Base 58: 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
231 max steps20 → 1u → s3o7gFQV4rm9cJIdKbGfOX8neHMZCjWP6piDUR2tq5kBYNAlaLEhST0vu1s3
331 max steps100 → 0vv → uv1 → tv2 → sv3 → rv4 → qv5 → pv6 → ov7 → nv8 → mv9 → lvA → kvB → jvC → ivD → hvE → gvF → fvG → evH → dvI → cvJ → bvK → avL → ZvM → YvN → XvO → WvP → VvQ → UvR → TvS → SvTSvT
421 max steps700M → M6oa → iDhE → VSSR → 3vvs → s2s4 → qn76 → kfFCYPVOA5pmkbJCYHdOM9lacDhKUHdSM1tasDh4oTR8g1tGsPV4o5p8kfFC
528 max steps10006 → 60vuq → vnv71 → unv72 → tmv83 → skvA4 → rhvD5 → qdvH6 → pYvM7 → oSvS8 → nLvZ9 → mRvTA → lKvaB → kQvUC → jJvbD → iPvVE → hIvcF → gOvWG → fHvdH → eNvXI → dGveJ → fKvaH → eKvaI → dJvbJ → cJvbK → cHvdKeIvcIdLvZJcHvdK
6211 max steps30000L → L2vvsb → taGeL3 → qOEgX6 → kS8mTC → eY0uNI → uMAkZ2 → saCiL4 → oWEgP8 → gS6oTG → iQ0uVE → uU4qR2 → sm2s94 → qocI76 → khJbEC → YTHdSO → MA0ula → ubDhK2 → sUGeR4 → oO2sX8 → qg8mF6 → keQUHC → YN3rYO → oB9lk8 → gcYMJG → QJBjcW → YJ5pcO → kJ9lcC → cYIcNK → KIAkdc → aLHdaM → MFDhga → URDhUS → U31tsS → sp1t64 → soiC74 → ohVPE8 → gT5pSG → kQ0uVC → uY4qN2 → smAk94 → odZLI8 → gLDhaG → UQEgVS → S51tqU → sl1tA4 → soaK74 → ohFfE8 → gTPVSG → Q60upW → uj5pC2 → skWOB4 → oZ7nM8 → hfCiGF → WSOWTQ → 860upo → ujfFC2 → sXPVO4 → o95pm8 → kgcIFC → YRJbUO → IA2sle → qbLZK6 → kHDheC → YUMYRO → CA2slk → qbXNK6 → kH9leC → cYMYNK → ICAkje → aXLZOM → FD8mih → eVRTQI → M51tqa → slDhA4 → obTRK8 → gH1teG → sQMYV4 → oC4qj8 → mgWOFA → cR7nUK → gI2sdG → qQKaV6 → kG4qfC → mYOWNA → cB7nkK → gZHdMG → QMCiZW → WD5piQ → kV5pQC → kY4qNC → mYAkNA → caAkLK → aIEgdM → SLDhaU → UF1tgS → sR1tU4 → so2s74 → qogE76 → khRTEC → YT1tSO → sA0ul4 → uoaK72 → shFfE4 → oTPVS8 → g60upG → ujPVC2 → sX5pO4 → ok8mB8 → geYMHG → QNBjYW → YB5pkO → kZ9lMC → cYCiNK → WIAkdQ → aL5paM → kFDhgC → YUQURO → A42srm → qnbJ86 → kfHdGC → YPLZWO → EA6oli → ibTRKE → UH1teS → sN1tY4 → soAk74 → ohZLE8 → gTDhSG → UQ0uVS → u51tq2 → trkA43 → qnZL86 → kfDhGC → YUOWRO → A82snm → qfbJG6 → kPHdWC → YM6oZO → iD9liE → cVTRQK → I51tqe → slLZA4 → obDhK8 → gUGeRG → QO2sXW → q95pm6 → ljcICB → aXJbOM → IE8mheeTLZSIME0uhauTDhS2sU0uR4uo2s72sqgE54olRTA8gb1tKGsQGeV4oO4qX8mg8mFAecQUJIMJ3rcaoJDhc8gUIcRGQK2sbWqH5pe6ljMYCBaXBjOMYE8mhOeT9lSIcM0uZKuICid2sWKaP4oG6of8igOWFEUR7nUSg31tsGspPV64oj5pC8kgWOFCYR7nUOgA2slGqbPVK6kH5peCkYMYNCYCAkjOaX9lOMcE8mhKeTHdSINL0uaZuFBjg2sYQUN4oB3rk8ogYMF8gRBjUGYQ2sVOqA4ql6mkaKBAcZFfMKQICidWWL5paQkF5pgCkYQUNCYB3rkOoZ9lM8gcCiJGWQIcVQK64qpcmjHdCAcXLZOKIE8mhe
