wikipedia has an entry on the Collatz conjecture with a section on As an abstract machine that computes in base two. this apparently describes a construction of a FSM transducer computing sequential iterates starting from lsb to msb (least sig. bit to most sig. bit). [this is more a TCS, theoretical computer science construction.] however, there is no specific ref cited.

does anyone know where this FSM iterate transducer construction appears, or first appeared in the literature?

note, there is some relation to ref [4].

^{[ps, have some apparently new/possibly groundbreaking results related to this construction & intend to write it up on a blog, may edit this post later to incl the ref.]}

[1] The ultimate challenge: the 3x+1 problem, Lagarias

[2] what is the nearest problem to the collatz conjecture that has been successfully resolved, tcs.se

[3] The 3x + 1 Problem: An Annotated Bibliography, Lagarias, arxiv

[4] Jeffrey O. Shallit and David W. Wilson (1991), The “3x + 1” Problem and Finite Au- tomata, Bulletin of the EATCS (European Association for Theoretical Computer Sci- ence), No. 46, 1991, pp. 182–185.

onlysay that you are in the process of writing something related to this and thus would be interested in a reference you can quote. $\endgroup$ – user9072 Mar 4 '13 at 18:21irrelevantto know whether (you think) this is "possibly groundbreaking." Indeed,Igave you some credit for including motivation, else it'd be closed already. $\endgroup$ – user9072 Mar 5 '13 at 20:01