User blog comment:Ikosarakt1/My Turing machine programs/@comment-25418284-20130330212946/@comment-1605058-20130331094744

When I was thinking about it, best OTM are machines with oracle tape, where nth cell is 1 iff for some k \(S(k)=n\), i.e. it has marked cells corresponding to some Busy Beaver number. Use of S is better than of Σ, because solving halting problem is easier.

Such OTM has  advantage that it doesn't depend on any numbering scheme and is unique. If we allow oracle tape head to stay in place when needed halting problem becomes almost trivial.