Base 54: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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
222 max steps20 → 1q → o3k7cFMV8jaHIZGbKXCfSP2pm5gBUN6leDQR0rq1o3
329 max steps100 → 0rr → qr1 → pr2 → or3 → nr4 → mr5 → lr6 → kr7 → jr8 → ir9 → hrA → grB → frC → erD → drE → crF → brG → arH → ZrI → YrJ → XrK → WrL → VrM → UrN → TrO → SrP → RrQ → QrRQrR
416 max steps700K → K6kY → eDdE → ROSR → 3rro → o2o4 → mj76 → gbFCULVOA5ligXJCUDdOQ5lSg1pCoTN4k5l8gbFC
527 max steps30000 → 2rrrp → p1rp3 → qlr52 → pkr63 → oir84 → nfrB5 → mbrF6 → lWrK7 → kQrQ8 → jJrX9 → iPrRA → hIrYB → gOrSC → fHrZD → eNrTE → dGraF → cMrUG → bFrbH → cJrXG → bIrYH → aIrYI → ZHrZJ → aFrbI → cIrYG → bJrXH → aHrZIaHrZI
6271 max steps3000Ih → hI2oZB → mWGaL6 → gKAgXC → WUCeNM → SA6khQ → eX1pKE → oQCeR4 → kS0qP8 → qc2oF2 → omMU54 → kh7jA8 → dbWKGF → OLBfWU → UB5lgO → gV5lMC → gU8iNC → aU6kNI → eI6kZE → eQGaRE → QK0qXS → qD1pe2 → pnQQ43 → mirr86 → lj3n87 → keaGD8 → cRJXQG → ME0qdW → qP9hS2 → oY2oJ4 → mkEc76 → gdNTEC → UP5lSO → g62olC → mfTNC6 → gT5lOC → gU4mNC → iU6kNA → eY6kJE → eQEcRE → QO0qTS → q51pm2 → pngA43 → mjVL86 → gb9hGC → YUKWNK → EC6kfe → eTPROE → Q51pmS → oh1pA4 → okWK74 → kdBfE8 → cUOSNG → M73nkW → kd9hE8 → cYOSJG → MF3ncW → kN9hU8 → cY6kJG → eMEcVE → QO8iTS → a51pmI → ohHZA4 → kXHZK8 → cICeZG → SMGaVQ → K91piY → oZDdI4 → kQGaR8 → cK0qXG → qMCeV2 → oS8iP4 → ka2oH8 → mcIYF6 → gNFbUC → UM6kVO → e95liE → gZPRIC → UH1paO → oJ5lY4 → kgEcB8 → cVNTMG → M95liW → gZ9hIC → YUGaNK → KE6kdY → ePDdSE → RP2oSR → m2rro6 → pl1p63 → omeC54 → khRPA8 → cX1pKG → oMCeV4 → kS8iP8 → ca2oHG → mMIYV6 → gG8ibC → aUKWNI → IC6kfa → eTHZOE → QI4mZS → iH1paA → oYIYJ4 → kGEcb8 → cOKWTG → MC4mfW → iT9hOA → ZX4mKJ → iGCebA → YSKWPK → EC2ofe → mTPRO6 → g51pmC → ohTNA4 → kX5lK8 → gcCeFC → USMUPO → 862olk → mfbFC6 → gTLVOC → UA4mhO → iX5lKA → gYCeJC → USEcPO → O62olU → mf5lC6 → hfSOCB → WT3nOM → kA4mh8 → icWKFA → YNBfUK → UE6kdO → eP5lSE → gQ2oRC → mU0qN6 → qg6kB2 → oeUMD4 → kR7jQ8 → db0qGF → qOKWT2 → oC4mf4 → kiSO98 → cZ3nIG → kMGaV8 → cK8iXG → aMCeVI → SI8iZQ → aH1paI → oJHZY4 → kIEcZ8 → cOGaTG → MK4mXW → iD9heA → ZXQQKJ → GCrrec → fb1pGD → oSKWP4 → kC2of8 → mcSOF6 → gN3nUC → kU6kN8 → ec6kFE → eQMURE → Q80qjS → qb1pG2 → pnKW43 → mjBf86 → gbTNGC → UL5lWO → 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
