Base 81: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits Max Steps Max Step Example
Cycle Start
11 max steps10
23 max steps10 → 0Τ → Σ1 → Π3
341 max steps100 → 0ΤΤ → ΣΤ1 → ΡΤ2 → ΠΤ3 → ΟΤ4 → ΞΤ5 → ΝΤ6 → ΜΤ7 → ΛΤ8 → ΚΤ9 → ΙΤA → ΘΤB → ΗΤC → ΖΤD → ΕΤE → ΔΤF → ΓΤG → ΒΤH → ΑΤI → zΤJ → yΤK → xΤL → wΤM → vΤN → uΤO → tΤP → sΤQ → rΤR → qΤS → pΤT → oΤU → nΤV → mΤW → lΤX → kΤY → jΤZ → iΤa → hΤb → gΤc → fΤd → eΤe
44 max stepsf000 → eΤΤe → edef → 1ΤΤΣ → Σ0Σ2
535 max stepse0000 → dΤΤΤf → fcΤfe → g0ΤΣd → ΤdΤe1 → ΣeΤd2 → ΡdΤe3 → ΠcΤf4 → ΟcΤf5 → ΞbΤg6 → ΝbΤg7 → ΜaΤh8 → ΛaΤh9 → ΚZΤiA → ΙZΤiB → ΘYΤjC → ΗYΤjD → ΖXΤkE → ΕXΤkF → ΔWΤlG → ΓWΤlH → ΒVΤmI → ΑVΤmJ → zUΤnK → yUΤnL → xTΤoM → wTΤoN → vSΤpO → uSΤpP → tRΤqQ → sRΤqR → rQΤrS → sOΤtR → uRΤqP → tSΤpQ → sQΤrR
6152 max stepsX000ΣΣ → ΣΣWl12 → ΡΠEΔ33 → ΞΝoT66 → ΘΗKxCC → vucfOO → XW2Πmm → ΞGEΔΓ6 → ΘplWTC → vMEΔwO → paWliU → LF7ΛΔy → ΔocfUG → nK2ΠyW → ΞeGΒe6 → ΘkΤΤXC → ΗlMvXD → tZDΕjQ → rT9ΙpS → zPLwtK → fbTohe → L60ΣΝy → ΣΗcfC2 → Πu2ΠO4 → ΞΜVm76 → ΘΕGΒEC → vqkXSO → XOCΖum → tWEΔmQ → pTFΓpU → nMKxwW → daGΒig → l82ΠΛY → ΞΓCΖG6 → ΘtlWPC → vUEΔoO → pXJylU → fLDΕxe → rc0ΣgS → ΣP3Οt2 → ΠΜTo74 → ΜΕKxE8 → ΔqcfSG → nO2ΠuW → ΞWGΒm6 → ΘlFΓXC → vnDΕVO → rXHΑlS → jPDΕta → rU8ΚoS → ΒPJytI → jfToda → L91ΡΚy → ΠΑcfI4 → Μi2Πa8 → ΞΔ7ΛF6 → ΘΔnUFC → voIzUO → hXJylc → fE4ΞΕe → Κq0ΣSA → ΣzNuJ2 → ΠgWlc4 → ΜF3ΟΔ8 → ΜΔnUF8 → ΔoIzUG → nhJybW → fH5ΝΒe → Θk0ΣYC → ΣvBΗN2 → ΠvXkN4 → ΜYCΖk8 → ΔtBΗPG → vnToVO → XLHΑxm → jcEΔga → p93ΟΚU → ΜΑKxI8 → ΔicfaG → n82ΠΛW → ΞΓGΒG6 → ΘmkXWC → vGCΖΓO → tmWlWQ → TGEΔΓq → pmMvWU → ZLFΓxk → ncAΘgW → xH3ΟΒM → ΜkahY8 → ΔC6ΜΗG → ΖumVOE → rWGΒmS → lPFΓtY → nUCΖoW → tKGΒyQ → leSpeY → NCΤΤΖw → Ηv8ΚND → ΒtXkPI → jUCΖoa → tK8ΚyQ → ΒeSpeI → jMΤΤva → wiBΗaN → vZ7ΛjO → ΔX9ΙlG → znDΕVK → rfHΑdS → jP1Ρta → ΠU8Κo4 → ΜΒJyH8 → ΔkedYG → nC0ΣΗW → ΣuGΒO2 → ΠlVmX4 → ΜHDΕΒ8 → ΔrjYRG → nQAΘsW → xSGΒqM → lbNuhY → XD5ΝΖm → ΘsEΔQC → vpRqTO → XPLwtm → bUEΔoi → pK6ΜyU → ΖeKxeE → rcΤΤfS → qgBΗcT → vN3ΟvO → ΜYWlk8 → ΔFBΗΔG → vomVUO → XKGΒym → leEΔeY → pCΤΤΖU → ΗoFΓUD → tnJyVQ → fTHΑpe → jM0Σwa → Σa8Κi2 → ΠΒ7ΛH4 → ΜΔjYF8 → ΔoAΘUG → xnJyVM → fbHΑhe → j60ΣΝa → ΣΗ8ΚC2 → ΠΒtOH4 → ΜkUnY8 → ΔJBΗzG → vnfcVO
744 max steps100005Τ → Τ50ΤΣΞ1 → ΤΣΜΤ611 → ΣΣΛΤ712 → ΣΠΚΤ832 → ΡΟΗΤB43 → ΠΝΓΤF64 → ΟΚwΤL95 → ΞΖnΤUD6 → ΝΑaΤhI7 → ΜuPΤsO8 → ΛnUΤnV9 → ΚgHΤΑcA → ΙsNΤuQB → ΘlTΤoXC → ΗeGΤΒeD → ΖqMΤvSE → ΕjSΤpZF → ΔcFΤΓgG → ΔnPΤsVG → ΓeMΤveH → ΒgGΤΒcI → ΓjOΤtZH → ΒeJΤyeI → ΑiJΤyaJ → zhNΤubK → ycIΤzgL → ΑeLΤweJ → zfHΤΑdK → ΒgLΤwcI → ΑgJΤycJ → zhLΤwbK → yeKΤxeL → ydIΤzfL → ΑeKΤxeJ → zgIΤzcK → ΑfMΤvdJ → zeHΤΑeK → ΒgKΤxcI → ΑhKΤxbJ → zgLΤwcK → yeJΤyeL → zdJΤyfK → zfKΤxdK → yfJΤydL