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### A The File 3k+1.xml

Here is the complete source of the example GAPDoc document 3k+1.xml discussed in SectionÂ 1.2.

  The <Package>ThreeKPlusOne</Package> Package Version 42 Dummy AuthĂ¶r 3kplusone@dev.null ©right; 2000 The Author.

You can do with this package what you want.

Really. The 3k+1 Problem

Theory Let k \in &NN; be a natural number. We consider the sequence n(i, k), i \in &NN;, 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 \in &NN; there is an m \in &NN; with n(m, k) = 1.

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

Program In this section we describe the main function of this package. This function computes for a natural number k the beginning of the sequence n(i, k) defined in section . 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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