735 max steps1000000 → 0vvvvvv → uvvvvv1 → u0vvvu2 → vt0vu21 → vurv311 → uuqv412 → uspv532 → trmv843 → spivC64 → rmcvI95 → qiTvRD6 → pdGveI7 → oZLvZM8 → nTCviS9 → mbFvfKA → lXKvaOB → kRBvjUC → kYHvdNC → jTFvfSD → iUCviRE → jUGveRD → iTCviSE → jUFvfRD → iUDvhRE → iUFvfRE → hTDvhSF → iSEvgTE → hUDvhRF → iSFvfTE → hTCviSF → jTEvgSDiVDvhQEiUGveREhSCviTFjTEvgSD
8646 max steps600000Qn → nQ5vvpV9 → qmPHdW96 → kdM6oZIC → iYLCiaNE → WUFAkgRQ → aR62spUM → qjE2shC6 → qkXSSOB6 → kZ8vvmMC → njQAkVC9 → eaX4qOLI → mMF8mgZA → ecRCiUJI → WMJ2scZQ → qJD5pic6 → ljVIcQCB → aXK4qbOM → mHE8mheA → ecTMYSJI → MJC0ujca → uXJDhcO2 → sUJ8mcR4 → oeJ2scH8 → qgNIcYF6 → kRKAkbUC → aYH2seNM → qNEAkhY6 → kaTAkSLC → aYF0ugNM → uREAkhU2 → saT2sSL4 → qoF0ug76 → ukhQUEB2 → sZT3rSM4 → pnD0ui87 → uifUQGD2 → sVP3rWQ4 → pn74qo87 → miheGEDA → cVTNXSQK → IA50uqle → ulbLZKA2 → sbHDheK4 → oUNGeYR8 → gOB2skXG → qZQ8mVM6 → keD4qiHC → mYVMYQNA → cCB4qkjK → mZXHdOMA → cMD8miZK → eVICidQI → WML4qaZQ → mFD5pigA → kcVQUQJC → YJ53rqcO → olJ9lcA8 → gcbIcKJG → QKJGecbW → OJH5pecY → kNJ9lcYC → cYJAkcNK → aJIAkdcM → aLJDhcaM → UJFDhgcS → URJ1tcUS → sJ31tsc4 → spoIc764 → ojhJbEC8 → gXTHdSOG → QM90umZW → udD5piI2 → skVKaQB4 → oZG4qfM8 → mgPCiWFA → cWR6oUPK → iI72sodE → qhUKaRE6 → kTG2sfSC → qYP0uWN6 → ukB6okB2 → siZYMMD4 → oVDBjiQ8 → gYV4qQNG → mQB4qkVA → mcZ4qMJA → mcJCicJA → cWJIccPK → KJI6odcc → iLJHdcaE → UMJEgcZS → SJD1ticU → sVJ1tcQ4 → soJ4qc74 → omhIcE98 → gdTJbSIG → QLI0udaW → uLF5pga2 → skREgUB4 → oZS2sTM8 → qgD0uiF6 → ukVQUQB2 → sZ53rqM4 → pnlCiA87 → ifbVPKGE → UPH5peWS → kN71toYC → shYAkNE4 → oaTAkSL8 → gaF0ugLG → uRQEgVU2 → sS52sqT4 → qol0uA76 → ukhaKEB2 → sZTFfSM4 → oQD0uiV8 → ugV4qQF2 → smR4qU94 → omd2sI98 → qgdKaIF6 → kRLFfaUC → YQF2sgVO → qRA4qlU6 → mkb2sKBA → qcZGeMJ6 → kOJCicXC → YWJ8mcPO → eJA6olcI → ibMIcZKE → UKHCiebS → WNH1teYQ → sNB5pkY4 → okZAkMB8 → gaZCiMLG → WQFCigVQ → WR64qpUQ → mj62spCA → qjcWOJC6 → kXJ7ncOC → gYJ8mcNG → eQJAkcVI → aMJ4qcZM → mJECihcA → cWTIcSPK → KI70uodc → uhLHdaE2 → sTMEgZS4 → oSD0uiT8 → ugV0uQF2 → usR4qU32 → spm2s964 → qojcIC76 → khXJbOEC → YTI8mdSO → eLA0ulaI → ubMEgZK2 → sSHCieT4 → oWN0uYP8 → ugB6okF2 → siZQUMD4 → oVD3riQ8 → ogV4qQF8 → mgR4qUFA → mcR2sUJA → qcJ2scJ6 → qkJIccB6 → kZKIcbMC → YKHCiebO → WNH9leYQ → cNB5pkYK → kZIAkdMC → aYLCiaNM → WFEAkhgQ → aTR5pUSM → kE30ushC → upYSSN62 → sjAvvkC4 → rlg0uFA5 → umbQUK92 → sdH3reI4 → pnNKaY87 → ifGAkfGE → aUPOWWRM → E872soni → qhfTRGE6 → kTP1tWSC → sY70uoN4 → uohAkE72 → shaSSLE4 → oTEvvgS8 → nhMCiZE9 → eWTCiSPI → WM70uoZQ → uhD5piE2 → skVSSQB4 → oZ4vvqM8 → rnUEgR85 → mfS2sTGA → qcP0uWJ6 → ukJ6ocB2 → siZIcMD4 → oVKCibQ8 → gWH4qePG → mQN6oYVA → icB4qkJE → mZUIcRMA → cKD2sibK → qVIGedQ6 → kOL4qaXC → mYF8mgNA → ecRAkUJI → aMJ2scZM → qJECihc6 → kWTIcSPC → YK70uobO → uhH9leE2 → scTMYSJ4 → oJC0ujc8 → ugXIcOF2 → sRK8mbU4 → oeH2seH8 → qgNMYYF6 → kRCAkjUC → aYX2sONM → qEB8mkh6 → keZSSMHC → YNCvviYO → jYJvvbND → icM2sZJE → qUJCicR6 → kWJ2scPC → qYJ6ocN6 → kiJAkcDC → aYVIcQNM → KEB4qkhc → mZTHdSMA → cMD0uiZK → uVICidQ2 → sWL4qaP4 → omF6og98 → igdQUIFE → URL3raUS → oF31tsg8 → spgQUF64 → ojR3rUC8 → ogX2sOF8 → qgR8mUF6 → keR2sUHC → qYN2sYN6 → qkBAkkB6 → kaZYMMLC → YFDBjigO → YVR9lUQO → cA52sqlK → qlbHdKA6 → kbMGeZKC → YOHCieXO → WNA8mlYQ → ebB5pkKI → kZMGeZMC → YODCiiXO → WVA8mlQQ → eb64qpKI → mjMGeZCA → cXOCiXOK → WI98mmdQ → edL5paII → kMLEgaZC → YSFCigTO → WRA0ulUQ → ub62spK2 → sqjGeC54 → olXNXOA8 → gbA8mlKG → ebQGeVKI → OMH4qeZY → mND9liYA → dbVAkQKJ → aKH4qebM → mNHDheYA → cUNAkYRK → aIB2skdM → qZLDhaM6 → kUFCigRC → YWR2sUPO → qA72sol6 → qkhaKEB6 → kZTFfSMC → YQD0uiVO → uVA4qlQ2 → smb4qK94 → omdGeI98 → gdOKaXIG → QLG8mfaW → ePF5pgWI → kRM6oZUC → iYD2siNE → qVUAkRQ6 → ka52sqLC → qlYEgNA6 → kbSAkTKC → aYH0ueNM → uNEAkhY2 → saTAkSL4 → oaF0ugL8 → ugREgUF2 → sSR2sUT4 → qo30us76 → upkgEB62 → sjZRTMC4 → oXD1tiO8 → sgV8mQF4 → oeR4qUH8 → mgN2sYFA → qcRAkUJ6 → kaJ2scLC → qYJEgcN6 → kSJAkcTC → aYJ0ucNM → uJEAkhc2 → saTIcSL4 → oKF0ugb8 → ugRGeUF2 → sRO2sXU4 → qo92sm76 → qkhcIEB6 → kZTJbSMC → YID0uidO → uVL9laQ2 → scF4qgJ4 → omRIcU98 → gdK2sbIG → qQLGeaV6 → kOF4qgXC → mYR8mUNA → ecB2skJI → qZMIcZM6 → kKDCiibC → YWVGeQPO → OA74qolY → mhb9lKEA → dbTGeSKJ → OKH0uebY → uNH9leY2 → scNAkYJ4 → oaJAkcL8 → gaJEgcLG → SQJEgcVU → SJ51tqcU → slJ1tcA4 → sobIcK74 → ohKGebE8 → gTOGeXSG → QO90umXW → ud95pmI2 → skdKaIB4 → oZLFfaM8 → gQFCigVG → WRQ4qVUQ → m652sqpA → qljbJCA6 → kbXHdOKC → YMH8meZO → eND9liYI → cVMAkZQK → aID4qidM → mVLDhaQA → cUF4qgRK → mRI2sdUA → qcL2saJ6 → qkJEgcB6 → kZSIcTMC → YKD0uibO → uVH9leQ2 → scN4qYJ4 → omJAkc98 → gdaIcLIG → QLKEgbaW → SHF5pgeU → kRN1tYUC → sYB2skN4 → qoZAkM76 → khaCiLEC → YWTEgSPO → SA70uolU → uhb1tKE2 → trTGeS43 → qnO0uX86 → ukf8mGB2 → seZOWMH4 → oND7niY8 → hfVAkQGF → aSP4qWTM → mE70uohA → uhcSSJE2 → sTIvvcS4 → rdQ8mVI5 → meL4qaHA → mcNEgYJA → cSJAkcTK → aJI0udcM → uLJDhca2 → sUJEgcR4 → oSJ2scT8 → qgJ0ucF6 → ukRIcUB2 → sZK2sbM4 → qoHCie76 → khWMYPEC → YTC6ojSO → iXA0ulOE → ubU8mRK2 → seH2seH4 → qoNMYY76 → khCAkjEC → aYXSSONM → EB8vvmki → nkY1tNB9 → seZAkMH4 → oaNCiYL8 → gWFAkgPG → aRQ6oVUM → iE52sqhE → qlUSSRA6 → kb2vvsKC → tjY8mNC3 → qeXAkOH6 → kaN8mYLC → eYFAkgNI → aRMAkZUM → aED2sihM → qVTDhSQ6 → kU50uqRC → ulY2sNA2 → sqbAkK54 → olaGeLA8 → gbOEgXKG → SQH8meVU → eN51tqYI → slMAkZA4 → obaCiLK8 → gWHEgePG → SQN6oYVU → iB51tqkE → slZTRMA4 → obD1tiK8 → sgVGeQF4 → oRO4qXU8 → mg92smFA → qdcQUJI6 → kLJ3rcaC → oYJEgcN8 → gSJAkcTG → aQJ0ucVM → uJE4qhc2 → smTIcS94 → odK0ubI8 → ugLGeaF2 → sROEgXU4 → oS92smT8 → qgd0uIF6 → ukRKaUB2 → sZG2sfM4 → qoPCiW76 → khW6oPEC → iYT6oSNE → iUB0ukRE → uZU2sRM2 → sqD2si54 → qolUQA76 → khb3rKEC → oYTGeSN8 → gOB0ukXG → uZQ8mVM2 → seD4qiH4 → omVMYQ98 → gdC4qjIG → mXQKaVOA → cG94qmfK → mdPHdWIA → cML6oaZK → iIFCigdE → WURKaURQ → G632sspg → qpjPVC66 → kjX5pOCC → kYX8mONC → eYB8mkNI → eZMAkZMI → aMDCiiZM → WVECihQQ → WT64qpSQ → mj60upCA → ujcWOJC2 → sXJ7ncO4 → ogJ8mcF8 → geRIcUHG → QNK2sbYW → qHB5pke6 → ljZMYMCB → aXDBjiOM → YVE8mhQO → eTA4qlSI → mbM0uZKA → ucHCieJ2 → sWNIcYP4 → oKB6okb8 → igZGeMFE → UROCiXUS → W931tsmQ → spd5pI64 → okjKaCB8 → gZXFfOMG → RPD8miWV → eV73roQI → ohM4qZE8 → mgTCiSFA → cWR0uUPK → uI72sod2 → sqhKaE54 → 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