Base 66: 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
235 max steps20 → 1Γ → Α3w7oFYVy5sBgNIlSb8vmHUZ4zu9kJQdCrePEpaT6xqDcRAtiLMhKjOfGnWXΓ1Α3
335 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 → WΔXWΔX
412 max steps800P → P7vf → oFnG → ZWWV → 3ΔΔΑ → Α2Α4 → yv76 → snFCgXVOI1ΒmΑTZ4w5x8snFC
531 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 → iLΔhMiLΔhM
6179 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 → cNDpgScJ9tkSkR9tcKkQAsdKiQCqdMeMCqhQeLDpiQcNDpgS
737 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 → pXGΔmWFoZFΔnUGoYIΔkVGnWEΔoXHpXGΔmWF
8337 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 → oQNAsgdGiYJCqkVMeRM2ΑhcQyLEAspi6sibMgSLCgNK8ujgOmPJHlkeIVTREocaZaB73zwsUwph5xME8sobKiSFCgZO8ufUOmIH4ymlIuVUSaZYAk852ΑyvKytnPdGA6sjXDpWKCgcP0ΓeROΓIFAsol2ΑiZSaUL4wN84yvg8uonIkGFAkZXRbWUKQA50ΓyteΓtjDpKA2ΑjcOeRK4wPGAsne8oiXEoWLGaYN0ΓgVUΓJ62Αxk2ΑyrQcC54wtfBrOA8ojgGmNKGYWPIkeXWSF20ΓΒocΓzZ9tU42Αvk4yJ84wunQcG98olXBrWIGgYT0ΓaVOΓI72Αwl2ΑypSaE54wtb7vSA8pnj8uKGFmaXOeWTIUG70ΓwnaΓpX5xWE2Αsb0ΓSB4Γwh8uM72ΑpmKiHE4wbVNfYS8oI92ΑulGylYSaVI6sT82ΑvaCyng6wNG6sqXIkWDCgdS0ΓbQOΓID8uql2ΑmdSaQH4wVD7vqY8pnd2ΑQGFyaXCqWT6se70ΓwPCΓpgEoNE2ΑbaIkTS4wS96wub8qol8uIFEmcZSaURIUB84yvsaunh5xMGAskXKiWJCgRO0ΓfcOΓIHAsml2ΑiVSaYL4wN82Αvg8yonIkGF6sZXRbWUCgA50ΓytOΓtjHlKA2ΑjUOeZK4wPG4yne8uoXEoWFAkaZ0ΓUTKΓQ74ywd2ΑupCqE94wleaSPI8oTF7voaGoZY6wVUGqY52ΑyVEytc2ΑRA6ysjAsKB6sihOeMLCgNLFnigOYNJHlkgWURJ1ΒkcaΑRB5xsc4wshAsMB8oihKiMLGYONKigfWOJH1ΒmkgΑVRHlcY4wUB2ΑsZ8yoh4yMF6usZKiUBAkhO4yfMKuQLGmidAkWNCqgXKeQJ0ΓkdQΓRECqpc2ΑebAsSP4wiF8uoL8omZMgUHGYVK4yjYWuP31ΒΑeAΑxkEoJ64wraQcTC8ofC6wrOGqfYGmVOEcWH2ΑmXSyVA0ΓtY6Γsj2ΑKB2ΑyhOeM54wtLFniA8ojYMgVKGYPK2ΑjeWyPF1Βoe6ΑsZEoUB4wha4yTM8uoL6wiFAqkZMgUJEcRK4yjcSuPB9tseAljhEoMKJaSPKiebUOF95xuogslZHlUICgUT4yaZOuI74ywlAupkSaJEAkbR7vcSKoQB8usdGmhYCqVMIeUL2ΑiZQyNE4ypg6usbIkSBAkhS8ubMKmQL8uidImUNCqgZIeUJ4ykZQuRE4ypcAukbAsSJAkiR8ucLKmQNAsgdIiUJCqkZMeRM4yhcQuLEAspiAkibMgSLKQNK8ujgemPJDpkeIcUREocZSaBA4ytsUujh5xMKAskPKieJCgROEofcOaIHAsmlUiVT5xaYMsM72ΑwhCypgKiNE6sbOIkfSCgSH8umbOmVI8ulYImUT2ΑaZIyU74ywZ6usp4yEBAukhaSMJAkRL7vicKoQNAsgdG