Base 66: 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 → 1Γ → Α3
334 max steps100 → 0ΔΔ → ΓΔ1 → ΒΔ2 → ΑΔ3 → zΔ4 → yΔ5 → xΔ6 → wΔ7 → vΔ8 → uΔ9 → tΔA → sΔB → rΔC → qΔD → pΔE → oΔF → nΔG → mΔH → lΔI → kΔJ → jΔK → iΔL → hΔM → gΔN → fΔO → eΔP → dΔQ → cΔR → bΔS → aΔT → ZΔU → YΔV → XΔW → WΔX
47 max steps800P → P7vf → oFnG → ZWWV → 3ΔΔΑ → Α2Α4 → yv76 → snFC
530 max steps1000A → A0ΔΓu → ΔrΔB1 → ΓrΔB2 → ΒqΔC3 → ΑoΔE4 → zlΔH5 → yhΔL6 → xcΔQ7 → wWΔW8 → vPΔd9 → uVΔXA → tOΔeB → sUΔYC → rNΔfD → qTΔZE → pMΔgF → oSΔaG → nLΔhH → mRΔbI → lKΔiJ → kQΔcK → jJΔjL → kNΔfK → jMΔgL → iMΔgM → hLΔhN → iJΔjM → kMΔgK → jNΔfL → iLΔhM
6172 max steps90000T → T8ΔΔub → vaIkT9 → mS6wbI → qU8uZE → mc4yRI → uUAsZA → ki4yLK → uQMgdA → kKCqjK → eQOedQ → GECqpo → ebXVSQ → E91Βuq → ΑlbRI4 → wT9ta8 → ok6wJG → qYQcVE → cC2ΑrS → yf9tO6 → skGmJC → gWQcXO → IC0Γrm → ΓfTZO2 → ΑH5xm4 → wsUYB8 → oh3zMG → wYKiV8 → oO2ΑfG → yYGmV6 → sW2ΑXC → yg0ΓN6 → ΓsIkB2 → ΑhRbM4 → wL9ti8 → okMgJG → YRJjcW → QB1Βse → ΑhDpM4 → wcKiR8 → oOAsfG → iYGmVM → WM2ΑhY → yL1Βi6 → ΑsMgB4 → whJjM8 → oQKidG → YOCqfW → eH1ΒmQ → ΑVDpY4 → wc2ΑR8 → yoAsF6 → siYULC → gN3zgO → wJHlk8 → oUQcZG → YC4yrW → uf1ΒOA → ΑkGmJ4 → wWQcX8 → oC0ΓrG → ΓfXVO2 → ΑH1Βm4 → ΑwUY74 → wp3zE8 → woaSF8 → oZ7vUG → oY4yVG → uY2ΑVA → yk2ΑJ6 → ysQcB6 → shBrMC → hfKiON → OKGmjg → WPHleY → UF1Βoa → ΑZ5xU4 → ws4yB8 → uogMFA → kZJjUK → RP4yed → uFBroA → kgYUNK → QJ3zke → wRDpc8 → ocAsRG → iYAsVM → iM2ΑhM → yMKih6 → sOKifC → gOGmfO → WIGmlY → WT1ΒaY → Α71Βw4 → ΑwoE74 → wpZTE8 → ob5xSG → sY8uVC → mg2ΑNI → yUIkZ6 → sS4ybC → ug8uNA → mkIkJI → USQcba → C95xus → slfNIC → gTHlaO → UI6wla → qT5xaE → sc6wRC → qgAsNE → icIkRM → SMAshc → iL9tiM → kNLhgK → QMIkhe → SLDpic → cN9tgS → kJ9tkK → kRPdcK → QEAspe → ibDpSM → cM8uhS → mL9tiI → kUMgZK → QK4yje → uPDpeA → kcEoRK → aQAsdU → iD5xqM → sdLhQC → gMCqhO → eLHliQ → UNDpga → cJ5xkS → sR9tcC → kgAsNK → iQIkdM → SMCqhc → eL9tiQ → kNDpgK → cQIkdS → SD9tqc → kd9tQK → kQCqdK → eQCqdQ → eECqpQ → ebDpSQ → cE8upS → mb9tSI → kU8uZK → mQ4ydI → uUCqZA → ke4yPK → uQEodA → kaCqTK → eQ6wdQ → qECqpE → ecaSRQ → EB7vsq → ohbRMG → YL9tiW → kN1ΒgK → ΑQIkd4 → wSCqb8 → oe8uPG → mYEoVI → aU2ΑZU → y64yx6 → usqCBA → khdPMK → QLDpie → cNDpgS
