem
can be examined from many disciplines of math in the attempt to find a solution. We discuss
a probability theory approach which gives a model to predict how many iterations it will
take to reach the number one for any given starting value.
We also present some major results on this problem, one which demonstrates that "most"
numbers eventually reach one and another which shows that any cycle that exists must be
extremely large.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Martiny, Theodore tim24@pitt.edu TIM24
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Wheeler, Jeffrey jwheeler@pitt.edu JWHEELER Committee Member Hales, Thomas hales@pitt.edu HALES Committee Member Kaveh, Kiumars kaveh@pitt.edu KAVEH Committee Member Neilan, Michael neilan@pitt.edu NEILAN
Date:	8 June 2015
Date Type:	Publication
Defense Date:	7 April 2015
Approval Date:	8 June 2015
Submission Date:	15 April 2015
Access Restriction:	No restriction; Release the ETD for access worldwide immediately.
Number of Pages:	63
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Mathematics
Degree:	MS - Master of Science
Thesis Type:	Master's Thesis
Refereed:	Yes
Uncontrolled Keywords:	Collatz conjecture, 3n+1 problem, 3n+1 cycle length, 3n+1 heuristic algorithm
Date Deposited:	08 Jun 2015 22:08
Last Modified:	15 Nov 2016 14:27
URI:	http://d-scholarship.pitt.edu/id/eprint/24817

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