Analysis of the kx+1 Problem for k>7

This paper presents an examination of kx+1 transformations for odd k>7, using binary pattern analysis to track the evolution of sequence elements. It is shown that for any starting integer, the binary length of these sequences grows without bound, thus diverging. The work extends previous studies on the Collatz-type problems. The carry propagation from higher-order bits of k is analyzed in detail and is shown to guarantee length growth in odd patterns.