Base 76: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
232 max steps20 → 1Ν → Λ3Η7yFiVoPOpQnMrUjEzkTGxgXwHeZΕ9uJadΙ5ΓBqNSlIvcbΝ1Λ3
340 max steps100 → 0ΞΞ → ΝΞ1 → ΜΞ2 → ΛΞ3 → ΚΞ4 → ΙΞ5 → ΘΞ6 → ΗΞ7 → ΖΞ8 → ΕΞ9 → ΔΞA → ΓΞB → ΒΞC → ΑΞD → zΞE → yΞF → xΞG → wΞH → vΞI → uΞJ → tΞK → sΞL → rΞM → qΞN → pΞO → oΞP → nΞQ → mΞR → lΞS → kΞT → jΞU → iΞV → hΞW → gΞX → fΞY → eΞZ → dΞa → cΞb → bΞcbΞc
419 max steps700C → C6ΗΓ → ΑpNE → mRlS → LIut → cXfc → 7ΞΞΗ → Η6Η8 → ΑxFE → mhVS → KBΒuqZdOS3ΚmΗJt8yZdGi3ΚWΗBΒ8ypNGiRlWKBΒu
534 max steps1000F → F0ΞΝz → ΞwΞG1 → ΝwΞG2 → ΜvΞH3 → ΛtΞJ4 → ΚqΞM5 → ΙmΞQ6 → ΘhΞV7 → ΗbΞb8 → ΖUΞi9 → ΕaΞcA → ΔTΞjB → ΓZΞdC → ΒSΞkD → ΑYΞeE → zRΞlF → yXΞfG → xQΞmH → wWΞgI → vPΞnJ → uVΞhK → tOΞoL → sUΞiM → rNΞpN → qTΞjO → pMΞqP → rQΞmN → qQΞmO → pPΞnP → oPΞnQ → oNΞpQqOΞoOpRΞlPoNΞpQ
6290 max stepsO000ss → ssNpLM → XWRlhh → KB9ΔΓu → urZdMK → aV3Κie → ΗD3ΚΑ8 → ΗymQF8 → yjLrUG → iWEyhW → kCAΓΒU → spFxOM → iWQmhW → MCAΓΒs → spVhOM → WRBΒmi → qLBΒsO → qXRlgO → SK8Εtm → wZJteI → ea4Ιda → Ε42ΛΚA → ΙΖtJ86 → ΓxZdGC → qh3ΚWO → ΗSAΓl8 → ysIuLG → icWgbW → CA0ΝΔΓ → ΝtpNK2 → ΛZRle4 → ΗK4Ιt8 → ΕyYeFA → uj5ΘUK → ΓaEydC → qk2ΛTO → ΙSGwl6 → ΓgIuXC → qc8ΕbO → wS0ΝlI → ΝeIuZ2 → Λc4Ιb4 → ΗΕ0Ν98 → ΝyuIF2 → ΛjbbU4 → ΗEΞΞy8 → Ζz7ΖE9 → ywkSHG → ifHvYW → eC6ΗΒa → Αp3ΚOE → ΗmQmR8 → yMKsrG → iYUifW → EC6ΗΒΑ → ΑplROE → mRJtmS → aLJtse → aX3Κge → Η93ΚΕ8 → ΗyuIF8 → yjbbUG → iEΞΞyW → zhFxWF → kiAΓVU → sGCΑxM → ohVhWQ → OCAΓΒq → spRlOM → WRJtmi → aLBΒse → qX3ΚgO → ΗS8Εl8 → ywIuHG → ifbbYW → C6ΞΞΗΓ → ΘΒ3ΚC7 → ΗΑoOD8 → ynPnQG → iOMqpW → URBΒmk → qLFxsO → iXRlgW → KC8ΕΒu → wpZdOI → eR3Κma → ΗL3Κs8 → ΗyWgF8 → yj9ΔUG → uiEyVK → kaCΑdU → oG2ΛxQ → ΙhNpW6 → ΓSAΓlC → sqIuNM → cWSkhc → IAΞΞΓw → Δv5ΘIB → ΓscaLC → qX1ΜgO → ΛS8Εl4 → ΗwIuH8 → yfbbYG → i6ΞΞΗW → ΘhNpW7 → ΑSAΓlE → smIuRM → cWKshc → YAΞΞΓg → ΔfLrYB → sW6ΗhM → ΑWAΓhE → smAΓRM → sWKshM → YWAΓhg → sB7ΖΓM → yrVhMG → iVBΒiW → qDBΒΑO → qnRlQO → SNJtqm → aTJtke → aH3Κwe → Ηf3ΚY8 → Ηy6ΗF8 → ΑyiUFE → mjDzUS → mKEytS → kZJteU → aG4Ιxe → Εh3ΚWA → ΗuAΓJ8 → ysacLG → iX1ΜgW → ΛC8ΕΒ4 → ΗwoOH8 → yfPnYG → iO6ΗpW → ΑRBΒmE → qmKsRO → YSKslg → YJ7Ζug → yb7ΖcG → yi0ΝVG → ΝiCΑV2 → ΛoCΑP4 → ΗoOoP8 → yQOonG → iQMqnW → UNBΒqk → qTFxkO → iSGwlW → gJBΒuY → qb7ΖcO → yS0ΝlG → ΝiIuV2 → ΛcCΑb4 → Ηo0ΝP8 → ΝyOoF2 → ΛjPnU4 → ΗOEyp8 → ykQmTG → iMGwrW → gVBΒiY → qD7ΖΑO → ynRlQG → iNJtqW → aTBΒke → qH3ΚwO → ΗfRlY8 → yK6ΗtG → ΑiYeVE → mD5ΘΑS → ΓnJtQC → qaMqdO → US2Λlk → ΙJFxu6 → ΓiacVC → qD1ΜΑO → ΛnRlQ4 → ΗNJtq8 → yaSkdG → iI2ΛvW → ΙdBΒa6 → Γq2ΛNC → ΙqSkN6 → ΓTHvkC → qeGwZO → gS4ΙlY → ΕJ7ΖuA → yuacJG → ib1ΜcW → ΛC0ΝΒ4 → ΝΗoO72 → ΛzPnE4 → ΗlNpS8 → ySIulG → icIubW → cC0ΝΒc → ΝoΞΞO2 → ΜpNpO3 → ΙSQml6 → ΓMIurC → qcUibO → SE0Νzm → ΝlJtS2 → ΛaIud4 → Ηc2Λb8 → Ιy0ΝF6 → ΝΓiUB2 → ΛrDzM4 → ΗmUiR8 → yLDzsG → miWgVS → KD9ΔΑu → unZdQK → aN3Κqe → ΗT3Κk8 → ΗyGwF8 → yjfXUG → iF7ΖyW → yjBΒUG → qiEyVO → kSCΑlU → oJFxuQ → ibNpcW → SC0ΝΒm → ΝpJtO2 → ΛaQmd4 → ΗM2Λr8 → ΙyUiF6 → ΓjDzUC → qmEyRO → kSKslU → YJFxug → ib7ΖcW → yC0ΝΒG → ΝphVO2 → ΛRBΒm4 → ΗqKsN8 → yYSkfG → iI6ΗvW → ΑdBΒaE → qm2ΛRO → ΙSKsl6 → ΓYIufC → qc6ΗbO → ΑS0ΝlE → ΝmIuR2 → ΛcKsb4 → ΗY0Νf8 → Νy6ΗF2 → ΛΑiUD4 → ΗnDzQ8 → ymMqRG → iUKsjW → YFBΒyg → qj7ΖUO → ySEylG → kiIuVU → cGCΑxc → ogΞΞWQ → nh7ΖWR → yMAΓrG → siUiVM → WECΑzi → olBΒSQ → qOIupO → cSQmlc → MIΞΞus → vr1ΜMJ → ΛcUib4 → ΗE0Νz8 → ΝykSF2 → ΛjHvU4 → ΗeEyZ8 → yk4ΙTG → ΕiGwVA → ugCΑXK → oa8ΕdQ → wO2ΛpI → ΙeQmZ6 → ΓM4ΙrC → ΕqUiNA → uTDzkKmaGwdSgK2ΛtYΙZ7Ζe6Γy4ΙFCΕqiUNAuTDzkK
749 max steps1000000 → 0ΞΞΞΞΞΞ → ΝΞΞΞΞΞ1 → Ν0ΞΞΞΝ2 → ΞΜ0ΞΝ21 → ΞΝΚΞ311 → ΝΝΙΞ412 → ΝΛΘΞ532 → ΜΚΕΞ843 → ΛΘΑΞC64 → ΚΕuΞI95 → ΙΑlΞRD6 → ΘvYΞeI7 → ΗpMΞqO8 → ΖkRΞlT9 → ΕeHΞvZA → ΔnLΞrQB → ΓiQΞmVC → ΒcGΞwbD → ΑlKΞsSE → zgPΞnXF → yaFΞxdG → yiMΞqVG → xcKΞsbH → wdGΞwaI → xeLΞrZH → wcHΞvbI → weJΞtZI → vdJΞtaJ → ucIΞubK → vaIΞudJvcJΞtbJucHΞvbKwbIΞucIveIΞuZJvcKΞsbJubGΞwcKxcIΞubHwfIΞuYIveLΞrZJuaHΞvdKwbJΞtcIvdHΞvaJwcKΞsbIvcGΞwbJxdJΞtaHweIΞuZIveKΞsZJubIΞucKvaIΞudJ