View source for 1RB1LE 0LC0LB 1RD1LC 1RD1RA 1RF0LA ---1RE

{{machine|1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE}}{{unsolved|Does this TM halt or run forever?}}
{{TM|1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE}} is a tetrational [[BB(6)]] [[Cryptid]] found by Racheline on 30 July 2024 ([https://discord.com/channels/960643023006490684/1239205785913790465/1267788732300398647 Discord link]). It is the first discovered Cryptid which is neither [[probviously]] halting or probviously non-halting. Racheline estimates that it has a 3/5 chance of become a [[Translated Cycler]] and 2/5 chance of halting eventually.

<pre>
1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE
A(n+6,m) = 0^inf <C (10)^n 1^m 0^inf

A(2n,m) -> A(3n,m-3)
A(2n+1,m) -> A(3n+1,m-2)
A(2n,0) -> translated cycler
A(2n+1,0) -> A(6,6n-15)
A(n,1) = A(n+1,0)
A(2n,2) -> halt
A(2n+1,2) -> A(6,6n-10)
start from A(6,3)

(6,3) -> (9,0) -> (6,9) -> (9,6) -> (13,4) -> (19,2) -> (6,44) -> ... -> (19,37) -> ... -> (5395,2) -> (6,16172) -> ... -> (6,11499706784674840553982963244335134925926292012180535894331458059790938778878968481621445560196932470184062569880553764866025123766354799684631203637298859743405413224499198074720853448543344037846492928533557309269754344024578940398650604022127671219212868204078482696840863421497983802250964886170004962960289410195027865266357767132492619285668547610786689057240759204449610723369114500644414980504801780095838843221096818761115062075635136327221478807478315079387140446926256956991460845996815269568899367429919830588305329333143088760745263315773849396110871808200715753985864340607449243323203432825658435566757684843141746344665372901933843352127530984700134774127941919667681053930904263388909263935331661538599899139106183915539213591614541216854566127559305092174287252340495305601083110420028359390503735043199218514769778963279448332394384065634487789305567164753945749722964276916798856029480119093613769743710050061532020376588252691451260866180293121510320047092727822141164473867037149648467306335820387292808041642440275447680218167244359914165331523654149803989876115624995378063107743975850563832540321335181838796733470)
</pre>

it's crazy how none of these are halting in reasonable amounts of time, even though their odds of doing so are usually 1/2, sometimes 1/3
and also this one is interesting because there's a reasonable chance it becomes a translated cycler. so we now have a TM such that not only do we have no chance of ever calculating when it stops being collatz-like, but we also have no way to know whether it actually halts after that
edit: the probability of becoming a translated cycler is 3/5

[[Category:BB(6)]][[Category:Cryptids]]