Base 63: 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
27 max steps10 → 0Α → z1 → x3 → t7 → lF → VV → 00
332 max steps100 → 0ΑΑ → zΑ1 → yΑ2 → xΑ3 → wΑ4 → vΑ5 → uΑ6 → tΑ7 → sΑ8 → rΑ9 → qΑA → pΑB → oΑC → nΑD → mΑE → lΑF → kΑG → jΑH → iΑI → hΑJ → gΑK → fΑL → eΑM → dΑN → cΑO → bΑP → aΑQ → ZΑR → YΑS → XΑT → WΑU → VΑV
44 max stepsW000 → VΑΑV → VUVW → 1ΑΑz → z0z2
531 max steps10000 → 0ΑΑΑΑ → zΑΑΑ1 → z0Αz2 → ΑwΑ31 → zwΑ32 → yvΑ43 → xtΑ64 → wqΑ95 → vmΑD6 → uhΑI7 → tbΑO8 → sUΑV9 → rNΑcA → qTΑWB → pMΑdC → oSΑXD → nLΑeE → mRΑYF → lKΑfG → kQΑZH → jJΑgI → iPΑaJ → hIΑhK → iMΑdJ → hLΑeK → gLΑeL → fKΑfM → gIΑhL → iLΑeJ → hMΑdK → gKΑfL
685 max steps4000Nw → wN3wd5 → trFk98 → liUVIG → VQ0zaW → zA0zq2 → zxfK32 → xuKf64 → toKfC8 → lcKfOG → VLDmfW → ZK0zgS → zM6te2 → xnHiD4 → taQZQ8 → lA8rqG → jgUVKI → RM0zea → zI8ri2 → xjPaH4 → tSApY8 → lf5uLG → pVJgVC → dMΑΑdO → ebΑΑON → dc2xOO → vFDml6 → pZVURC → d80zsO → zkElG2 → xXTWT4 → t42xw8 → vskF86 → pkUVGC → dU0zWO → zF1yl2 → ywVU43 → vs0z86 → zpjGB2 → xeSXM4 → tI4vi8 → rlPaFA → hWApUK → fN1ydM → xJFkh4 → tVNcV8 → lEΑΑlG → mjΑΑGF → lk2xGG → vVTWV6 → p2ΑΑxC → yo7sC3 → vlbOF6 → pWCnUC → db1yPO → xFBol4 → tdVUN8 → lG0zkG → zVTWV2 → x2ΑΑx4 → yvΑΑ43 → xw2x44 → vtr876 → pmiHEC → dYQZSO → F95urm → piWTIC → dQ2xaO → vF9ql6 → phVUJC → dO0zcO → zFDml2 → xZVUR4 → t80zs8 → zljGF2 → xWSXU4 → t51yv8 → xqkFA4 → tgUVK8 → lM0zeG → zVHiV2 → xQΑΑZ4 → waNcQ5 → rF9qlA → igVUKJ → PM0zec
740 max stepsF0000GG → GGEΑlkl → mVUΑVVF → lHΑΑΑiG → kjHΑiHH → jTRΑYXI → iI4ΑviJ → wdOΑbN5 → vZEΑlR6 → uhJΑgJ7 → tbNΑcP8 → sWCΑnU9 → rgIΑhKA → qZMΑdRB → pUBΑoWC → pdJΑgNC → oWIΑhUD → nWCΑnUE → oZIΑhRD → nWFΑkUE → mYFΑkSF → lXHΑiTG → kUEΑlWH → mUFΑkWF → lXFΑkTG → lVGΑjVG → kVDΑmVH → nVEΑlVE → mZFΑkRF → lXIΑhTG → kTDΑmXH → nVGΑjVE → mXDΑmTF → nXIΑhTE → mVDΑmVF → nXGΑjTE → mXFΑkTF → lXGΑjTG → kVFΑkVH → lTEΑlXG → mVHΑiVF
8239 max stepsF0000JJN → NJJElhhe → XOOGjccU → TEE2xmmY → vYY4vSS6 → rp65uuBA → pohdMJCC → dcOGjcOO → TFEDmmlY → ZYW4vUSS → r761yutA → xomgJEC4 → tcYMdSO8 → lHE5umjG → pYVRYVSC → d75ΑΑutO → vtWFkU76 → pmV1yVEC → xdXΑΑSN4 → wdV5uVN5 → rpFΑΑkBA → qpc4vOBB → rfeDmMLA → hZKHigRK → RNM7seda → lIG8rkiG → jVUPaWVI → RB1ΑΑypa → zpXElTB2 → xeX3wTM4 → usI3wi87 → tnkPaGD8 → laUApWQG → fVA1yqVM → xgIΑΑhK4 → wid0zNI5 → zrQFka92 → xiV9qVI4 → thPΑΑaJ8 → shU6tWJ9 → njO1ycHE → xZSDmYR4 → tZ85usR8 → plk7sGFC → ldWTWUNG → VG31yxkW → xuU0zW64 → zto1yC72 → ywmbOE43 → vsYCnS86 → pkb5uPGC → pdUBoWNC → ecG1ykON → xUHDmjW4 → tZS1yYR8 → xl85usF4 → tpkVUGB8 → leU0zWMG → zVI1yiV2 → ywPΑΑa43 → xwZLeR44 → tsJ7sh88 → mkkNcGGF → XUUElWWU → X321yyxU → xwu2x644 → vtsnC876 → pmkaPGEC → dYUApWSO → fF61yulM → xoWIhUC4 → tcP1ybO8 → xlEBomF4 → tdYVUSN8 → lG60zukG → zoVTWVC2 → xc2ΑΑxO4 → ywZKfR43 → vsL7sf86 → plkJgGFC → dWUMdWUO → HF21yylk → xwWSXU44 → ts51yv88 → xqljGFA4 → tgWSXUK8 → lM51yveG → xqVHiVA4 → tgQΑΑZK8 → sgT6tXK9 → njM3weHE → tZSHiYR8 → lR85usZG → pkV7sVGC → ldTΑΑWNG → kdI6tiNH → nTQFkaXE → ZVA3wqVS → tg6ΑΑtK8 → usZCnR87 → nkb7sPGE → lZUBoWRG → dV81ysVO → xkEΑΑlG4 → wmh0zJE5 → zrYNcS92 → xiF5ulI4 → tpWPaUB8 → leB1ypMG → xeVHiVM4 → tRHΑΑiZ8 → sjS8rYH9 → kiS5uYIH → pTQ5uaXC → pdA3wqNC → tgdFkNK8 → lVMFkeVG → WUHΑΑiWV → jWCΑΑnUI → oiJCnhID → caQNcaQP → FDA9qqnm → hgaWTQKK → NMA2xqee → vgIGjiK6 → pTQLeaXC → dJA3wqhO → tgOElcK8 → lXMDmeTG → ZVI3wiVS → tQ6ΑΑta8 → usTIhX87 → nkP3wbGE → tZUBoWR8 → ld81ysNG → xkVFkVG4 → tVTΑΑWV8 → sXO0zcT9 → zjE3wmH2 → xtYRYS74 → tm75utE8 → pmlXSFEC → dYW4vUSO → rF61yulA → xohVUJC4 → tcO0zcO8 → zlEDmmF2 → xZYVUSR4 → t860zus8 → zoljGFC2 → xcWSXUO4 → tE51yvm8 → xqlXSFA4 → tgW4vUK8 → rlM1yeFA → xhWHiUJ4 → tRO1ycZ8 → xlE7smF4 → tlYVUSF8 → lW60zuUG → zoV1yVC2 → ywbΑΑO43 → xwaKfQ44 → tsL9qf88 → lkhJgJGG → VUOMdcWW → HE20zymk → zwYSXS42 → xs64vu84 → trojGC98 → licSXOIG → VQE4vmaW → rYA0zqSA → zhg5uKJ2 → xpOLecB4 → teJDmhM8 → lZOHicRG → VRE7smZW → lY80zsSG → zkV5uVG2 → xpTΑΑWB4 → wpUIhWB5 → reP1ybMA → xhIBoiJ4 → tdQNcaN8 → lGF9qlkG → hWVTWVUK → N31ΑΑyxe → zxbIhP32 → xuPBob64 → todBoNC8 → ldcFkONG → WUGDmkWV → ZU20zyWS → zw71yt42 → ywslE843 → vskWTG86 → pkU2xWGC → vdU1yWN6 → xpG1ykB4 → xteTWM74 → tmI2xiE8 → vlYPaSF6 → pWB5upUC → ped1yNMC → xdIFkiN4 → tVQFkaV8 → lV9ΑΑqVG → rkLFkfGA → hVUJgWVK → OM1ΑΑyed → zea0zQM2 → zxI9qi32 → xuhPaJ64 → toOApcC8 → lfcDmOLG → ZVKDmgVS → ZM6ΑΑteS → ueR4vZM7 → rnI7siDA → lhaPaQJG → VOB9qpcW → heE0zmMK → zYNHidS2 → xRG5ukZ4 → tpU7sWB8 → mke1yMGF → xXUHiWT4 → tR41ywZ8 → xsl7sF84 → tlkVUGF8 → lWU0zWUG → zV21yyV2 → ywvΑΑ443 → xwu0z644 → ztsnC872 → xmkaPGE4 → tYUApWS8 → lf61yuLG → xoVJgVC4