Base 61: 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
23 max steps10 → 0y → x1 → v3
331 max steps100 → 0yy → xy1 → wy2 → vy3 → uy4 → ty5 → sy6 → ry7 → qy8 → py9 → oyA → nyB → myC → lyD → kyE → jyF → iyG → hyH → gyI → fyJ → eyK → dyL → cyM → byN → ayO → ZyP → YyQ → XyR → WyS → VyT → UyU
44 max stepsV000 → UyyU → UTUV → 1yyx → x0x2
525 max stepsU0000 → TyyyV → VSyVU → W0yxT → yTyU1 → xUyT2 → wTyU3 → vSyV4 → uSyV5 → tRyW6 → sRyW7 → rQyX8 → qQyX9 → pPyYA → oPyYB → nOyZC → mOyZD → lNyaE → kNyaF → jMybG → iMybH → hLycI → gLycJ → fKydK → eKydL → eIyfL
6128 max stepsH000JP → PJGhfa → RMAncY → dG6riM → lSGhWE → XR3uXS → r64ts8 → pmiFCA → faSVOK → LC2vme → taIfO6 → nNBmbC → caDkON → XFBmjS → bU4tUO → pCyylA → om3uCB → rdZOL8 → jIAngG → dTNaVM → HD1wli → vYQXQ4 → r86rq8 → ljhGFE → XUQXUS → 74yyts → ur0x75 → xpjE92 → vgUTI4 → rO0xa8 → xjBmF2 → vbTUN4 → rE0xk8 → xjVSF2 → vU2vU4 → tqyy76 → sr2v77 → tljED6 → nYUTQC → b80xqO → xiClG2 → vZRWP4 → rA4to8 → pjdKFA → fUIfUK → NKyydc → eb0xNL → xJDkf2 → vXLcR4 → rH5sh8 → njPYFC → bU8pUO → hCyylI → mg3uID → rZNaP8 → jD9olG → fYSVQK → L82vqe → tiIfG6 → nSMbWC → bF3ujO → rUClU8 → jYyyPG → iZAnPH → dR9oXM → fH5shK → nQKdYC → bJ7qfO → jMClcG → ZTFiVQ → T91wpW → vg2vI4 → trNa76 → nkClEC → bZVSPO → DA2vom → teYPK6 → nK8peC → hbJeNI → PLDkda → XIAngS → dO4taM → pHBmhA → fbPYNK → LE8pke → hWIfSI → PN3uba → rEAnk8 → jdVSLG → TI2vgW → tO2va6 → tnBmB6 → ncaNMC → bGCliO → ZSClWQ → Z93upQ → rg8pI8 → jhNaHG → TQClYW → Z82vqQ → ti8pG6 → nhRWHC → bQ4tYO → pD7qlA → jfXQJG → TM6rcW → lG2viE → tXRWR6 → n64tsC → pmaNCA → faClOK → ZLBmdQ → bI8pgO → hOClaI → ZPBmZQ → bA8poO → heClKI → ZPJeZQ → LA8poe → heIfKI → PNJeba → LEAnke → dWIfSM → NH3uhc → rQEjY8 → jV7qTG → jT1wVG → vT1wV4 → vr1w74
736 max stepsU00000d → dTyyyUM → cVTyUTN → b91ywpO → xnQyXB2 → wmMybC3 → vkPyYE4 → uhKydH5 → tdMybL6 → sYGyhQ7 → rcGyhM8 → qbKydN9 → pWFyiSA → oaFyiOB → nZJyePC → mUEyjUD → lYEyjQE → kXIyfRF → jSDykWG → lUGyhUE → kVCylTF → mWGyhSD → lWEyjSE → kXGyhRF → jUFyiUG → jTDykVG → lUFyiUE → kWDykSF → lVHygTE → kUCylUF → mWFyiSD → lXFyiRE → kWGyhSF → jUEyjUG → kTEyjVF → kVFyiTF → jVEyjTG
