Base 60: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1w → u3
331 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
413 max steps200D → D1vl → uXP4 → q7p8 → jgGF → UPXU → 7xxq → q6q8 → khFE → WRVS → 52ut → sn96 → mdJC → aJdO
529 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
6112 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
725 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
8385 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