734 max stepsR00000q → qQrrrQ2 → pRQrQQ3 → oP0rqS4 → rmOrS51 → qmNrT52 → plOrS63 → ojMrU84 → ngMrUB5 → mcJrXF6 → lXIrYK7 → kTDrdO8 → jXErcK9 → iVHrZMA → hRCreQB → gVDrdMC → fTGraOD → ePBrfSE → gRErcQC → fSBrfPD → gSFrbPC → fRBrfQD → gSErcPC → fSCrePD → fSErcPD → eRCreQE → fQDrdRD → eSCrePE → fQErcRD → eRBrfQE → gRDrdQCfTCreODfSFrbPDeQBrfREgRDrdQC
8562 max steps50000FFl → lFF4mcc7 → ieNMUUDA → YR86kjQK → ebE0qdGE → qQPKWSR2 → oC30qof4 → qlkSO762 → ofd3nEC4 → ljTOSO87 → eb53nmGE → khQKWRA8 → cXC0qfKG → qTMCeVO2 → oS94miP4 → kiZ2oI98 → mcZGaIF6 → gNKGaXUC → UKD6keXO → eRD5leQE → gRQ0qRQC → qU10qqN2 → qpo6k322 → onldD644 → kjfPRC88 → cbT1pOGG → oML4mWV4 → kiB8ig98 → caZUMIHG → MJH7jaYW → cJF9hcYG → YNMEcVUK → OE96kidU → eZP5lSIE → gQH2oaRC → mUJ0qYN6 → qgF6kcB2 → oeVMUMD4 → kR97jiQ8 → dbZ0qIGF → qOLGaWT2 → oKB4mgX4 → kiVCeM98 → cZS8iPIG → aMH2oaVI → mJI8iZY6 → gaHEcaHC → UOJIYYTO → GF64mlcc → ifNLVUCA → YTA6khOK → eXE4mdKE → iQPCeSRA → YS30qoPK → qlE2od62 → omfOSC54 → khT3nOA8 → kcX4mKF8 → icNCeUFA → YSN6kUPK → eE72okdE → mdQOSRE6 → gP40qnSC → qjU2oN82 → omb6kG54 → kheKWDA8 → cXRBfQKG → UMD0qeVO → qR95liQ2 → ogZ0qIB4 → qkVGaM72 → odK8iXE4 → kaPCeSH8 → cSJ2oYPG → mMF2ocV6 → mgN8iUB6 → gaV6kMHC → eUJ8iYNE → aQF6kcRI → eNI0qZUE → qQH6kaR2 → oeJ0qYD4 → qkREcQ72 → odO0qTE4 → qkP4mS72 → oid2oE94 → mkZOSI76 → gdH3naEC → kUPIYSN8 → cG72okbG → mdMKWVE6 → gPC8ifSC → aUT2oONI → mI74mkZ6 → igdGaEBA → YVPJXSMK → FD92oied → mZRNTQI6 → gH60qlaC → qfUIYNC2 → oTG6kbO4 → keL4mWD8 → icRAgQFA → YWN0qULK → qEB6kgd2 → oeVOSMD4 → kR93niQ8 → kcZ0qIF8 → qcNGaUF2 → oNK6kXU4 → keD6keD8 → ecRQQQFE → QN0rrqUS → rUQ1pRN1 → qo70qk32 → qolcE632 → olfNTC64 → kfT5lOC8 → gcT4mOFC → iUN4mUNA → iY76kkJA → edYEcJEE → QPOEcTSS → O531pomU → olh5lA64 → kgfWKCB8 → cVTBfOMG → UM94miVO → iZ95liIA → gZYGaJIC → UKHEcaXO → OJD5leYU → gRF5lcQC → gUN0qUNC → qU76kkN2 → oed6kED4 → keROSQD8 → cR40qnQG → qjM0qV82 → qob8iG32 → olaKWH64 → kfJBfYC8 → cUTEcONG → OM74mkVU → id95liEA → gZYOSJIC → UHF3ncaO → kNJ5lYU8 → gcF6kcFC → eUNMUUNE → Q876kkjS → edb1pGEE → oQPKWSR4 → kC30qof8 → qlcSOF62 → ofN3nUC4 → ljT6kO87 → fdb4mGED → iSPKWSPA → YC32oofK → mlTDdO66 → gfQ4mRCC → iUT0qONA → qY74mkJ2 → oidEcE94 → kZPNTSI8 → cH62olaG → mfMIYVC6 → gTG8ibOC → aUL4mWNI → iIB6kgZA → eYVGaMJE → QKF8icXS → aND1peUI → oRI6kZQ4 → keH0qaD8 → qcRIYQF2 → oNG0qbU4 → qkL6kW72 → oedAgED4 → kWROSQL8 → cB40qngG → qjVLVM82 → obA8ihG4 → kaXKWKH8 → cJDBfeYG → URMEcVQO → O960qliU → qfZ5lIC2 → ogTGaOB4 → kVK4mXM8 → icD8ieFA → aYRMUQJI → IF80qjca → qbNHZUG2 → oLI6kZW4 → keHAgaD8 → cWRIYQLG → MGB0qgbW → qVL9hWM2 → oYB8igJ4 → kaVEcMH8 → cOJ8iYTG → aMF4mcVI → iNI8iZUA → aYH6kaJI → eJIEcZYE → QOHEcaTS → OJ51pmYU → ohF5lcA4 → kgXMUKB8 → cVD7jeMG → cRM8iVQG → aM90qiVI → qZI8iZI2 → oaHGaaH4 → kKJIYYX8 → cGFCecbG → SNMKWVUQ → C971pkig → odZTNIE4 → kPH5laS8 → gcJ2oYFC → mUNEcUN6 → gO76kkTC → edU4mNEE → iQP6kSRA → eY30qoJE → qlQEcR62 → ofO0qTC4 → qkT4mO72 → oid4mE94 → kiZOSI98 → cZH3naIG → kMJGaYV8 → cKF8icXG → aNMCeVUI → SI96kiZQ → eZH1paIE → oQJGaYR4 → kKF0qcX8 → qcNCeUF2 → oSN6kUP4 → ke72okD8 → mdcQQFE6 → gPMrrUSC → fVH1paMD → oSJ8iYP4 → kaF2ocH8 → mcNIYUF6 → gNG6kbUC → eUL6kWNE → eQB6kgRE → eVQ0qRME → qQ90qiR2 → qoZ0qI32 → qolGa632 → olfJXC64 → kfTDdOC8 → cTQ4mROG → iM50qmVA → qhY8iJA2 → oaXEcKH4 → kOJCeYT8 → cSF4mcPG → iNM2oVUA → mY96kiJ6 → geZEcIDC → UROGaTQO → K650qmlY → qhfDdCA2 → oXTPROK4 → kD51pme8 → ohcQQFA4 → kXMrrUK8 → jXO2oTK9 → maD4meH6 → igRIYQBA → YVG0qbMK → qLE8idW2 → oaPAgSH4 → kWJ2oYL8 → mcFAgcF6 → gWNMUULC → UB86kjgO → ebV5lMGE → gQL8iWRC → aUB0qgNI → qVI6kZM2 → oeH8iaD4 → kaRIYQH8 → cJG0qbYG → qMLEcWV2 → oOB8igT4 → kaV4mMH8 → icJ8iYFA → aYNEcUJI → OIF6kcZU → eNH5laUE → gQJ6kYRC → eUF0qcNE → 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