Base 105: 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--
21 cycle 26 nodes1ς → π3 → μ7 → δF → ΜV → fΒ → LΧ → zh → Hβ → ΘZ → XΚ → bΖ → TΞ → jx → Dζ → ΠR → nt → 5ξ → θB → ΥN → vl → 9κ → ΩJ → Δd → PΣ → rp
31 cycle 2 nodespσr → qσq
4124 cycles12 nodesN8κΦ → βwjI → ΘCζa → ΣWΚQ → rcΔq → R0ςΡ → ςor2 → π2π4 → ξλ76 → θγFC → ΥΛVO → veΒm
51 cycle (fixed) 1 node ΙYσΘZ
64 cycles342 nodesDA0ςιη → ςΨΡPK2 → πΓqpe4 → μO0ςΤ8 → ςδtmF2 → πΝ6μU4 → μζhyD8 → δΡGβQG → ΜΚpqXW → fc0ςΕΓ → ςSMΥΟ2 → πxluj4 → μE8κε8 → δβΞSHG → ΜΙkvYW → faAθΗΓ → ΧWMΥΛM → zxdΓji → PHDεβΤ → ΠΙsnYS → na4ξΗu → κW6μΛA → ζΩdΓJE → ΠΕOΣcS → tnRΟto → n64ξνu → κη6μCA → ζΩΣOJE → ΠΕsncS → nS4ξΟu → κm6μuA → ζΩ7λJE → δΠΔcRG → ΜoQΠsW → pf3οΒs → μM2πΦ8 → ξδxiF6 → θΝEδUC → ΥΞhyTO → vkGβwm → ΚC8κηY → βΤaΖOI → ΘuUΜma → hX7λΚΑ → δcIΩΕG → ΜΖRΟbW → nfTΝΒu → jM6μΦy → ζyEδiE → ΠΞFγTS → ΜnjwtW → fD5νζΓ → θΡMΥQC → ΥxpqjO → vE0ςεm → ςΟ8κS2 → πβluH4 → μΙ8κY8 → δβZΗHG → ΜΙWΚYW → fdZΗΔΓ → XQMΥΡΛ → xqcΔqk → RCσσζΡ → ηΠCζRD → ΤΡnsQP → tq4ξqo → κ4σσξA → οι3οA5 → μκΧK98 → δαΑfIG → ΜΗKΧaW → ΒfVΛΒg → fMKΧΦΓ → ΒyMΥig → xLFγΧk → ΜΑCζgW → ΣfJΨΒQ → ΔrLΦpe → zP1ρΣi → πsGβo4 → μΚ3οX8 → μδbΕF8 → δΝSΞUG → ΜlhyvW → fH9ιβΓ → ΩΙMΥYK → ΔxZΗje → XPDεΣΛ → ΠscΔoS → nR3οΠu → μo6μs8 → ζδ3οFE → μΠΜUR8 → δogzsG → ΜJ3οΩW → μΕeΒc8 → δSMΥΟG → ΜxlujW → fE8κεΓ → βΟMΥSI → Θxluja → XE8κεΛ → βΟcΔSI → ΘmQΠua → pX7λΚs → δc2πΕG → ξΜRΟV6 → θnfΑtC → ΥL5νΧO → θΑulgC → ΥK8κΨO → βΓuleI → ΘO8κΤa → βuWΚmI → Θd7λΔa → δXPΡΚG → ΜrbΕpW → fT1ρΞΓ → πkMΥw4 → μxBηj8 → δΥDεNG → ΠΜvkVS → ngAθΑu → ΧK6μΨM → ζΓyheE → ΠOGβΤS → ΚumtmY → b86μλΗ → ζγUΜGE → ΠΛgzWS → neIΩΓu → ΖO6μΤc → ζuSΞmE → Πl7λvS → δn9ιtG → ΩΜ5νVK → θΔfΑdC → ΥQKΧΡO → Βvpqlg → LA0ςιΨ → ςΨΑfK2 → πΓKΧe4 → μΒNΤf8 → δvLΦlG → Μz9ιhW → ΩfHαΒK → ΘΔLΦda → zXPΡΚi → rcGβΕq → ΚS0ςΟY → ςmaΖu2 → πV7λΜ4 → μδfΑF8 → δΝKΧUG → ΜΒhyfW → fMGβΦΓ → ΚyMΥiY → xbFγΖk → ΜUCζΝW → ΣieΒyQ → rNFγΥq → Μw0ςkW → ςfBηΒ2 → πΥLΦN4 → μzvkh8 → δIAθαG → ΧΜΖaVM → zgUΜΑi → hKGβΨΑ → ΚΓIΩeY → ΖbNΤΖc → vUSΞΝm → li8κyw → βGAθγI → ΧΛΗZWM → zeWΚΓi → dOGβΤΕ → ΚuQΠmY → pb7λΖs → δU2πΝG → ξΜhyV6 → θgGβΑC → ΥΚJΨXO → ΔvbΕle → TP9ιΣΟ → ΩskvoK → ΔB3οθe → μΦOΣM8 → δysniG → ΜG4ξγW → κΛeΒWA → ΩeMΥΓK → ΔxNΤje → vPDεΣm → Πs8κoS → βn3οtI → μΘ5νZ8 → θδXΙFC → ΥΝaΖUO → viUΜym → hG8κγΑ → βΛIΩWI → ΘΖdΓba → XUOΣΝΛ → ticΔyo → RG4ξγΡ → κΛorWA → Ωe2πΓK → ξΔNΤd6 → θvPΡlC → Υr9ιpO → Ωv1ρlK → πΔ9ιd4 → μΩPΡJ8 → δΕqpcG → ΜS0ςΟW → ςmeΒu2 → πN7λΥ4 → μδvkF8 → δΝAθUG → ΧΜhyVM → zgGβΑi → ΚKGβΨY → ΚΓaΖeY → bVNΤΜΗ → vgUΜΑm → hK8κΨΑ → βΓIΩeI → ΘΖNΤba → vXTΝΚm → jc8κΕy → βSEδΟI → ΞΘluZU → jY8κΙy → βaEδΗI → ΞΘVΛZU → jfXΙΒy → bMEδΦΗ → ΞyUΜiU → jhFγzy → ΜIEδαW → ΞΗeΒaU → jWMΥΛy → xeEδΓk → ΞOCζΤU → ΣuixmQ → rF7λδq → δΝ0ςUG → ςΜhyV2 → πgGβΑ4 → μΚJΨX8 → δΔbΕdG → ΜTPΡΞW → rkeΒwq → NC0ςηΦ → ςΤwjO2 → πuCζm4 → μΣ7λP8 → εγroGF → ΞΛ2πWU → ξjdΓx6 → θPDεΣC → ΥΠroRO → vo2πsm → ξ93οκ6 → μθΩIB8 → δΦΕbMG → ΜySΞiW → lfFγΒw → ΜMAθΦW → ΧyeΒiM → zNFγΥi → ΜwGβkW → ΚfBηΒY → ΥbLΦΖO → zvTΝli → jH9ιβy → ΩΙEδYK → ΞΔZΗdU → jXPΡΚy → rcEδΕq → ΞS0ςΟU → ςmixu2 → πF7λδ4 → μδΜUF8 → δΝgzUG → ΜiIΩyW → ΖfFγΒc → ΜTLΦΞW → zkeΒwi → NHBηβΦ → ΥΙwjYO → vaCζΗm → ΣW8κΛQ → βrdΓpI → ΘP1ρΣa → πsWΚo4 → μd3οΔ8 → μδPΡF8 → δΝqpUG → Μi0ςyW → ςfFγΒ2 → πΜLΦV4 → μzfΑh8 → δLHαΧG → ΜΘzgZW → fYIΩΙΓ → ΖaMΥΗc → xWSΞΛk → leCζΓw → ΣOAθΤQ → ΧuqpmM → z80ςλi → ςγGβG2 → πΛΙXW4 → μeaΖΓ8 → δVNΤΜG → ΜvfΑlW → fL9ιΧΓ → ΩΑMΥgK → ΔxJΨje → ΔPDεΣe → ΠsOΣoS → tn3οto → μ64ξν8 → κηγFCA → ΩΤΛVOK → ΔueΒme → PN7λΥΤ → δwsnkG → ΜC4ξηW → κΤeΒOA → ΩuMΥmK → Δx7λje → δPDεΣG → ΠΜroVS → ng2πΑu → ξK6μΨ6 → θζΒeDC → ΥΡMΥQO → xvpqlk