Base 99: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
22 cycles10 nodes3κ → ζ7 → ΧF → ΖV → ZΒ → RΚ → ht → Bβ → ΞN → pl
31 cycle 2 nodesmνo → nνn
496 cycles15 nodesP0μΝ → μmn2 → κ0μ4 → με72 → κΦF4 → ζΕV8 → ΧYΒG → ΖSΘW → fYΒw → TGΥΙ → ΔevY → VGΥΗ → ΔazY → VOΜΗ → nazo
51 cycle (fixed) 1 node ΕWνΔX
65 cycles351 nodesB91λδγ → κΤΟLI4 → ζΑsha8 → ΧQAβΛG → ΠΖjqVM → ta6ζΑi → ΩQAβΛE → ΠΚjqRM → ti6ζsi → ΩB9γβE → ΣΟΙRMK → xsgtie → JD9γΩΤ → ΣΛybQK → xkMΞqe → rJ5ηΣk → βy6ζcC → ΩΞLΟNE → ΚtpkhS → hC4θαu → δΝCΩOA → ΣΜnmPK → xm0μoe → μJ1λΣ2 → λιxc43 → θεKΠ86 → βΦufGC → ΞΕEΧWO → ΘpXΓlU → dV3ιΖy → ζaKΠΑ8 → ΧvPΛfG → ΖlFΦpW → ΖZ3ιΒW → ζZRΙΒ8 → ΧhRΙtG → ΖhBαtW → ΞZBαΒO → ΞpRΙlO → ph3ιtm → ζC2κα8 → θΧΜOF6 → βΗmnUC → Ξc0μyO → μpLΟl2 → κt3ιh4 → ηεBα87 → ΩΦΝNGE → ΚΕolWS → hY2κΓu → θUCΩΗ6 → βΜbyPC → ΞmMΞoO → rp1λlk → κ73ιζ4 → ηεΧE87 → ΩΦΗTGE → ΚΕcxWS → hYKΠΓu → vUCΩΗg → ΜcEΧyQ → ΘlLΟpU → td3ιxi → ζKAβΡ8 → ΧΠveLG → ΖuGΥgW → ΔZDΨΒY → ΚVRΙΖS → igZΑut → REAβΨΛ → ΠΙirSM → tg8δui → ΥEAβΨI → ΠΙΑZSM → tgQΚui → jEAβΨs → ΠΙ8δSM → ΥtfuhI → ΒFBαΧa → ΞΗQΚUO → pjbyrm → N82κεΟ → θΦqjG6 → βΕ6ζWC → ΩΞXΓNE → ΚqUΖkS → hb5ηzu → βOCΩΝC → ΞΜnmPO → pm0μom → μ31λκ2 → λιζ643 → θεΨD86 → βΦΙRGC → ΞΕgtWO → pYCΩΓm → ΜU2κΗQ → θlbyp6 → βN3ιΞC → ζΞpkN8 → Χq4θkG → δΖ5ηVA → βΣZΑJC → ΞyQΚcO → pjLΟrm → t82κεi → θΦAβG6 → βΠΔWLC → ΞuWΔgO → pXDΨΔm → ΚW2κΕS → θhXΓt6 → βVBαΖC → ΟΝZΑON → roQΚmk → j71λζs → κΨ8δE4 → ζΥΘSH8 → ΧΓevYG → ΖUGΥΗW → ΔcYΒyY → VTLΟΘΗ → teazwi → PIAβΤΝ → ΠΑmnaM → tQ0μΛi → μkAβq2 → κΠ5ηL4 → ζβtgB8 → ΧΟCΩMG → ΜΖriVQ → la8δΑq → ΥQ4θΛI → δΒjqZA → ΣS6ζΙK → ΩxfudE → ΚKEΧΡS → ΘwgteU → dICΩΤy → ΜΑKΠaQ → vlPΛpg → lF3ιΧq → ζΗ4θU8 → δΧbyFA → ΣΗMΞUK → xrbyje → NJ7εΣΟ → ΧyqjcG → ΖM6ζΟW → ΩsYΒiE → ΚT9γΘS → ΣhdwtK → xJBαΣe → ΞyIΣcO → zpLΟlc → tN3ιΞi → ζqAβk8 → ΧΠ5ηLG → βΖtgVC → ΞaCΩΑO → ΜpPΛlQ → mk3ιqp → ζ62κη8 → θαΦFC6 → βΝΕVOC → ΞoYΒmO → pT1λΘm → κe2κw4 → θζHΤ76 → βΨΑZEC → ΞΙQΚSO → pjfurm → F82κεΨ → θΦΗTG6 → βΕcxWC → ΞYKΠΓO → vpTΗlg → dF3ιΧy → ζΗKΠU8 → ΧvbyfG → ΖNFΦΞW → ΖqYΒkW → ZT5ηΘΓ → βeSΘwC → ΞfHΤvO → ΒpFΦla → ΖR3ιΚW → ζiYΒs8 → ΧT9γΘG → ΣΖdwVK → xaIΣΑe → zQIΣΛc → zkMΞqc → rN5ηΞk → βq6ζkC → ΩΞ5ηNE → βΚpkRC → Ξi4θsO → δp9γlA → ΤΡ3ιKJ → ζzveb8 → ΧOGΥΝG → ΖΔnmXW → ZW0μΕΓ → μYSΘΓ2 → κfTΗv4 → ζdFΦx8 → ΧΖJΡVG → ΖxZΑdW → ZRJΡΚΓ → xiSΘse → fJ9γΣw → ΣyGΥcK → ΔxLΟdY → tVJΡΖi → xaAβΑe → ΠQIΣΛM → ztjqhc → NC6ζαΟ → ΩΝqjOE → Κo6ζmS → Ωh1λtE → κΚBαR4 → ζΞhsN8 → ΧqAβkG → ΠΖ5ηVM → βtZΑhC → ΞRBαΚO → ΞphslO → pB3ιβm → ζΟ2κM8 → θΧriF6 → βΗ8δUC → ΥΞbyNI → ΒqMΞka → rR5ηΚk → βi6ζsC → ΩΞ9γNE → ΣΚpkRK → xi4θse → δJ9γΣA → ΤΡxcKJ → zwKΠec → vNHΤΞg → ΒqEΧka → ΘR5ηΚU → βicxsC → ΞL9γΠO → ΣuolgK → xE2κΨe → θΙIΣS6 → βzfubC → ΞOEΧΝO → ΘpnmlU → d40μιy → μεKΠ82 → κΦufG4 → ζΕEΧW8 → ΧΘXΓTG → ΖeUΖwW → bZHΤΒΑ → ΒSOΜΙa → ngQΚuo → jE0μΨs → μΙ8δS2 → κΥfuH4 → ζΓEΧY8 → ΧΘTΗTG → ΖecxwW → ZLHΤΠΓ → ΒuSΘga → fRDΨΚw → ΚiGΥsS → Δh9γtY → ΣVBαΖK → ΞxZΑdO → pRJΡΚm → xi2κse → θJ9γΣ6 → βΣxcJC → ΞyKΠcO → vpLΟlg → tF3ιΧi → ζΗAβU8 → ΧΠbyLG → ΖuMΞgW → rZDΨΒk → ΚS6ζΙS → ΩhfutE → ΚFBαΧS → ΞΗgtUO → pcCΩym → ΜM2κΟQ → θskpi6 → βA4θγC → δΡΝNKA → ΣwoleK → xI2κΤe → θΑIΣa6 → βzPΛbC → ΞlNΝpO → qo3ιml → ζ51λθ8 → κγΦFA4 → ζΡΕVK8 → ΧwYΒeG → ΖTHΤΘW → ΒeYΒwa → TRHΤΚΙ → Βievsa → RH9γΥΛ → ΣΓirYK → xU8δΗe → ΥcIΣyI → ΒzLΟba → tRNΝΚi → piAβsm → ΠA2κγM → θΡshK6 → βwAβeC → ΠΞHΤNM → Βtpkha → RC4θαΛ → δΝirOA → Σo8δmK → Υx1λdI → κΒJΡZ4 → ζxRΙd8 → ΧhJΡtG → ΖxBαdW → ΞZJΡΒO → xpRΙle → hJ3ιΣu → ζyCΩc8 → ΧΜLΟPG → ΖtlohW → ZC2καΓ → θΝSΘO6 → βoevmC → ΞH1λΥO → κΓolY4 → ζU2κΗ8 → θΧbyF6 → βΗMΞUC → ΞrbyjO → pN7εΞm → Χq2κkG → θΖ5ηV6 → γαZΑCB → ΠΝQΚOM → toirmi
71 cycle 8 nodesΝnLνΟnP → ΠpOνΜlM → ΟrPνΛjN → ΞpQνΚlO → ΝnNνΝnP → ΞnOνΜnO → ΝpNνΝlP → ΞnQνΚnO