[1X1 [33X[0;0YThe [22X3k+1[122X[101X[1X Problem[133X[101X [1X1.1 [33X[0;0YTheory[133X[101X [33X[0;0YLet [22Xk ∈ [122ℕX be a natural number. We consider the sequence [22Xn(i, k), i ∈ ℕ,[122X with [22Xn(1, k) = k[122X and else [22Xn(i+1, k) = n(i, k) / 2[122X if [22Xn(i, k)[122X is even and [22Xn(i+1, k) = 3 n(i, k) + 1[122X if [22Xn(i, k)[122X is odd.[133X [33X[0;0YIt is not known whether for any natural number [22Xk ∈ [122ℕX there is an [22Xm ∈ [122ℕX with [22Xn(m, k) = 1[122X.[133X [33X[0;0Y[5XThreeKPlusOne[105X provides the function [2XThreeKPlusOneSequence[102X ([14X1.2-1[114X) to explore this for given [22Xn[122X. If you really want to know something about this problem, see [Wir98] or [7Xhttp://www.ku.de/mgf/mathematik/lehrstuhlstatistik/team/dr-guenther-wirsching/[107X for more details (and forget this package).[133X [1X1.2 [33X[0;0YProgram[133X[101X [33X[0;0YIn this section we describe the main function of this package.[133X [1X1.2-1 ThreeKPlusOneSequence[101X [33X[1;0Y[29X[2XThreeKPlusOneSequence[102X( [3Xk[103X[, [3Xmax[103X] ) [32X function[133X [33X[0;0YThis function computes for a natural number [3Xk[103X the beginning of the sequence [22Xn(i, k)[122X defined in section [14X1.1[114X. The sequence stops at the first [22X1[122X or at [22Xn([3Xmax[103X, k)[122X, if [3Xmax[103X is given.[133X [4X[32X Example [32X[104X [4X[25Xgap>[125X [27XThreeKPlusOneSequence(101);[127X[104X [4X[28X"Sorry, not yet implemented. Wait for Version 84 of the package"[128X[104X [4X[32X[104X
Generated by dwww version 1.15 on Fri Jun 28 17:09:42 CEST 2024.