Base 60: 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 steps1 → 0 → 0
232 max steps20 → 1w → u3 → q7 → iF → SV → 2v → s5 → mB → aN → Cl → YP → 8p → gH → OZ → An → cL → Gh → QX → 6r → kD → WR → 4t → o9 → eJ → Kd → If → Mb → Ej → UT → 0x → w1 → u3
332 max steps100 → 0xx → wx1 → vx2 → ux3 → tx4 → sx5 → rx6 → qx7 → px8 → ox9 → nxA → mxB → lxC → kxD → jxE → ixF → hxG → gxH → fxI → exJ → dxK → cxL → bxM → axN → ZxO → YxP → XxQ → WxR → VxS → UxT → TxU → TxU
415 max steps200D → D1vl → uXP4 → q7p8 → jgGF → UPXU → 7xxq → q6q8 → khFE → WRVS → 52ut → sn96 → mdJC → aJdO → KBle → aJdO
530 max steps10000 → 0xxxx → wxxx1 → w0xw2 → xtx31 → wtx32 → vsx43 → uqx64 → tnx95 → sjxD6 → rexI7 → qYxO8 → pRxV9 → oNxZA → nQxWB → mMxaC → lPxXD → kLxbE → jOxYF → iKxcG → hNxZH → gJxdI → fMxaJ → eIxeK → fJxdJ → eLxbK → dIxeL → fIxeJ → fLxbJ → eJxdK → eJxdK
6178 max steps5000Oj → jO4sZF → oUAmTA → ec0wLK → wKGgd2 → uQIeX4 → qM6qb8 → kiEiFE → WUSUTS → 420wvu → wtp742 → uphF84 → qhRVG8 → iR3tWG → qS4sV8 → oi2uFA → seSUJ6 → mL1vcC → uaGgN4 → qQCkX8 → iY6qPG → kS8oVE → gW2uRI → sO4sZ6 → omAmBA → ecaMLK → KHDjge → WPJdYS → K93toe → qfJdI8 → iNJdaG → SKCkdW → YJ3teQ → qL7pc8 → jhGgGF → URPXWU → 84xxsq → tp1v85 → uogG94 → qfPXI8 → iN7paG → iSCkVG → YS2uVQ → s82up6 → smgGB6 → mbPXMC → aF7piO → iTBlUG → aS0wVO → wC2ul2 → usYO54 → qn9nA8 → iecKJG → SLHfcW → OH3tga → qPBlY8 → ia8oNG → gSCkVI → YO2uZQ → sB7pm6 → miaMFC → aTDjUO → WC0wlS → wZ3tO2 → uqAm74 → qjbLE8 → iVFhSG → TR2uWV → s51vs6 → unlBA4 → qdZNK8 → iJBleG → aSKcVO → IC2ulg → sZNZO6 → mCAmlC → caYONM → GD9nki → eXRVQK → K73tqe → qjJdE8 → iVJdSG → SK2udW → sJ3te6 → qmKcB8 → ibHfMG → SOEiZW → UB3tmU → qaxxM8 → pbFhM9 → gSEiVI → UO2uZU → sAxxm6 → rn5rA7 → mkcKDC → aXHfQO → OC6qla → kZBlOE → aWAmRO → cC4slM → oZFhOA → eSAmVK → cK2udM → sJFhe6 → mSKcVC → aI2ufO → sNBla6 → maCkNC → aYCkPO → YC8olQ → gZ7pOI → iOAmZG → cSAmVM → cG2uhM → sRFhW6 → mS4sVC → oa2uNA → seCkJ6 → mYKcPC → aI8ofO → gNBlaI → aOCkZO → YCAmlQ → cZ7pOM → iGAmhG → cSQWVM → G62uri → slRVC6 → mZ3tOC → qaAmN8 → icCkLG → YSGgVQ → Q82upY → sh7pG6 → miQWFC → aT5rUO → mC0wlC → waYON2 → uD9nk4 → qeWQJ8 → iL5rcG → mSGgVC → aQ2uXO → sC6ql6 → mkYODC → aX9nQO → eC6qlK → kZJdOE → WKAmdS → cJ3teM → qLFhc8 → iSGgVG → SQ2uXW → s73tq6 → qmiEB8 → ibTTMG → SExxiW → jVBlSF → aU2uTO → sC0wl6 → wmYOB2 → ub9nM4 → qeEiJ8 → iUKcTG → SI0wfW → wN3ta2 → uqCk74 → qjXPE8 → iV7pSG → iS2uVG → sS2uV6 → sm2uB6 → smaMB6 → mbDjMC → aWEiRO → UC4slU → oYxxOA → nZFhOB → cSAmVM
