Base 61: 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
28 max steps10 → 0y → x1 → v3r7jFTV1xv3
333 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 → UyUTyVUyU
434 max stepsV000 → UyyU → UTUV → 1yyx → x0x2xu32vq74riF8jSVGT2vWt2v6tmB6naNCbClOZClQZ8pQh8pIhOZIPAnadAnMdGhMRGhYR6rYl6rElWREX4tSp4tApeJAfKdKLIfeNIfcNEjcVEjUV0xUx0x2
528 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 → eIyfLgJyeJfMybKeIyfL
6173 max stepsR000pp → ppQX9A → gf6rJJ → lNLcbE → XHDkhS → XQ4tYS → p84tqA → pieJGA → fSKdWK → LJ3ufe → rMIfc8 → jNFibG → USDkWV → X40xuS → xq4t82 → vphG94 → rgQXI8 → jO6raG → lTBmVE → bX1wRO → vD5sl4 → rnXQB8 → jc6rMG → lTFiVE → XT1wVS → v51wt4 → vrnA74 → rkcLE8 → jWGhSG → TR3uXW → r62vs8 → tmiFC6 → naSVOC → bC2vmO → taClO6 → nZBmPC → ca9oON → fFBmjK → bUKdUO → JCyylg → mf4tJD → pZLcPA → fH9ohK → fQKdYK → LJ7qfe → jMIfcG → TNFibW → TE2vkW → tW2vS6 → tn3uB6 → rnbMB8 → jcEjMG → VTFiVU → T20xwW → xu2v42 → vtp854 → rogHA8 → jeOZKG → TKAneW → dK2veM → tKGhe6 → nRJeXC → bL5sdO → nIClgC → bZNaPO → EC9oml → faWROK → LC4tme → paIfOA → fNBmbK → bLDkdO → XIClgS → ZO4taQ → pC8pmA → hfZOJI → PMAnca → dGAniM → dSGhWM → RH3uhY → rQ6rY8 → lj7qFE → jXTURG → T60xsW → xm2vC2 → vtZO54 → roAnA8 → jecLKG → TKGheW → RK2veY → tK6re6 → nlJeDC → bYKdQO → JD7qlg → jYMbQG → TF7qjW → jU2vUG → tSyyV6 → sWNaS7 → lD3ulE → rYWRQ8 → j84tqG → piSVGA → fS2vWK → tL3ud6 → rnHgB8 → jcOZMG → TGAniW → dS2vWM → tH3uh6 → rnPYB8 → jc8pMG → hTFiVI → TP1wZW → vA2vo4 → trdK76nkIfECbWMbSOFD3ulkrYUTQ8j80xqGxiSVG2vS2vW4tr3u76rnjEB8jcUTMGTG0xiWxS2vW2vt3u54sqnA87licLGEXSGhWSR53utYro6rA8ljdKFEXUIfUSN4yytcubGhN5pRDkXAfX5sRKnL5sdCnbHgNCbPDkZOXD9olSfY4tQKpL7qdAjfHgJGTPLcZWHA2voiteQXK6nK6reClbJeNEXLDkdSXI4tgSpO4taApfBmJAfbLcNKLHDkheXQIfYSN84tqcpiEjGAfVRWTKL51wtevoIfA4reMbK8jKEjeGVTJeVUL20xwexuIf42vqMb84riEjG8jVRWTGT51wtWvo2vA4trdK76
738 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 → jVEyjTGkTFyiVFjVEyjTG
8346 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 → 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