Base 69: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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 → 0Η → Ζ1 → Δ3
335 max steps100 → 0ΗΗ → ΖΗ1 → ΕΗ2 → ΔΗ3 → ΓΗ4 → ΒΗ5 → ΑΗ6 → zΗ7 → yΗ8 → xΗ9 → wΗA → vΗB → uΗC → tΗD → sΗE → rΗF → qΗG → pΗH → oΗI → nΗJ → mΗK → lΗL → kΗM → jΗN → iΗO → hΗP → gΗQ → fΗR → eΗS → dΗT → cΗU → bΗV → aΗW → ZΗX → YΗY
44 max stepsZ000 → YΗΗY → YXYZ → 1ΗΗΖ → Ζ0Ζ2
531 max steps30000 → 2ΗΗΗΕ → Ε1ΗΕ3 → ΖΑΗ52 → ΕzΗ63 → ΔxΗ84 → ΓuΗB5 → ΒqΗF6 → ΑlΗK7 → zfΗQ8 → yYΗX9 → xQΗfA → wWΗZB → vPΗgC → uVΗaD → tOΗhE → sUΗbF → rNΗiG → qTΗcH → pMΗjI → oSΗdJ → nLΗkK → mRΗeL → lKΗlM → mOΗhL → lNΗiM → kNΗiN → jMΗjO → kKΗlN → mNΗiL → lOΗhM → kMΗjN
6193 max stepsN000VX → XVMjba → N62ΔΑk → ΒuMjC6 → viMjOC → jNJmjO → TMKlke → ROAvig → lKErmM → dSOheU → JC8xuo → piUbOI → XK6zma → tS2ΔeE → ΒfBuR6 → vjDsNC → jfLkRO → PLDsli → fQIngS → VGCtqc → ha6zWQ → tH3ΓpE → zfXYR8 → rE0ΖsG → ΖeaVS2 → ΔC4Βu4 → zxhO98 → roInIG → bWUbaW → 753ΓΒΑ → zwsDA8 → rmeRKG → bSCteW → hC4ΒuQ → xiGpOA → nZJmXK → US1Εed → ΔC8xu4 → zphOH8 → rYInYG → bUΗΗbW → cZΗΗWV → ba2ΔWW → Β53ΓΒ6 → zwuBA8 → rmiNKG → bSKleW → RC4Βug → xiErOA → ndJmTK → US9wed → nC8xuK → piSdOI → XKAvma → lS2ΔeM → ΒPBuh6 → vjHoNC → jXLkZO → PL1Εli → ΔQIng4 → zVFqb8 → rb5ΑVG → vb5ΑVC → vj5ΑNC → vjLkNC → jPLkhO → PLHoli → XQInga → VG2Δqc → Βa6zW6 → vt3ΓDC → zjfQN8 → rMErkG → dbNiVU → L95Αxm → voQfIC → jWEraO → dL3ΓlU → zQ8xg8 → rpFqHG → caXYWV → 740ΖΓΑ → ΖysD82 → ΔqeRG4 → zaCtW8 → rh3ΓPG → zbHoV8 → rX5ΑZG → vb1ΕVC → Δj5ΑN4 → zvLkB8 → rkOhMG → bOIniW → VK4Βmc → xS6zeA → tnBuJE → jfTcRO → LE8xsm → peQfSI → XFBura → jc2ΔUO → ΒL7yl6 → vrPgFC → jcGpUO → ZL7ylY → rQ0ΖgG → ΖbFqV2 → Δb5ΑV4 → zv5ΑB8 → vrjMFC → jcMjUO → NL7ylk → rQMjgG → bNFqjW → bM4ΒkW → xO4ΒiA → xnJmJA → nUSdcK → TB7yve → rkAvMG → lbNiVM → PL5Αli → vQIngC → jVFqbO → bL5ΑlW → vQ4ΒgC → xjFqNA → nbLkVK → TP5Αhe → vIAvoC → ljVaNM → PM4Βki → xOIniA → nVJmbK → US5Αed → vC8xuC → pjhONI → XMInka → VO2Δic → ΒK6zm6 → vtReDC → jgCtQO → hLFqlQ → bQGpgW → ZG4ΒqY → xa0ΖWA → Ζn3ΓJ2 → ΔzTc74 → zs8xE8 → rpdSHG → bYAvYW → l4ΗΗΒM → ΓkFqM5 → xbNiVA → nL5ΑlK → vTPgdC → jH9wpO → nYKlYK → TQΗΗfe → gd0ΖTR → ΖF9wr2 → ΔnbUJ4 → zU6zc8 → tr7yFE → rfbURG → bE6zsW → te4ΒSE → xfBuRA → njDsNK → fTLkdS → PD9wti → ngInQK → VTFqdc → bA6zwW → tm4ΒKE → xfReRA → nECtsK → heSdSQ → HCAvuq → liYXOM → PK0Ζmi → ΖSIne2 → ΔVBub4 → zj5ΑN8 → vrLkFC → jcOhUO → LJ7ynm → rUQfcG → bF7yrW → rc4ΒUG → xb7yVA → rn5ΑJG → vbTcVC → j95ΑxO
740 max stepsY000000 → XΗΗΗΗΗZ → ZWΗΗΗZY → aYWΗZYX → a30ΗΖΔX → ΗΓVΗa41 → ΖΓWΗZ42 → ΕΒVΗa53 → ΔzVΗa74 → ΓwTΗcA5 → ΒsSΗdE6 → ΑnPΗgJ7 → zhNΗiP8 → ycIΗnU9 → xgIΗnQA → wfMΗjRB → vaHΗoWC → ueHΗoSD → tdLΗkTE → sYGΗpYF → rcGΗpUG → qbKΗlVH → pWFΗqaI → rYIΗnYG → qZEΗrXH → saIΗnWF → raGΗpWG → qbIΗnVH → pYHΗoYI → pXFΗqZI → rYHΗoYG → qaFΗqWH → rZJΗmXG → qYEΗrYH → saHΗoWF → rbHΗoVG → qaIΗnWH → pYGΗpYI → qXGΗpZH → qZHΗoXH → pZGΗpXI
8441 max steps100000CΓ → ΓC0ΗΗΖu5 → ΗΒt7yD51 → ΖwrfQFA2 → ΔmcErUK4 → zdS7yeT8 → sqC9wuGF → nidZWTOK → TKA2Δwme → ΒmSAveK6 → vlSBueLC → kiQBugON → jNKFqmjO → bSMKlkeW → ROC4Βuig → xiKErmOA → ndSJmeTK → USC9wued → niC8xuOK → piTJmdOI → XTK9wmda → nSA2ΔweK → ΒmTBudK6 → vjS9weNC → njMBukNK → jTOLkidO → PLK9wmli → nSQIngeK → VTGBuqdc → jaA6zwWO → tmL3ΓlKE → zfSPgeR8 → rHEBuspG → jebXYVSO → LC60ΖΑum → ΖuiQfOC2 → ΔiKErmO4 → zdSJmeT8 → rTC9wudG → nib9wVOK → nTK5ΑmdK → vTS9wedC → njC9wuNK → niTLkdOK → TPK9wmhe → nSIAvoeK → lWTBudaM → jPA3ΓwhO → zmLHolK8 → rXSPgeZG → bHC1ΕupW → ΔiY4ΒYO4 → zxJΗΗm98 → yxgAvQ99 → polFqLII → bXWPgaZW → H541ΕΓΒq → ΔywYXA84 → zqm0ΖKG8 → ΖraReWF2 → ΔcD3ΓtU4 → Αyg7yQ87 → trqFqGFE → fcbZWVUS → D862ΔΑyu → ΒuqgPGC6 → viaGpWOC → jZK3ΓmXO → zSL1Εle8 → ΔrQBugF4 → zjcFqUN8 → rbM7ykVG → rbO5ΑiVG → vbK5ΑmVC → vjS5ΑeNC → vjMBukNC → kiOLkiON → PNKJmmji → TSMInkee → VOCAvuic → liK6zmOM → tSPJmheE → fTIBuodS → jWD9wtaO → ngL3ΓlQK → zTQFqgd8 → rbG9wqVG → nba5ΑWVK → vT63ΓΑdC → zuj9wNC8 → rniLkOJG → bUPJmhcW → TI84Βyoe → xqWAvaGA → nla3ΓWLK → zTQ3Γgd8 → zrG9wqF8 → rncZWUJG → bU82ΔycW → Βq84ΒyG6 → xvqZWGBA → nka2ΔWMK → ΒTO3Γid6 → zvK9wmB8 → rnkReMJG → bUOCticW → hK84ΒymQ → xqSGpeGA → naZBuXWK → jT41ΕΓdO → ΔyL9wl84 → zqnPgJG8 → raUGpcWG → bZ83ΓyXW → zq51ΕΒG8 → ΔwrZWFA4 → zmc2ΔUK8 → ΒrS7yeF6 → vrcBuUFC → kic7yUON → rNK7ymjG → rbSLkeVG → bPC5ΑuhW → viI4ΒoOC → xjWJmaNA → nTM3ΓkdK → zTO9wid8 → rnK9wmJG → nbURecVK → TD85Αyte → vqgAvQGC → ljaFqWNM → bPM3ΓkhW → zOI4Βoi8 → xrWJmaFA → ncT3ΓdUK → zTA7ywd8 → sqm9wKGF → ndaReWTK → TDA3Γwte → zmgAvQK8 → rlSFqeLG → caQBugWV → jG73ΓzqO → zsaKlWE8 → reR3ΓfSG → zbEBusV8 → rje5ΑSNG → vbMBukVC → kiO5ΑiON → vNKJmmjC → jTSLkedO → PLC9wuli → niQIngOK → VTKFqmdc → bSA6zweW → tmC4ΒuKE → xifReROA → nKECtsmK → heTRedSQ → HDC9wutq → nigYXQOK → TKG0Ζqme → ΖaSAveW2 → ΔlC3ΓuL4 → ΑyiPgO87 → tqKGpmGE → faZReXWS → EC41ΕΓut → ΔyieRO84 → zqKCtmG8 → rhaReWPG → bID3ΓtoW → zgW4ΒaQ8 → xrG3ΓqFA → zncZWUJ8 → rU82ΔycG → Βqb7yVG6 → vra5ΑWFC → vjc3ΓUNC → zjM7ykN8 → sqOLkiGF → daPJmhWU → TI93Γxoe → zoWAvaI8 → rlW3ΓaLG → zbQ3ΓgV8 → zrG5ΑqF8 → vrcZWUFC → jc82ΔyUO → ΒqL7ylG6 → vraPgWFC → jcH3ΓpUO → zYL7ylY8 → sqPΗΗgGF → rqT9wdGG → nba9wWVK → nT63ΓΑdK → zuT9wdC8 → rni9wOJG → nbUJmcVK → US85Αyed → vqC8xuGC → pjiZWONI → XMK2Δmka → ΒSO2Δie6 → ΒvKBumB6 → vkjReNMC → jOMCtkiO → hOLJmliQ → TQKGpmge → ZSGAvqeY → laC0ΖuWM → ΖiP3ΓhO2 → ΔzKHom74 → zsXReZE8 → reD1ΕtSG → ΔgbBuVQ4 → zjG5ΑqN8 → vraLkWFC → jcP3ΓhUO → zLI7yol8 → sqWPgaGF → daH3ΓpWU → zY93ΓxY8 → zrnΗΗIF8 → yrh3ΓPF9 → zpcHoUH8 → rYX7yZYG → rb1ΗΗΕVG → ΖqZFqXG2 → Δba1ΕWV4 → Δz63ΓΑ74 → ΑyurEC87 → tqicTOGE → faK8xmWS → pSD3ΓteI → zgXBuZQ8 → rjG1ΕqNG → ΔbaLkWV4 → zP63ΓΑh8 → zurHoFC8 → ricWZUOG → bK82ΔymW → ΒqS4ΒeG6 → xvaBuWBA → nkj3ΓNMK → zTOLkid8 → rPK9wmhG → nbSHoeVK → XTC5Αuda → viA2ΔwOC → ΒmjJmNK6 → vTSLkedC → jPC9wuhO → niLHolOK → XTQJmgda → TGA2Δwqe → ΒmaAvWK6 → vlS3ΓeLC → zjQBugN8 → rjMFqkNG → caOLkiWV → PK73Γzmi → zsSIneE8 → reVBubSG → jbC5ΑuVO → viL5ΑlOC → vjQJmgNC → jTMFqkdO → bOL9wliW → nQK4ΒmgK → xTSFqedA → nbC9wuVK → niT5ΑdOK → vTK9wmdC → njS9weNK → nTMBukdK → jTO9widO → nLK9wmlK → nTSPgedK → THC9wupe → niYAvYOK → lTJΗΗmdM → nkJ7ynMK → rUTNidcG → bLA7ywlW → rmQ4ΒgKG → xbSFqeVA → nbC5ΑuVK → viT5ΑdOC → vjK9wmNC → njSLkeNK → TPMBukhe → jOIAvoiO → lWLJmlaM → TQP3Γhge → zIGAvqo8 → rlaVaWLG → bQ53ΓΒgW → zwG4ΒqA8 → xrmZWKFA → ncS2ΔeUK → ΒTC7yud6 → vri9wOFC → njcJmUNK → USM7yked → rOC8xuiG → pibJmVOI → XTK5Αmda → vSA2ΔweC → ΒmjBuNK6 → vjSLkeNC → jPMBukhO → jOLHoliO → XQLJmlga → TQG2Δqge → ΒaGAvqW6 → vla3ΓWLC → zjQ3ΓgN8 → zrMFqkF8 → rcbNiVUG → bL85ΑylW → vqQ4ΒgGC → xjaFqWNA → nbM3ΓkVK → zTO5Αid8 → vrK9wmFC → njcReUNK → TMD7ytke → rgOAviQG → lbKFqmVM → bSP5ΑheW → vIC4ΒuoC → xjiVaONA → nMK4ΒmkK → xTSNiedA → nLC9wulK → niTPgdOK → TKH9wpme → nYSAveYK → lTBΗΗudM → vkR7yfMC → rjODsiNG → fbMJmkVS → TOD5Αtie → vgKAvmQC → ljSFqeNM → bPMBukhW → jOI4ΒoiO → xWLJmlaA → nTQ3ΓgdK → zTG9wqd8 → rna9wWJG → nbU3ΓcVK → zT85Αyd8 → vrq9wGFC → njcZWUNK → TM82Δyke → ΒqOAviG6 → vlaJmWLC → jTQ3ΓgdO → zLG9wql8 → rnaPgWJG → bUH3ΓpcW → zY84ΒyY8 → xrpΗΗGFA → wrh1ΕPFB → ΔlcHoUL4 → zXQ7ygZ8 → sqG1ΕqGF → ΔdaZWWT4 → zA42ΔΓw8 → ΒyrlKF86 → vqcQfUGC → jaF7yrWO → rcL3ΓlUG → zbQ7ygV8 → sqG5ΑqGF → vdaZWWTC → jA42ΔΓwO → ΒymKlK86 → vqSQfeGC → jaFBurWO → jcL3ΓlUO → zQL7ylg8 → sqQFqgGF → dbaFqWVU → b963ΓΑxW → zuo4ΒIC8 → xriVaOFA → ncK4ΒmUK → xTS7yedA → rnC9wuJG → nibTcVOK → TK95Αxme → voSAveIC → ljWBuaNM → jPM3ΓkhO → zOLHoli8 → rXQJmgZG → bTG1ΕqdW → ΔaA4ΒwW4 → zxm3ΓK98 → zroReIF8 → rcWCtaUG → hb83ΓyVQ → zqH5ΑpG8 → vraXYWFC → jc40ΖΓUO → ΖyL7yl82 → ΔrqPgGF4 → zcaGpWU8 → rZ83ΓyXG → zqb1ΕVG8 → Δra5ΑWF4 → zvc3ΓUB8 → zrk7yMF8 → sqcNiUGF → daL7ylWU → rQ93ΓxgG → zobFqVI8 → rbW5ΑaVG → vb63ΓΑVC → zuj5ΑNC8 → vriLkOFC → jcPJmhUO → TLI7yole → rWQAvgaG → lbG3ΓqVM → zaP5ΑhW8 → vrI3ΓoFC → zjcVaUN8 → rM84ΒykG → xqbNiVGA → naL5ΑlWK → vTQ3ΓgdC → zjG9wqN8 → rnaLkWJG → bUP3ΓhcW → zI84Βyo8 → xrqVaGFA