Base 83: 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
210 max steps10 → 0Φ → Υ1 → Σ3 → Ξ7ΖFpVhdΞ7
344 max steps100 → 0ΦΦ → ΥΦ1 → ΤΦ2 → ΣΦ3 → ΡΦ4 → ΠΦ5 → ΟΦ6 → ΞΦ7 → ΝΦ8 → ΜΦ9 → ΛΦA → ΚΦB → ΙΦC → ΘΦD → ΗΦE → ΖΦF → ΕΦG → ΔΦH → ΓΦI → ΒΦJ → ΑΦK → zΦL → yΦM → xΦN → wΦO → vΦP → uΦQ → tΦR → sΦS → rΦT → qΦU → pΦV → oΦW → nΦX → mΦY → lΦZ → kΦa → jΦb → iΦc → hΦd → gΦe → fΦfeΦgfΦf
445 max stepsg000 → fΦΦf → fefg → 1ΦΦΥ → Υ0Υ2ΥΡ32ΣΝ74ΞΕF8ΖoVGpIΒWjIΒcj6ΞcΘ6ΞEΘsREtQtSTQtsTOvsXOvoXGΔonGΔYnEΖYrEΖUrMxUbMxkb8ΜkΔ8ΜIΔkZIlAΚazAΚMzchMd4ΠiΜ4ΠAΜΑJAΒgdKh2ΣeΠ2Σ6ΠΙB6ΚwNCxYlOZCΘmvCΘQvUpQVKzqfKzgf0ΥgΥ0Υ2
537 max stepse0000 → dΦΦΦh → hcΦhe → i2ΦΣd → ΤdΦg3 → ΣeΦf4 → ΡcΦh5 → ΠdΦg6 → ΟbΦi7 → ΞcΦh8 → ΝaΦj9 → ΜbΦiA → ΛZΦkB → ΚaΦjC → ΙYΦlD → ΘZΦkE → ΗXΦmF → ΖYΦlG → ΕWΦnH → ΔXΦmI → ΓVΦoJ → ΒWΦnK → ΑUΦpL → zVΦoM → yTΦqN → xUΦpO → wSΦrP → vTΦqQ → uRΦsR → tSΦrS → sQΦtT → uPΦuR → vSΦrQ → uSΦrRtRΦsStQΦtSuQΦtRuSΦrR
6330 max steps6000II → II5ΟΓΔ → ΚljaZC → xC8ΜΙO → ΔwYlOI → lYCΘma → vEAΚΗQ → zsUpSM → dQKzui → fU4Πqg → ΜM0ΥyA → ΥΒbiJ2 → Σi6Ξc4 → ΞΘ5ΟD8 → ΚΖtQFC → xqSrUO → ZPLyvm → dWCΘoi → vI4ΠΓQ → ΜkUpaA → ΒL9ΛzK → ΒhdgdK → h42ΣΡe → ΠΝ2Σ86 → ΠΚΔGB6 → ΚymXMC → xcEΖiO → rZ5ΟlU → ΚNBΙxC → ywZkON → bYAΚmk → zE8ΜΗM → ΔschSI → lQ4Πua → ΜUAΚqA → ΒzLyLK → hechge → 531ΤΣΡ → ΣΟΛ964 → ΞΙΑJC8 → ΖwgdOG → pY2ΣmW → ΠJDΗΒ6 → ΚthcRC → xS4ΠsO → ΜZPulA → ΒVBΙpK → xhJΑdO → hZ3Ρle → ΞC2ΣΙ8 → ΠΖvOF6 → ΚqWnUC → xMGΔyO → ncYliY → FD5ΟΘΗ → ΚuqTQC → xUMxqO → bZLylk → dC8ΜΙi → Δw4ΠOI → ΜlXmZA → ΒFBΙΖK → xqgdUO → ZM2Σym → ΠcCΘi6 → Κv5ΟPC → ΚxVoNC → xaIΒkO → jZ9Λlc → ΒC6ΞΙK → ΘwgdOE → tY2ΣmS → ΠRDΗt6 → ΚtRsRC → xSQtsO → ZTPurm → VOCΘwq → vYKzmQ → fVDΗpg → tK0ΥΑS → ΥgQte2 → ΣT1Τr4 → ΣΞNw74 → ΞΗYlE8 → ΖsCΘSG → vpPuVQ → WUJΑqp → hMIΒye → jc2Σic → Π75ΟΞ6 → ΛΙΖECB → zwqTOM → dYMxmi → bE4ΠΗk → Μs8ΜSA → ΔΒPuJI → liUpca → LB5ΟΚΑ → ΚyefMC → xc0ΥiO → ΥZ5Οl2 → ΣΚBΙB4 → ΞywNM8 → ΖcYliG → pD5ΟΘW → ΚuIΒQC → xjTqbO → ZN7Νxm → ΖaCΘkG → vp9ΛVQ → ΒVJΑpK → igJΑed → h51ΤΠe → ΣΛ2ΣA4 → ΠΞzK76 → ΚΗefEC → xs0ΥSO → ΥZPul2 → ΣVBΙp4 → ΞxJΑN8 → ΖhZkdG → pB3ΡΚW → ΞyIΒM8 → ΖjbibG → p86ΞΝW → ΘΕIΒGE → toibWS → RI6ΞΓu → ΘkSraE → tP9ΛvS → ΒWQtoK → hTHΓre → lO2Σwa → ΠYAΚm6 → ΚzDΗLC → xtdgRO → ZS2Σsm → ΠQCΘu6 → ΚvTqPC → xWMxoO → bZHΓlk → lC8ΜΙa → ΔwAΚOI → zlXmZM → dFBΙΖi → xq4ΠUO → ΜZLylA → ΒdBΙhK → xh3ΡdO → ΞZ3Ρl8 → ΞΖBΙF8 → ΖxpUNG → paKzkW → fJ9ΛΒg → Βi0ΥcK → Υh5Οd2 → ΣΚ3ΡB4 → ΟΝxM87 → ΘΕajGE → to8ΜWS → ΔRHΓtI → mkRsaZ → RD9ΛΘu → ΒuSrQK → hUOvqe → XM2Σyo → ΠcGΔi6 → Κn5ΟXC → ΚxFΕNC → xpZkVO → ZKAΚΑm → zgCΘeM → vd1ΤhQ → ΣV3Ρp4 → ΟΝJΑ87 → ΘΕgdGE → to2ΣWS → ΠRHΓt6 → ΚlRsZC → xRBΙtO → xZRslO → ZRBΙtm → xSCΘsO → vZPulQ → WUBΙqp → xMIΒyO → jcYlic → D75ΟΞΙ → ΚΗuPEC → xsUpSO → ZQKzum → fUCΘqg → vM0ΥyQ → ΥcUpi2 → ΣL5Οz4 → ΞΚdgB8 → Ζy2ΣMG → ΠpbiV6 → ΚK6ΞΑC → ΘxfeNE → ta0ΥkS → ΥR9Λt2 → ΣΒRsJ4 → ΞiQtc8 → ΖT5ΟrG → ΚpNwVC → xZJΑlO → hZBΙle → xC2ΣΙO → ΠwYlO6 → ΚYCΘmC → xvDΗPO → tZVolS → RJBΙΒu → xiSrcO → ZP5Οvm → ΚWCΘoC → xvHΓPO → lZVola → JCAΚΙΓ → zwibOM → dY6Ξmi → ΘE4ΠΗE → ΜtrSRA → ΒSOvsK → hXPune → VG2ΣΕq → ΠoKzW6 → ΚfHΓfC → xkΦΦZO → wlCΘZP → vXBΙnQ → xVFΕpO → pZJΑlW → hJBΙΒe → xi2ΣcO → ΠZ5Οl6 → ΛΙBΙCB → zxvONM → daWnki → HA4ΠΛΕ → ΜΑmXKA → ΒgEΖeK → rh1ΤdU → ΣN3Ρx4 → ΟΝZk87 → ΘΕAΚGE → ztnWRM → dSGΔsi → nQ4ΠuY → ΜUEΖqA → ΒrLyTK → hdNwhe → Z42ΣΡm → ΠΝCΘ86 → ΚΕuPGC → xoUpWO → ZLHΓzm → leCΘga → vB1ΤΚQ → ΣyUpM4 → ΞcKzi8 → Ζf5ΟfG → ΚoΦΦVC → ΙpKzVD → vfJΑfQ → hUΦΦpe → qg7ΝeV → ΖL1ΤzG → ΣpdgV4 → ΞK2ΣΑ8 → ΠΖfeF6 → Κq0ΥUC → ΥxLyN2 → ΣdZkh4 → ΞB3ΡΚ8 → ΞΖxMF8 → ΖqajUG → pM8ΜyW → ΔcIΒiI → lj5Οba → ΚB7ΝΚC → ΖywNMG → pcYliW → JD5ΟΘΓ → ΚuibQC → xU6ΞqO → ΘZLylE → tdBΙhS → xR3ΡtO → ΞZRsl8 → ΖRBΙtG → xpRsVO → ZRJΑtm → hSCΘse → vQ2ΣuQ → ΠVTqp6 → ΚNJΑxC → xhZkdO → ZB3ΡΚm → ΞyCΘM8 → ΖvbiPG → pW6ΞoW → ΘJHΓΒE → tlhcZS → RC4ΠΙu → ΜwSrOA → ΒYOvmK → hXDΗne → tG2ΣΕS → ΠoQtW6 → ΚTHΓrC → xlNwZO → aYBΙml → xEAΚΗO → zsYlSM → dQCΘui → vU4ΠqQ → ΜVLypA → ΒdJΑhKig3ΡedΞ51ΤΠ8ΣΛΕFA4ΞΑoVK8ΖgIΒeGpj1ΤbWΣJ7ΝΒ4ΞΖhcF8Ζq4ΠUGΜpLyVAΒdJΑhK
754 max steps700000Φ → Φ6ΦΦΦΞ1 → ΥΟ6ΦΞ62 → ΤΞΘΦC73 → ΣΜΑΦJ94 → ΡΙrΦSC5 → ΠΕfΦeG6 → ΟzPΦuL7 → ΞtZΦkR8 → ΝmJΦΑY9 → ΜtRΦsRA → ΛkRΦsaB → ΚjHΦΓbC → ΙsQΦtSD → ΘiQΦtcE → ΗhGΦΔdF → ΖqPΦuUG → ΕgPΦueH → ΔfFΦΕfI → ΖmNΦwYG → ΕiNΦwcH → ΔhJΦΑdI → ΓkMΦxaJ → ΒgMΦxeK → ΑfIΦΒfL → ΓgKΦzeJ → ΒiKΦzcK → ΑhMΦxdL → zeJΦΑgM → ΒeKΦzgK → ΑhKΦzdL → ΑfLΦyfL → zfIΦΒfM → ΓfJΦΑfJ → ΒjKΦzbK → ΑhNΦwdL → zdIΦΒhM → ΓfLΦyfJ → ΒhIΦΒdK → ΓhNΦwdJ → ΒfIΦΒfK → ΓhLΦydJ → ΒhKΦzdK → ΑhLΦydL → zfKΦzfM → ΑdJΦΑhL → ΒfMΦxfKΑfHΦΓfLΔhKΦzdIΓjLΦybJΒhMΦxdKΑfJΦΑfLΒfKΦzfKΑhJΦΑdLΒfMΦxfK