Homologues to (3n+1)/2i
-Collatz iteration is the j=0 case.
return to slide index
-j must run from 0 to infinity for the homologues.
-These homologues were not previously recognized, it seems.
-Iterations converge to 3j.
-Youngest children in the j>0 case don't necessarily come at
-Internal nodes are congruent to 0 mod 3. (0 are leaves in (3n+1)/2i)
-Leaf nodes are congruent to 1 or 2 mod 3. (These are internal in (3n+1)/2i)
-Tree shapes are much different, and aren't amenable to summing
-The l.d.a.s of the j=0 case DO appear buried within left
descents in predecessor trees for j>0 cases .
-Steps down the l.d.a.s don't necessarily reduce the power of 3 in
the d coefficient.
-Extension of odd integer m is at 2*m+3(j-1).
has corrected me: the homologues are (more inclusively) (3n+3*k)/2i for odd k