Base 67: 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
24 max steps10 → 0Ε → Δ1 → Β3 → x7
334 max steps100 → 0ΕΕ → ΔΕ1 → ΓΕ2 → ΒΕ3 → ΑΕ4 → zΕ5 → yΕ6 → xΕ7 → wΕ8 → vΕ9 → uΕA → tΕB → sΕC → rΕD → qΕE → pΕF → oΕG → nΕH → mΕI → lΕJ → kΕK → jΕL → iΕM → hΕN → gΕO → fΕP → eΕQ → dΕR → cΕS → bΕT → aΕU → ZΕV → YΕW → XΕX
44 max stepsY000 → XΕΕX → XWXY → 1ΕΕΔ → Δ0Δ2
528 max steps30000 → 2ΕΕΕΓ → Γ1ΕΓ3 → ΔyΕ52 → ΓxΕ63 → ΒvΕ84 → ΑsΕB5 → zoΕF6 → yjΕK7 → xdΕQ8 → wWΕX9 → vPΕeA → uVΕYB → tOΕfC → sUΕZD → rNΕgE → qTΕaF → pMΕhG → oSΕbH → nLΕiI → mRΕcJ → lKΕjK → kQΕdL → jJΕkM → lNΕgK → kNΕgL → jMΕhM → iMΕhN → iKΕjN
692 max stepsK000mm → mmJkIJ → UTQdbb → D86xws → roePGE → dYEpWS → bB1ΓtU → Βi6xM4 → xrLiD8 → peMhQG → ZLDqjW → dO2ΒgS → zIAtm6 → tjTaLC → hO6xgO → rJHmlE → dVRcZS → CA3Αut → xkgNK8 → pQIleG → ZTDqbW → d82ΒwS → zoAtG6 → tjXWLC → hO0ΔgO → ΔJHml2 → ΒVRcZ4 → xB3Αt8 → xphMF8 → paKjUG → ZP5yfW → tG2ΒoC → zhXWN6 → tK0ΔkC → ΔhPeN2 → ΒKEpk4 → xbPeT8 → pF7wpG → paYVUG → Z62ΒyW → zs2ΒC6 → ztfOB6 → tiGnMC → hXLiXO → NIΕΕli → mh2ΒNJ → zTJkb6 → tR7wdC → phBsNG → hZJkVO → RJ3Αle → xSCrc8 → pf9uPG → lZFoVK → ZR3ΑdW → xC2Βs8 → zpfOF6 → taGnUC → hX5yXO → tIΕΕlC → sm7wID → pfTaPG → ZG6xoW → rY2ΒWE → zd1ΓR6 → ΒtBsB4 → xigNM8 → pMIliG → ZTLibW → N82Βwi → zoKjG6 → tYOfWC → hH1ΓnO → ΒWIlY4 → xT1Γb8 → Βp7wF4 → xpZUF8 → pa4zUG → vZ5yVA → tl3ΑJC → xhRcN8 → pKAtkG → jZPeVM → NF3Αpi → xaKjU8 → pP5yfG → tZFoVC → hZ3ΑVO → xJ3Αl8 → xpRcF8 → paAtUG → jZ5yVM → tN3ΑhC
742 max stepsP00000X → XOΕΕΕfY → gXVΕYXP → fB0ΕΔtQ → ΕsSΕbC1 → ΔsPΕeC2 → ΓrSΕbD3 → ΒpOΕfF4 → ΑmQΕdI5 → ziLΕiM6 → yeLΕiQ7 → xdHΕmR8 → wgKΕjO9 → vcKΕjSA → ubGΕnTB → teJΕkQC → saJΕkUD → rZFΕoVE → qcIΕlSF → pYIΕlWG → oXEΕpXH → qYGΕnWF → paGΕnUG → oZIΕlVH → nWFΕoYI → pWGΕnYG → oZGΕnVH → oXHΕmXH → nXEΕpXI → qXFΕoXF → pbGΕnTG → oZJΕkVH → nVEΕpZI → qXHΕmXF → pZEΕpVG → qZJΕkVF → pXEΕpXG → qZHΕmVF → pZGΕnVG → oZHΕmVH → nXGΕnXI → oVFΕoZH → pXIΕlXG
