>>142591583 7 11 15 19 23 27 31 35 39 43 47 51 55
5 11 17 23 29 35 41 47 55
17 35 55
I think it could be correct to generalize that every odd number in the form of 2n-1 will increase n-times in a row. (increase-halving-increase-halving-increase....)
I think from this can be safely concluded that there can be no odd number tgat results in a permament chain of increase-division-increase.
All that remains to prove that the interruptions between the chains occur frequently enough to overcome the possible chains of increase.