8235 max stepsF0000JJM → MJJEjffd → VMMGhccU → RGG0xiiY → xSS6rWW2 → vl43uuD4 → sqqXQ887 → lii6rGGE → lXSRWWRE → X653utsS → rom4tCA8 → pjeZOKFA → fUKAneUK → dLJyyedM → fdHyygLK → heL1wdKI → vPKHgeZ4 → rPK9oeZ8 → jfK9oeJG → fTMJecVK → MKG1wied → vSKGheW4 → rRK3ueX8 → rjK5seF8 → njUJeUFC → bUKyydUO → ea96rpOL → lgJBmfIE → bXOLcaRO → HDC5smli → naYQXQOC → bC86rqmO → liaClOGE → ZXSBmWRQ → b963uspO → rmgClIC8 → jaZNaPOG → TDC9omlW → faY2vQOK → tLC7qmd6 → njaHgOFC → bUPBmZUO → bD9yyolO → plQ9oYDA → geY7qQKJ → jNK7qebG → jTKDkeVG → XTK1weVS → vK51wte4 → vroJeA74 → rkeKdKE8 → jWKIfeSG → TNK3uebW → rKE2vke8 → tjWJeSF6 → nUL3udUC → rbHyygN8 → qhU4tUH9 → phPyyYHA → ohQ8pYHB → hdQ7qYLI → jPI7qgZG → jTO9oaVG → fTC1wmVK → vaL1wdO4 → vrIBmg74 → rkbNaNE8 → jWEClkSG → ZWT3uVSQ → r941wup8 → vqjfIF84 → riUMbUG8 → jSEyyjWG → kiHClhGF → ZVSPYWTQ → A841wuqp → vqieJG84 → riSKdWG8 → jSJ3ufWG → rTM3ucV8 → rjG1wiF8 → vjURWUF4 → rU4yytU8 → uqPMbZ85 → piF9ojGA → geURWUKJ → NK4yytec → ueW1wSK5 → vpK3ue94 → sqgJeI87 → liOKdaGE → XSJBmfWS → bM53utcO → roGCliA8 → jeZRWPKG → TKA4toeW → peK2veKA → tfKJeeJ6 → nMLJedcC → bLIFigdO → TOIClgaW → ZOC2vmaQ → taC8pmO6 → nhaBmOHC → caQBmYON → bFC7qmjO → jaUClUOG → ZTByymVQ → nYJ3ufQC → rbM7qcN8 → kiGDkiGF → XVSRWWTS → 6441wuut → vqqmB884 → riiaNGG8 → jSSClWWG → ZT43uuVQ → rq91wp88 → vjifIGF4 → rUSMbWU8 → jF3yyujG → vjdyyKF4 → ujb5sNF5 → pnUDkUBA → fcWyyRMK → ecE5skML → nWJFifSC → bTM3ucVO → rGD1wli8 → vjYRWQF4 → rU84tqU8 → pjhyyGFA → ojZ1wPFB → vdU9oUL4 → rfHyygJ8 → qhY0xQH9 → xhQ7qYH2 → vjQ7qYF4 → rjU7qUF8 → kiTyyUGF → jiHDkhGG → XTSPYWVS → 9541wutq → vqogHA84 → rieOZKG8 → jSKAneWG → dTK3ueVM → rKH1whe8 → vjQJeYF4 → rUL7qdU8 → kiHyygGF → jiT1wVGG → vTS1wWV4 → vr41wu74 → vrqjE874 → rkiUTGE8 → jWS0xWSG → xT43uuV2 → vrq1w874 → vrkhGE74 → rkWQXSE8 → jW73urSG → rkT3uVE8 → rjW1wSF8 → vjU3uUF4 → sqTyyU87 → rqPLcZ88 → jiH9ohGG → fTSPYWVK → L941wupe → vqgIfI84 → riOMbaG8 → jSFBmjWG → bUT3uVUO → rD1yywl8 → xqj5sF82 → vniTUGB4 → rcS0xWM8 → xjG3uiF2 → vrURWU74 → rk4yytE8 → uqf6rJ85 → pliLcGDA → fYSGhWQK → RL83uqdY → riI6rgG8 → ljSNaWFE → XUD3ulUS → rY4yytQ8 → uqTIfV85 → piN1wbGA → vfSDkWJ4 → rXM3ucR8 → rjG5siF8 → njURWUFC → bU4yytUO → uaP6rZO5 → plC9omDA → geaXQOKJ → NKC6rmec → laKEjeOE → XVKBmeTS → bK51wteO → voKCleA4 → reZJePK8 → jLK9oedG → fTKHgeVK → PLK1weda → vKIAnge4 → rdOJeaL8 → jLIBmgdG → bTOHgaVO → PDC1wmla → vaYAnQO4 → rdC7qmL8 → kiaHgOGF → VSPBmZWU → bA40xuoO → xqeClK82 → viZJePG4 → rSL9odW8 → jfI3ugJG → rTOLcaV8 → jHC1wmhG → vaTPYVO4 → rC91wpm8 → vjgZOIF4 → rUOAnaU8 → jdByymLG → niR5sXGC → nbS5sWNC → nbE3ukNC → rbWDkSN8 → jXE3ukRG → rWT5sVS8 → nj41wuFC