Base 78: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
241 max steps20 → 1Ο → Ν3Ι7ΑFkVmTIxebΛ5ΕBsNUlGziXuLYhyHgZΓDoRMtWjqPQpOrSnKvafΗ9wJcdΟ1Ν3
341 max steps100 → 0ΠΠ → ΟΠ1 → ΞΠ2 → ΝΠ3 → ΜΠ4 → ΛΠ5 → ΚΠ6 → ΙΠ7 → ΘΠ8 → ΗΠ9 → ΖΠA → ΕΠB → ΔΠC → ΓΠD → ΒΠE → ΑΠF → zΠG → yΠH → xΠI → wΠJ → vΠK → uΠL → tΠM → sΠN → rΠO → qΠP → pΠQ → oΠR → nΠS → mΠT → lΠU → kΠV → jΠW → iΠX → hΠY → gΠZ → fΠa → eΠb → dΠc → cΠdcΠd
419 max stepsA00T → T9Ζn → wJvK → daed → 3ΠΠΝ → Ν2Ν4 → ΛΘ76 → ΕzFCsjVOUDΒmoHxSgLtaY5ΚiΕ9ΖCwrNKcTleI1ΞyΝfZ4Ι5Κ8ΕzFC
537 max steps10000 → 0ΠΠΠΠ → ΟΠΠΠ1 → Ο0ΠΟ2 → ΠΜΠ31 → ΟΜΠ32 → ΞΛΠ43 → ΝΙΠ64 → ΜΖΠ95 → ΛΒΠD6 → ΚwΠI7 → ΙqΠO8 → ΘjΠV9 → ΗbΠdA → ΖUΠkB → ΕaΠeC → ΔTΠlD → ΓZΠfE → ΒSΠmF → ΑYΠgG → zRΠnH → yXΠhI → xQΠoJ → wWΠiK → vPΠpL → uVΠjM → tOΠqN → sUΠkO → rNΠrP → sRΠnO → rQΠoP → qQΠoQ → pPΠpR → qNΠrQ → sQΠoO → rRΠnP → qPΠpQqPΠpQ
6360 max steps5000JΒ → ΒJ4ΛwF → ΗmccTA → wIΠΠwK → xuΠΠKJ → wv2ΝKK → Λcaed6 → Ε40ΟΜC → ΟΘrN82 → ΝzTlG4 → ΙjHxW8 → ΑgCΓZG → qk6ΙVQ → ΓQEΑpE → omOqTS → SMIwto → eXLtic → YB1ΞΕi → Νt9ΖM4 → ΙwWiJ8 → ΑdBΔcG → sk0ΟVO → ΟUEΑl2 → ΝmGyT4 → ΙiIwX8 → ΑeAΕbG → uk2ΝVM → ΛYEΑh6 → Εm8ΗTC → ysIwNI → geUkba → G62ΝΚΑ → ΛΔjVC6 → ΕrDΒOC → soSmRO → UNJvsm → cVHxke → gF1ΞΑa → Νl5ΚU4 → ΙΕGyB8 → ΑthXMG → kX9ΖiW → wEAΕΒK → unbdSM → YL1Ξui → ΝZ9Ζg4 → Ιw6ΙJ8 → ΓΑccFE → okΠΠUS → nl3ΜUT → ΙKGyv8 → ΑiaeXG → kB3ΜΕW → ΙtDΒM8 → ΑoWiRG → kNBΔsW → sVDΒkO → oUEΑlS → mMGytU → iXHxiY → gB9ΖΕa → wt5ΚMK → ΕcWidC → sC0ΟΔO → ΟrTlO2 → ΝTHxm4 → ΙgIwZ8 → Αe6ΙbG → Γk2ΝVE → ΛoEΑR6 → ΕmMsTC → sWIwjO → eUCΓlc → qH1ΞyQ → ΝhPpY4 → ΙQ8Ηp8 → ΑyOqHG → khRnYW → ME8ΗΒu → ynXhSI → gL9Ζua → wZ5ΚgK → Εc6ΙdC → Γs0ΟNE → ΟoUkR2 → ΝNFzs4 → ΙkUkV8 → ΑGEΑzG → mkiWVU → IFBΔΑy → slfZUO → UH5Κym → ΕhHxYC → sg8ΗZO → yU6ΙlI → ΓgGyZE → oi6ΙXS → ΓMAΕtE → uoWiRM → YNBΔsi → sV9ΖkO → wUEΑlK → mcGydU → iI0ΟxY → Οf9Ζa2 → Νw4ΛJ4 → ΙΗcc98 → ΑwΠΠIG → zx3ΜIH → ΙieaX8 → ΑB3ΜΕG → ΙtjVM8 → ΑXDΒiG → okAΕVS → uMEΑtM → mYWihU → IC8ΗΔy → yrfZOI → gT5Κma → ΕJ5ΚwC → ΕsccNC → sUΠΠkO → rl7ΘUP → ΑSGynG → kiKuXW → aEAΕΒg → un5ΚSM → ΕYKuhC → sa8ΗfO → yU4ΛlI → ΗgGyZA → wi6ΙXK → ΓcAΕdE → uo0ΟRM → ΟYMsh2 → ΝW8Ηj4 → ΙyCΓH8 → ΑqgYPG → kR7ΘoW → ΑNDΒsG → okUkVS → MGEΑzu → mjXhWU → ID9ΖΓy → wpfZQK → cP5Κqe → ΕR1ΞoC → ΝsMsN4 → ΙWUkj8 → ΑGCΓzG → qkiWVQ → QFBΔΑq → slPpUO → UQGypm → iPHxqY → gR9Ζoa → wN5ΚsK → ΕcUkdC → sG0ΟzO → ΟjTlW2 → ΝICΓx4 → ΙqeaP8 → ΑR3ΜoG → ΙkMsV8 → ΑWEΑjG → mkCΓVU → qIEΑxQ → mfPpaU → QI4Λxq → ΗfPpaA → wQ4ΛpK → ΗcOqdA → wS0ΟnK → ΟcKud2 → Νa0Οf4 → ΟΙ4Λ72 → ΝΗΑE94 → ΙxlTI8 → ΑfHxaG → kg4ΛZW → ΗE6ΙΒA → ΓwmSJE → odJvcS → cM0Οte → ΟX1Ξi2 → ΞΜAΕ43 → ΛΘtL86 → ΕzXhGC → sj9ΖWO → wUCΓlK → qcGydQ → iQ0ΟpY → ΟP9Ζq2 → ΝwQoJ4 → ΙdNrc8 → ΑU0ΟlG → ΟkGyV2 → ΝiEΑX4 → ΙmAΕT8 → ΑuIwLG → keYgbW → E82ΝΘΓ → ΛznRG6 → ΕjLtWC → sYCΓhO → qU8ΗlQ → yQGypI → igOqZY → SA6ΙΖo → ΓvLtKE → obXheS → MA2ΝΖu → ΛvXhK6 → Εb9ΖeC → ws2ΝNK → ΛcUkd6 → ΕG0ΟzC → ΟsiWN2 → ΝVBΔk4 → ΙsEΑN8 → ΑmUkTG → kJFzwW → kdDΒcW → oE0ΟΒS → ΟnLtS2 → ΝYKuh4 → Ιa8Ηf8 → Αy4ΛHG → ΗkgYVA → wF7ΘΑK → ΑlbdUG → kH1ΞyW → ΝhDΒY4 → Ιo8ΗR8 → ΑyMsHG → khVjYW → FD8ΗΓΒ → yplTQI → gPHxqa → gR5Κoa → ΕN5ΚsC → ΕsUkNC → sVFzkO → kUEΑlW → mHDΒyU → ohHxYS → gM8Ηta → yX5ΚiI → ΕgAΕZC → us6ΙNM → ΓYUkhE → oG8ΗzS → yjLtWI → gYCΓha → q95ΚΗQ → ΕxPpIC → sfPpaO → UQ4Λpm → ΗPHxqA → wgQoZK → cO6Ιre → ΓT1ΞmE → ΝoIwR4 → ΙeMsb8 → ΑW2ΝjG → ΛkCΓV6 → ΕqEΑPC → smQoTO → UOIwrm → eTHxmc → gJ1Ξwa → Νd5Κc4 → ΙΕ0ΟB8 → ΟΑsMF2 → ΝlVjU4 → ΙHDΒy8 → ΑogYRG → kN7ΘsW → ΑVDΒkG → okEΑVS → mMEΑtU → mXHxiU → gIAΕxa → uf5ΚaM → ΕY4ΛhC → Ηs8ΗNA → ywUkJI → gdFzca → k60ΟΚW → ΟΔDΒC2 → ΝrnRO4 → ΙTLtm8 → ΑYIwhG → ke8ΗbW → yE2ΝΒI → ΛnfZS6 → ΕL5ΚuC → ΕsYgNC → sV7ΘkO → ΑUEΑlG → mkGyVU → iIEΑxY → mf9ΖaU → wI4ΛxK → ΗfbdaA → w51ΞΛK → ΝΖbdA4 → Ιv1ΞK8 → ΝΑaeF4 → Ιl3ΜU8 → ΙΑGyF8 → ΑlhXUG → kH9ΖyWwhDΒYKoc8ΗdSyM0ΟtIΟgWiZ2ΝC6ΙΔ4ΙΓqOD8ΑpRnQGkPLtqWYRDΒoioN9ΖsSwVLtkKcYEΑhem91ΞΗUΝxHxI4ΙgeaZ8Α73ΜΙGΙΒjVE8ΑnDΒSGokKuVSaMEΑtgmX5ΚiUΕIAΕxCuseaNMYV3ΜkiΙF9ΖΑ8ΑwkUJGkdFzcWkE0ΟΒWΟnDΒS2ΝoKuR4ΙaMsf8ΑW4ΛjGΗkCΓVAwqEΑPKmcQodUOI0ΟxsΟfTla2ΝI4Λx4ΙΗea98Αx3ΜIGΙkeaV8ΑF3ΜΑGΙljVU8ΑHDΒyGokgYVSMF7ΘΑuΑlXhUGkH9ΖyW
740 max steps1000000 → 0ΠΠΠΠΠΠ → ΟΠΠΠΠΠ1 → Ο0ΠΠΠΟ2 → ΠΞ0ΠΟ21 → ΠΟΜΠ311 → ΟΟΛΠ412 → ΟΝΚΠ532 → ΞΜΗΠ843 → ΝΚΓΠC64 → ΜΗwΠI95 → ΛΓnΠRD6 → ΚxaΠeI7 → ΙrMΠsO8 → ΘmTΠlT9 → ΗeIΠwbA → ΖoKΠuRB → ΕlSΠmUC → ΔcHΠxdD → ΓmKΠuTE → ΒiQΠoXF → ΑbGΠyeG → zkMΠsVH → ydMΠscI → xcFΠzdJ → ΑgKΠuZG → zgKΠuZH → yfKΠuaI → xeJΠvbJ → weJΠvbK → wcJΠvdK → wcIΠwdK → xcJΠvdJ → weIΠwbK → xcKΠudJ → wdHΠxcK → ydJΠvcIxfIΠwaJxeLΠtbJwcHΠxdKydJΠvcI