733 max stepsA00000X → X9ΔΔΔtX → uWVΔXXA → tP0ΔΓeB → ΔrTΔZC1 → ΓrNΔfC2 → ΒqTΔZD3 → ΑoMΔgF4 → zlRΔbI5 → yhJΔjM6 → xfMΔgO7 → wbHΔlS8 → vfIΔkO9 → udLΔhQA → tZGΔmUB → sdHΔlQC → rbKΔiSD → qXFΔnWE → pbGΔmSF → oZJΔjUG → nVEΔoYH → pXHΔlWF → oYEΔoVG → pYIΔkVF → oXEΔoWG → pYHΔlVF → oYFΔnVG → oYHΔlVG → nXFΔnWH → oWGΔmXG → nYFΔnVH → oWHΔlXG → nXEΔoWH → pXGΔmWF
8161 max steps100000IQ → QI0ΔΔΓle → Δlc6wRI1 → ΓqTAsaD2 → Αid6wQL4 → wqNCqgD8 → oedIkQPG → YSFCqobW → eZ91ΒuUQ → ΑlE4ypI4 → wubSaS98 → ol97vuIG → olYSaVIG → YT82ΑvaW → yn71ΒwG6 → ΑspWWEB4 → whaΔΔSM8 → vhU6wZM9 → qmL4yiHE → ucVMgYRA → kKB2ΑsjK → yhQOedM6 → sLGCqniC → geXMgWPO → KIF0Γolk → ΓZTPdaU2 → ΑE74ywp4 → wupaSE98 → olb7vSIG → oYT8uaVG → mY72ΑwVI → ypU2ΑZE6 → ysb4ySB6 → ush8uMBA → mkhKiMJI → UROKifca → OHB5xsmg → shVHlYMC → gUL2ΑiZO → yNI4ylg6 → usTIkaBA → khS6wbMK → qQL8uidE → mcNCqgRI → eUJAskZQ → iRE4ypcM → ubMAshSA → kiL8uiLK → mQNMggdI → UKJCqkja → eRP5xecQ → sFEAspoC → igbYUSNM → MJ93zuki → wlRLhcI8 → oTMAshaG → iYL6wiVM → qNM2ΑhgE → ycLIkiR6 → sSNAsgbC → igJ8ukNM → mRMIkhcI → USLAsiba → iN95xugM → slMIkhIC → gTSKibaO → OI96wulg → qlTHlaIE → cUT6waZS → qA74ywtE → upjbRKEA → kbP9teSK → kQF8uodK → mZQCqdUI → eUD4yqZQ → udE4ypQA → ukbCqSJA → keR8ucPK → mQFAsodI → iZUCqZUM → eM54yyhQ → utLDpiAA → kjcMgRKK → QPKAsjee → iPFDpoeM → cZMEohUS → aLA4ytiU → ujN5xgKA → skPIkeJC → gSREocbO → aIB8uslU → mhT5xaMI → sUL6wiZC → qgN4ygNE → ucJIkkRA → kSRAscbK → iQB8usdM → mhMCqhMI → eULKiiZQ → ONE4ypgg → ubJHlkSA → kUR8ucZK → mQB4ysdI → uhUCqZMA → keL4yiPK → uQNEogdA → kaJCqkTK → eRQ6wdcQ → qEDAsqpE → idcaSRQM → MDB7vsqi → ohdLhQMG → YMLCqihW → eNL1ΒigQ → ΑNJDpkg4 → wcRIkcR8 → oSBAssbG → ihY8uVMM → mML2ΑihI → yUNKigZ6 → sOJ4ykfC → ugRGmcNA → kWJAskXK → iRQ0ΓdcM → ΓMDAsqh2 → ΑidKiQL4 → wONCqgf8 → oeJGmkPG → YWREocXW → aB20ΓΒsU → Γzh5xM42 → ΑvsKiB84 → wnhNfMG8 → oXLHliWG → YUN0ΓgZW → ΓJ51Βyk2 → ΒztQcA43 → yvjBrK86 → sngOeNGC → gXJFnkWO → YRI0ΓlcW → ΓTB1Βsa2 → Βzh6wM43 → yvqKiD86 → sndNfQGC → gXICqlWO → eTI0ΓlaQ → ΓTE6wpa2 → Αqb6wSD4 → wqd8uQD8 → omdCqQHG → eYVCqYVQ → eE32ΑΑpQ → yxbDpS66 → src8uRCC → mgfAsONI → iUJGmkZM → WRM4yhcY → uLB1ΒsiA → ΑkhMgMJ4 → wRLJjic8 → oQNAsgdG