Base 72: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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
22 max steps20 → 1Ι → Η3
337 max steps100 → 0ΚΚ → ΙΚ1 → ΘΚ2 → ΗΚ3 → ΖΚ4 → ΕΚ5 → ΔΚ6 → ΓΚ7 → ΒΚ8 → ΑΚ9 → zΚA → yΚB → xΚC → wΚD → vΚE → uΚF → tΚG → sΚH → rΚI → qΚJ → pΚK → oΚL → nΚM → mΚN → lΚO → kΚP → jΚQ → iΚR → hΚS → gΚT → fΚU → eΚV → dΚW → cΚX → bΚY → aΚZ → ZΚa
417 max steps5009 → 94ΕΒ → ΑrHA → qZZK → VΚΚe → eUeW → A7ΒΑ → upJG → eVdW → 96ΓΒ → wrHE → iZZS → FΚΚu → uEuG → gdVU → C7Βy → ulNG → eNlW
532 max steps10000 → 0ΚΚΚΚ → ΙΚΚΚ1 → Ι0ΚΙ2 → ΚΖΚ31 → ΙΖΚ32 → ΘΕΚ43 → ΗΓΚ64 → ΖzΚ95 → ΕvΚD6 → ΔqΚI7 → ΓkΚO8 → ΒdΚV9 → ΑVΚdA → zUΚeB → yUΚeC → xTΚfD → wTΚfE → vSΚgF → uSΚgG → tRΚhH → sRΚhI → rQΚiJ → qQΚiK → pPΚjL → oPΚjM → nOΚkN → mOΚkO → lNΚlP → mLΚnO → oOΚkM → nPΚjN → mNΚlO
6154 max steps7000Zn → nZ6ΓaN → wQ0ΙjE → ΙiIqR2 → ΗYGsb4 → Γc2ΗX8 → Εu4ΕF6 → ΑyeUBA → qn9zMK → qWQidK → WI6Γre → wZ7ΒaE → ui0ΙRG → ΙeGsV2 → Ηc8ΑX4 → Γs4ΕH8 → ΑuaYFA → qf1ΘUK → ΗWAyd4 → Γo6ΓL8 → wuSgFE → ifDvUS → iGAytS → odFtWM → eS6ΓhW → wF7ΒuE → uieURG → eH9zsW → qb7ΒYK → uW2ΗdG → Εe6ΓV6 → yw8ΑDC → smiQNI → aPHrka → aKΚΚoa → pZDvaL → iU0ΙfS → ΙGAyt2 → ΗocWL4 → ΓT5Δg8 → yuCwFC → mkeUPO → OL9zom → qTNlgK → WOCwle → kN7ΒmQ → uPJpkG → eWKodW → U86ΓΒg → wtBxGE → micWRO → OH5Δsm → ybNlYC → mO2ΗlO → ΕOMml6 → yQMmjC → mQIqjO → YOIqlc → YN3Ζmc → ΓP3Ζk8 → ΓuKoF8 → ufTfUG → eCAyxW → ol7ΒOM → uSMmhG → eQEujW → gJ7ΒqU → uXBxcG → me4ΕVO → ΑO8ΑlA → sqMmJI → aXPjca → K4ΚΚΕq → ΖpDvK5 → ΑiUeRA → qH9zsK → qbVdYK → W82ΗΒe → Εt7ΒG6 → yucWFC → mf5ΔUO → yOAylC → omMmNM → SQOkji → MJFtqo → eXRhcW → G84ΕΒu → ΑtdVGA → qd7ΒWK → uW6ΓdG → we6ΓVE → wi8ΑRE → siGsRI → caGsZY → c40ΙΖY → ΙΒ3Ζ82 → ΗΓsG74 → ΓvbXE8 → uh3ΖSG → ΓeEuV8 → ug8ΑTG → seCwVI → ka8ΑZQ → sK0ΙpI → ΙaUeZ2 → ΗA0Ιz4 → ΙΓoK72 → ΗvTfE4 → ΓhBxS8 → umEuNG → geOkVU → MC8Αxo → slRhOI → aNFtma → eOΚΚkW → ld5ΔWP → yM6ΓnC → wmQiNE → iPHrkS → aLFtoa → eSΚΚgW → hd1ΘWT → ΗE6Γv4 → ΓwgSD8 → ujDvQG → ieIqVS → YG8Αtc → sd3ΖWI → Γa6ΓZ8 → wu0ΙFE → ΙieUR2 → ΗH9zs4 → ΓqaYJ8 → uX1ΘcG → Ηe4ΕV4 → ΓΑ8Α98 → usqIHG → ebXbYW → 842ΗΖΓ → ΕΒtF86 → ytdVGC → md7ΒWO → uO6ΓlG → weMmVE → iQ8ΑjS → sJFtqI → eaWcZW → 860ΙΔΓ → ΙxtFC2 → ΗldVO4 → ΓN7Βm8 → vtOkGF → gdLnWU → SC6Γxi → wlFtOE
728 max stepsI00000t → tHΚΚΚrH → ssHΚrHI → sbZΚZYI → rK1ΚΘpJ → ΙoWΚcL2 → ΘnHΚrM3 → ΗqUΚeJ4 → ΖnLΚnM5 → ΕkQΚiP6 → ΔfJΚpU7 → ΓkKΚoP8 → ΒiOΚkR9 → ΑdIΚqWA → ziJΚpRB → ygNΚlTC → xbHΚrYD → wgIΚqTE → veMΚmVF → uZGΚsaG → teIΚqVH → sbKΚoYI → rYFΚtbJ → uaIΚqZG → tcGΚsXH → tcKΚoXH → sZGΚsaI → taIΚqZH → sbGΚsYI