744 max stepsF00000k → kExxxiE → jjExiEF → jVTxTSF → iH1xvgG → wfQxWI2 → veExiJ3 → uhOxYG4 → teIxeJ5 → sbKxcM6 → rYFxhP7 → qcHxfL8 → pZJxdO9 → oWExiRA → naGxgNB → mXIxeQC → lUDxjTD → kYFxhPE → jVHxfSF → iSCxkVG → lUFxhTD → kWDxjRE → kWHxfRE → jTDxjUF → kUFxhTE → jVDxjSF → kUGxgTE → jUCxkTF → lVFxhSD → kWExiRE → jWGxgRF → iTExiUG → jSExiVF → jUFxhTF → iUDxjTG → kTExiUE → jWExiRF → jUGxgTF → iTCxkUG → lUExiTD → kXExiQE → jWHxfRF → iSDxjVG → kTFxhUE → jVDxjSF
8388 max stepsC0000CDI → IDCBllkg → aZXNZQOO → DBB6qmml → kbbXPMME → WFF7piiS → iTT3tUUG → qS10wwV8 → wvi2uF22 → utsSU544 → qpn1vA88 → uihcKGF4 → qTRHfWU8 → iO50wsZG → wnSAmVA2 → udc2uLK4 → sqJGge76 → mjQKcXEC → aVI6qfSO → kNC2ulaE → sZWCkRO6 → mYB4smPC → oba8oNMA → geFCkiJI → YTOKcZUQ → IB80wpmg → whbNZMG2 → uRFBliW4 → qaT4sUN8 → oiD0wkFA → weXSUQJ2 → uL71vqc4 → uqjGgE74 → qjVPXSE8 → iV82upSG → shS2uVG6 → smR2uWB6 → smb4sMB6 → ombEiMBA → ebUEiTMK → UKF0widU → wTIxxeU2 → vfT9nUI3 → seN0waJ6 → wmLCkcB2 → ubYGgPM4 → qQF8oiX8 → igT6qUHG → kSP0wYVE → wW92uoR2 → usf4sI54 → qonMaA98 → ifdDjKIG → WSNIeaVS → MD42utkc → spXFhQ86 → mhS6qVGC → kaR2uWNE → sWD4skR6 → omX4sQBA → oeb6qMJA → keLEicJE → WULGgcTS → QH40wtgY → wpP7pY82 → uih8oGF4 → qgTQWUH8 → iP60wrYG → wlS8oVC2 → ugZ2uOH4 → sqPAmY76 → mjc8oLEC → gaVGgSNI → QOD2ukZY → sXB7pmQ6 → mib6qMFC → kaTEiUNE → WUD0wkTS → wX40wtQ2 → wup6q832 → urkgGD64 → qlXPXQC8 → iZ86qpOG → khSAmVGE → cWR2uWRM → sG54ssh6 → onmQWBAA → edb5rMKK → mKJEiedC → aULIecTO → MHC0wlgc → wZPFhYO2 → uSB8omV4 → qgb2uMH8 → siPEiYF6 → mUT8oUTC → ga10wwNI → wvOCkZ22 → utYAmP44 → qpc8oL88 → ihgGgHGG → SRQOYXWW → A753tsqo → qnjdJEA8 → idVJdSKG → SKJ2uedW → sLJ3tec6 → qmLGgcB8 → ibQGgXMG → SQF6qiXW → kT73tqUE → qjW0wRE8 → wiV4sSF2 → uoT2uU94 → sqf0wI76 → wmjMaEB2 → ubVDjSM4 → qWF2uiR8 → siT4sUF6 → omT0wUBA → web0wMJ2 → wuLEic32 → urUGgT64 → qlQ0wXC8 → wiZ6qOF2 → ukTAmUD4 → qcX0wQL8 → wiH6qgF2 → ukTOYUD4 → qXA0wnQ8 → wid6qKF2 → ukTIeUD4 → qXM0wbQ8 → wiF6qiF2 → ukTSUUD4 → qX20wvQ8 → wti6qF42 → upkSUD84 → qhX1vQG8 → uiR6qWF4 → qkT4sUD8 → oiX0wQFA → weT6qUJ2 → ukL0wcD4 → wqXGgQ72 → ujQ6qXE4 → qkV6qSD8 → kiX2uQFE → sWT6qUR6 → mk50wsDC → wnaWQNA2 → udD5rkK4 → qmXIeQB8 → ibM6qbMG → kSFEiiVE → WUT2uUTS → s410wwt6 → wvplB822 → uthZNG44 → qpRBlW88 → iha4sNGG → oSRCkWVA → eY52usPK → snK8odA6 → mgdIeKHC → aPMIebYO → MFC8olic → gZTFhUOI → SOB0wmZW → wbB3tmM2 → uqbEiM74 → qjUEiTE8 → iVU0wTSG → wS30wuV2 → wur2u632 → usrkC654 → qnlXPCA8 → idZ7pOKG → iSJAmeVG → cSL2ucVM → sHG2uhg6 → smROYWB6 → mbA4snMC → odaEiNKA → eUJCkeTK → YLK0wdcQ → wJH7pge2 → uiPKcYF4 → qTI8ofU8 → igN0waHG → wSPCkYV2 → uY92uoP4 → sqf8oI76 → mjgMaHEC → aVPDjYSO → WC92uolS → sfZ3tOI6 → qmNAmaB8 → icbCkMLG → YSHEigVQ → UP82upYU → sh8xxoG6 → rpc6qL87 → ljhGgGED → YVRPXWSQ → 9752usqp → snjfHEA6 → mdVNZSKC → aJC2uleO → sZLBlcO6 → maHAmgNC → caPCkYNM → YGD8okhQ → gXR7pWQI → iO74sqZG → ojSAmVEA → ecV2uSLK → sKH2ugd6 → smPIeYB6 → mbM8obMC → gaFEiiNI → UTOCkZUU → YB0xxwmQ → xmWDjRB1 → wbW4sRM2 → uoF4si94 → qofSUI98 → ifN1vaIG → uSNCkaV4 → qYD2ukP8 → siX8oQF6 → mgT6qUHC → kaP0wYNE → wWD8okR2 → ugX4sQH4 → qoP6qY98 → kif8oIFE → gWTMaURI → OE50wsja → wnVBlSA2 → uda2uNK4 → sqJCke76 → mjYKcPEC → aVI8ofSO → gNC2ulaI → sZOCkZO6 → mYBAmmPC → cba8oNMM → gGFCkihI → YTRNZWUQ → C850wspm → wnhZNGA2 → udRBlWK4 → qaJ4seN8 → oiLCkcFA → eYTGgUPK → QK90wodY → wfJ7peI2 → uiNKcaF4 → qTICkfU8 → iYN0waPG → wSD8okV2 → ugX2uQH4 → sqP6qY76 → mkj8oEDC → gaXUSQNI → OD71vqka → ujXBlQE4 → qaV6qSN8 → kiD2ukFE → sXWSURQ6 → m751vsqC → unjZNEA4 → qdVBlSK8 → iaJ2ueNG → sSLCkcV6 → mYH2ugPC → saP8oYN6 → mgD8okHC → gaXOYQNI → ODA6qnka → kdXBlQKE → aWJ6qeRO → kLC4slcE → oZWGgROA → eQB4smXK → obK6qdMA → keJEieJE → WULKccTS → IH40wtgg → wpPNZY82 → uhC8olG4 → qgZQWOH8 → iPB5rmYG → mbS8oVMC → gaF2uiNI → sTOCkZU6 → mYB0wmPC → wba8oNM2 → ugFCkiH4 → qYTOYUP8 → iA90wonG → wfdRVKI2 → uNJ3tea4 → rpLCkc87 → khYGgPGE → WRQ8oXWS → g753tsqI → qnjNZEA8 → idVBlSKG → aSJ2ueVO → sLC2ulc6 → smZGgOB6 → mbQAmXMC → caF6qiNM → kTGCkhUE → YWR0wWRQ → w854ssp2 → uongGA94 → qfdPXKI8 → iNJ7peaG → iSLCkcVG → YSH2ugVQ → sP82upY6 → smh8oGB6 → mgbQWMHC → aPF5riYO → mTC8olUC → gaZ0wONI → wODAmkZ2 → ucXAmQL4 → qcH6qgL8 → kiPGgYFE → WTQ8oXUS → g740wtqI → wpjNZE82 → uhVBlSG4 → qaR2uWN8 → siD4skF6 → omXSUQBA → eb71vqMK → ujKEidE4 → qVUIeTS8 → iM30wubG → wrSEiV62 → ulU2uTC4 → sqZ0wO76 → wmjAmEB2 → ucbUSML4 → qHF1vig8 → uiTOYUF4 → qTA0wnU8 → wid0wKF2 → wuTIeU32 → urM0wb64 → wqlEiC72 → ujZTTOE4 → qVAxxmS8 → pnOGgZA9 → gdQAmXKI → cOJ6qeZM → kLGAmhcE → cWRGgWRM → QG54sshY → onR7pWAA → ied4sKJG → oSLIecVA → eMH2ugbK → sPKEidY6 → mUJ8oeTC → gaL0wcNI → wOHCkgZ2 → uYPAmYP4 → qc98ooL8 → igfGgIHG → SQPMaYXW → E973tqok → qjfVRIE8 → iVN3taSG → qSD2ukV8 → siX2uQF6 → smT6qUB6 → mkb0wMDC → waXEiQN2 → uUD6qkT4 → qkX0wQD8 → wiX6qQF2 → ukT6qUD4 → qkX0wQD8