GAP (3k+1) - Chapter 1: The 3k+1 Problem

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1 The 3k+1 Problem
1.1 Theory
1.2 Program
1.2-1 ThreeKPlusOneSequence

### 1 The 3k+1 Problem

#### 1.1 Theory

Let k ∈ ℕ be a natural number. We consider the sequence n(i, k), i ∈ ℕ, with n(1, k) = k and else n(i+1, k) = n(i, k) / 2 if n(i, k) is even and n(i+1, k) = 3 n(i, k) + 1 if n(i, k) is odd.

It is not known whether for any natural number k ∈ ℕ there is an m ∈ ℕ with n(m, k) = 1.

ThreeKPlusOne provides the function `ThreeKPlusOneSequence` (1.2-1) to explore this for given n. If you really want to know something about this problem, see [Wir98] or http://mathsrv.ku-eichstaett.de/MGF/homes/wirsching/ for more details (and forget this package).

#### 1.2 Program

In this section we describe the main function of this package.

##### 1.2-1 ThreeKPlusOneSequence

`‣ ThreeKPlusOneSequence`( k[, max] ) | ( function )

This function computes for a natural number k the beginning of the sequence n(i, k) defined in section 1.1. The sequence stops at the first 1 or at n(max, k), if max is given.

    gap> ThreeKPlusOneSequence(101);
    "Sorry, not yet implemented. Wait for Version 84 of the package"

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