Base 93: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
226 max steps10 → 0η → ζ1 → δ3Ω7ΠFzVXxfpΜJrdΔRbtvZnhΥBΘNjlδ3
349 max steps100 → 0ηη → ζη1 → εη2 → δη3 → γη4 → βη5 → αη6 → Ωη7 → Ψη8 → Χη9 → ΦηA → ΥηB → ΤηC → ΣηD → ΡηE → ΠηF → ΟηG → ΞηH → ΝηI → ΜηJ → ΛηK → ΚηL → ΙηM → ΘηN → ΗηO → ΖηP → ΕηQ → ΔηR → ΓηS → ΒηT → ΑηU → zηV → yηW → xηX → wηY → vηZ → uηa → tηb → sηc → rηd → qηe → pηf → oηg → nηh → mηi → lηj → kηkjηlkηk
414 max stepsl000 → kηηk → kjkl → 1ηηζ → ζ0ζ2ζγ32δΨ74ΩΟF8ΠyVGzSΒWZSΒwZMΘwlMΘkl0ζkζ0ζ2
540 max stepsk0000 → jηηηl → liηlk → m0ηζj → ηjηk1 → ζkηj2 → εjηk3 → δiηl4 → γiηl5 → βhηm6 → αhηm7 → Ωgηn8 → Ψgηn9 → ΧfηoA → ΦfηoB → ΥeηpC → ΤeηpD → ΣdηqE → ΡdηqF → ΠcηrG → ΟcηrH → ΞbηsI → ΝbηsJ → ΜaηtK → ΛaηtL → ΚZηuM → ΙZηuN → ΘYηvO → ΗYηvP → ΖXηwQ → ΕXηwR → ΔWηxS → ΓWηxT → ΒVηyU → ΑVηyV → zUηzW → ΑSηΒV → ΓVηyT → ΒWηxU → ΑUηzVΑUηzV
6272 max stepsF000HN → NHEΠΞΙ → ΒwkjYU → XO0ζΗy → ζiQΔm2 → δd3γr4 → αΨDΡ87 → ΣΟΓRGE → ΔyatWS → bSIΜΓu → taIΜuc → tKGΞΛc → xqGΞeY → xPBΤΖY → ΘgOΖoO → jh7Ψnm → Π62δαG → βΤyVC6 → ΥΗSΒOC → ΘiYvmO → jN3γΘm → Ωk2δk8 → βΟηηF6 → αΠAΥF7 → ΣΚzULE → ΔoUzgS → bV7Ψzu → ΠUIΜΑG → ztVybW → USHΝΓΒ → vaWxua → RLJΛΚΕ → rocrge → FD7ΨΣΡ → ΠΕΑTQG → zeWxqW → TRBΤΔΓ → ΘcYvsO → jNFΟΘm → zk2δkW → βSηηΒ6 → αΓNΗS7 → ΣjZulE → ΔL1εΚS → δoatg4 → ΩJ7ΨΜ8 → ΡΟrcGF → ΒyEΠWU → ΒXRΓxU → bXPΕxu → fQIΜΕq → teAΥqc → ΚHBΤΞM → ΘwmhYO → jO4βΗm → Χi2δmA → βΜ3γJ6 → ΩΥrcB8 → ΠΙEΠMG → ΒzliVU → XU2δΑy → βWQΔy6 → ΥdRΓrC → ΘbDΡtO → ΔjHΝlS → vb1εta → δLHΝΚ4 → ΩvngZ8 → ΠM6ΩΙG → ΣzliVE → ΔU2δΑS → βbVyt6 → ΥTHΝΒC → ΘvXwZO → jPLΙΖm → ng2δoi → β84βΨ6 → ΧΥΞGBA → ΜΙwXMK → rmOΖie → hD3γΣo → ΩΕ6ΩQ8 → ΣΠdqFE → ΔΑCΣUS → ΖbVytQ → fTHΝΒq → vYAΥwa → ΚOKΚΗM → pnhmhg → 964βαΨ → ΧΤΝHCA → ΜΗuZOK → riKΚme → pD3γΣg → ΩΕ8ΧQ8 → ΠΞdqHG → zwCΣYW → ΖTNΗΒQ → jfXwpm → PA2δΦΗ → βΛgnK6 → Υq6ΩeC → ΣΘBΤNE → ΘΔjkRO → jc0ζsm → ζG2δΟ2 → δβxW54 → ΩΦQΔA8 → ΠΛcrKG → zqEΠeW → ΒTBΤΒU → ΘYWxwO → jRNΗΔm → jc2δsm → βG2δΟ6 → βΥxWB6 → ΥΙQΔMC → ΘmcriO → jF3γΠm → ΩΑ2δU8 → βΠVyF6 → ΥΑSΒUC → ΘZVyvO → jTLΙΒm → nY2δwi → βO4βΗ6 → ΧΥhmBA → ΜΙ4βMK → ΧrlidA → ΜE2δΡK → βΓqdS6 → ΥaCΣuC → ΘΖJΛPO → rjfole → D91εΧΤ → δΝΕPI4 → Ωuepa8 → ΠKAΥΛG → ΚzpeVM → nUAΥΑi → ΚW4βyM → ΧnRΓhA → Μb5αtK → ΥrHΝdC → ΘvDΡZO → ΔjLΙlS → nb1εti → δI4βΝ4 → ΩΧta98 → ΠΝIΜIG → zusbaW → TKGΞΛΓ → xqYveY → PNBΤΘΗ → ΘkgnkO → j6ηηΩm → αlatj7 → ΣJ1εΜE → δΔrcR4 → ΩcEΠs8 → ΠΒFΟTG → ΑyXwWV → VSOΖΓΑ → haUzuo → VK6ΩΛΑ → ΣqUzeE → ΔVBΤzS → ΘbTΑtO → jXHΝxm → vQ2δΕa → βeKΚq6 → ΥpBΤfC → ΙΗ9ΦON → ΜlhmjK → r51εβe → δΦCΣA4 → ΩΛΕPK8 → ΠqepeG → zCAΥΤW → ΚΗSΒOM → niYvmi → N53γβΙ → ΩΦkjA8 → ΠΛ0ζKG → ζzpeV2 → δUAΥΑ4 → ΩΚVyL8 → ΠoSΒgG → zZ7ΨvW → ΠTLΙΒG → znXwhW → TP5αΖΓ → ΥgYvoC → ΘN7ΨΘO → ΠkilkG → z2ηηδW → εyRΓW3 → βbRΓt6 → ΥbHΝtC → ΘvHΝZO → vjLΙla → nL1εΚi → δo4βg4 → ΩΧ7Ψ98 → ΡΟΜIGF → ΒysbWU → XSGΞΓy → xaQΔuY → dPJΛΖs → rgEΠoe → ΒD7ΨΣU → ΠΕWxQG → zeQΔqW → dTBΤΒs → ΘYEΠwO → ΒjNΗlU → jX1εxm → δQ2δΕ4 → βΩdq76 → ΥΡCΣEC → ΘΖΒSPO → jgYvom → N82δΨΙ → βΟkjG6 → Υy0ζWC → ζΘRΓN2 → δkatk4 → ΩIηηΜ8 → ΨΝBΤI9 → ΞΘtaNI → vkIΜka → tKηηΚc → ΛsFΟcL → zpFΟfW → zT9ΦΒW → ΜYSΒwK → rZNΗve → jMCΣΙm → Ζm2δiQ → βf3γp6 → ΩΥ9ΦB8 → ΠΜΘMJG → zskjcW → TG0ζΟΓ → ζyYvW2 → δSMΘΓ4 → ΩlZuj8 → ΠL1εΚG → δzngV4 → ΩU6ΩΑ8 → ΣΠVyFEΔΑSΒUSbZVyvuTMIΜΙΓtmYvicNH3γΞΙΩwkjY8ΠO0ζΗGζzhmV2δU4βΑ4ΩΧVy98ΠΝSΒIGzuYvaWTNJΛΘΓrkYvkeNCηηΣΙΤΘ8ΧNDΞΖjkPIvg0ζoaζL7ΨΚ2δΠngF4ΩΑ6ΩU8ΣΠVyFE
748 max stepsk00000v → vjηηηka → uljηkjb → tB1ηεΥc → ζΣgηnD2 → εΡaηtE3 → δΟfηoG4 → γΜYηvJ5 → βΘcηrN6 → αΓUηzS7 → ΩwXηwY8 → ΨqNηΗe9 → ΧzRηΓVA → ΦuWηxaB → ΥoMηΘgC → ΤxQηΔXD → ΣsVηycE → ΡmLηΙiF → ΠvPηΕZG → ΟqUηzeH → ΞkKηΚkI → ΝtOηΖbJ → ΜoTηΑgK → ΛiJηΛmL → ΜpRηΓfK → ΛkMηΘkL → ΚoMηΘgM → ΙnQηΔhN → ΘiLηΙmO → ΚkOηΖkM → ΙlKηΚjN → ΛmOηΖiL → ΚmMηΘiM → ΙnOηΖhN → ΘkNηΗkO → ΘjLηΙlO → ΚkNηΗkM → ΙmLηΙiN → ΚlPηΕjM → ΙkKηΚkN → ΛmNηΗiL → ΚnNηΗhM → ΙmOηΖiN → ΘkMηΘkO → ΙjMηΘlN → ΙlNηΗjN → ΘlMηΘjOΙjNηΗlNΘlMηΘjO