8199 max steps10000EGΕ → ΕGE0Δqo1 → ΕΓcXWS21 → ΔΑA0Δu42 → ΔΒwjK832 → ΒyoOfG64 → xsYGnWC8 → pgX1ΓXOG → ΒZHΕΕmV4 → ΑnWCrYH5 → vfW1ΓYPA → ΒlG1ΓoJ4 → ΒxYRcW74 → xqB1ΓtE8 → ΒpibSMF4 → xaM8viU8 → pnM5yiHG → tZWLiYVC → hN41ΓΑhO → ΒwKIlk84 → xoTPebG8 → pYF7wpWG → paZ1ΓVUG → ΒZ63ΑyV4 → yws3ΑC87 → xrofOGD8 → peYGnWQG → ZXE1ΓqXW → Βc2ΕΕΒS4 → ΓΑZOfV43 → zwH3Αn86 → xtoVYGB8 → piY2ΒWMG → zZM1ΓiV6 → ΒtM3ΑiB4 → ywiLiM87 → roNLihGE → dYNJkhWS → RKB1Γtke → ΒiQCreM4 → xfMDqiP8 → pdMFoiRG → aYMBsiWV → hM51ΓziO → ΒuMIliA4 → xkTLibK8 → pQN7wheG → pZKDqkVG → dZQ3ΑeVS → xEB3Αtq8 → xpibSMF8 → paM8viUG → nZM5yiVI → tVM3ΑiZC → xhM3ΑiN8 → xpMJkiF8 → paRLidUG → ZNC5yshW → tgK2ΒkOC → zhQHmeN6 → tVKDqkZC → hdQ3ΑeRO → xJEBsql8 → phcRcSNG → ZKB9utkW → liQ2ΒeMK → zRMDqid6 → tdMBsiRC → igMBsiON → hMLHmjiO → VOMIliga → TMI4zmic → vUM8viaA → nlM5yiJI → tVSLicZC → hNA3ΑuhO → xkKIlkK8 → pTQPeebG → ZFE7wqpW → pca2ΒUSG → zZA5yuV6 → usk3ΑKCB → xjgPeOL8 → pOIEpmgG → bZUHmaVU → V763Αyxa → xsq4zEC8 → vpgbSOFA → laI8vmUK → nUR5ydaI → tVC5ysZC → thg3ΑONC → xhKHmkN8 → pVQJkeZG → ZRE3ΑqdW → xcC2ΒsS8 → zpg9uOF6 → tlaHmUJC → hVS5ycZO → tJA3ΑulC → xkhRcNK8 → pQKAtkeG → jZQDqeVM → dNE3ΑqhS → xcKAtkS8 → pjQ9ueLG → lZODqgVK → dRI3ΑmdS → xUCAtsa8 → pjg5yOLG → tZOHmgVC → hVI3ΑmZO → xUJ3Αla8 → xpS5ycF8 → tpa9uUFC → lha5yUNK → tRK5ykdC → thQBseNC → igKDqkON → dQLHmjeS → VOEAtqga → jcI4zmSM → vUN9uhaA → mkK5ykKJ → tTQPeebC → hFE7wqpO → pcaIlUSG → ZTA5yubW → tk82ΒwKC → zohPeNG6 → tYKEpkWC → hbQ1ΓeTO → ΒJE7wql4 → xpcRcSF8 → paB9utUG → liZ5yVMK → tRM3ΑidC → xhMBsiN8 → phMJkiNG → ZRMJkidW → RMC2Βsie → zgMCriO6 → tfMHmiPC → hVMFoiZO → ZMJ3ΑliW → xSM2Βic8 → zpM9uiF6 → tlaLiUJC → hSN5yhcO → tKJ9ulkC → lhSPecNK → RKF9upke → laQCreUK → fRE5yqdQ → tcFBspSC → iga9uUON → lLI5ymjK → tURNgdaC → hJC5yslO → tgSIlcOC → hTI9umbO → lUJ7wlaK → pSR5ydcG → tZC9usVC → lhg3ΑONK → xRKHmkd8 → pVQBseZG → hZE3ΑqVO → xcJ3ΑlS8 → xpS9ucF8 → pla9uUJG → lZS5ycVK → tRA3ΑudC → xkhBsNK8 → phQJkeNG → ZRKDqkdW → dQC2ΒseS → zgEAtqO6 → tjcHmSLC → hVO9ugZO → lJI3ΑmlK → xUSQdca8 → pDA5yurG → tkeYVQKC → hQE2ΒqeO → zcJDqlS6 → tdS9ucRC → lhC9usNK → lgRJkdOK → SQIBsmed → hUEAtqaO → jcJ5ylSM → tSN9uhcC → lhK9ukNK → lRQJkedK → SQEBsqed → hcEAtqSO → jcJ9ulSM → lSN9uhcK → lRK9ukdK