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### 3x+1 Problem - OeisWiki

The 3x+1 problem concerns an iterated function and the question of whether it always reaches 1 when starting from any positive integer. It is also known as the ...
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### Research Article The 3x 1 Problem As A String Rewriting System

May 11, 2010 ... The 3x 1 problem can be viewed, starting with the binary form for any n ∈ N, as a string of. “runs” of 1s and 0s, using methodology ...
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### Number Theory - Besides The $3x + 1$ Problem, For Which Similar ...

Jan 21, 2019 ... As in the case of Collatz problem, it is conjectured that the orbit of arbitrary positive integer always reaches the cycle passing through 1. – ...
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### Help Me Solve (2x + 1) ( 3x - 1) / And Find The Equation Of The Line That ...

Jan 16, 2013 ... Hello I need help can you please help me solve by showing me how you solve and not just the answer. Problem 1. perform the operation (2X ...
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### The \(3x + 1\) Problem And Its Generalizations | Mathematical ...

Sep 24, 2008 ... The "3x+1" problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, or Ulam's problem, ...
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### The Collatz (3x + 1) Problem -- From Wolfram Library Archive

This package computes the iterates of the Collatz map: x -> x/2, if x is even; x -> (3x+1)/2, if x is odd, until an iterate reaches one of the four known ...
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### The 3x+1 Problem And Its Generalizations

The 3x+1 problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem, concerns the behavior ...
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### The $3x + 1$ Problem: Two Stochastic Models

The $3x + 1$ problem concerns the behavior under iteration of the function $T: \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ defined by $T(n) = n/2$ if $n$ is even and $T(n) = (3n + 1)/2$ if $n$ is odd. The $3x + 1$ conjecture asserts that for each $n \geq 1$ some $k$ exists with $T^{(k)}(n) = 1$; let $\sigma_\infty(n)$ equal the minimal such $k$ if one exists and $+\infty$ otherwise. The behavior of $\sigma_\infty(n)$ is irregular and seems to defy simple description. This paper describes two kinds of stochastic models that mimic some of its features. The first is a random walk that imitates the behavior of $T (\operatorname{mod}2^j)$; the second is a family of branching random walks that imitate the behavior of $T^{-1} (\operatorname{mod}3^j)$. For these models we prove analogues of the conjecture that $\lim \sup_{n \rightarrow \infty}(\sigma_\infty(n)/\log(n)) = \gamma$ for a finite constant $\gamma$. Both models produce the same constant $\gamma_0 \doteq 41.677647$. Predictions of the stochastic models agree wit This paper describes two kinds of stochastic models that mimic some of its features. The first is a random walk that imitates the behavior of T(mod2j) T ( mod ...
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### Keith Matthews' 3x+1 Page

Dec 7, 2020 ... 34 (1978) 219-226) which related the 3x+1 problem to 2-adic analysis. The 3x+1 problem is a special case of a more general class of problems ...
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### Solved Problem 9.3. For This Problem, Y F(x) 2x2-3x-1 On The | Chegg ...

Question: Problem 9.3. For this problem, y f(x) 2x2-3x-1 on the domain of all real numbers. (a) Sketch the function graph and find ...
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### The Analysis Of Convergence For The 3X + 1 Problem And Crandall ...

The 3X + 1 problem is known as the Collatz problem. It focuses on the behavior of the iteration of the function which takes odd integers n to 3n + 1 and even ...
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