Base 117: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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 29 nodes1Д → В3 → ψ7 → πF → ΩV → rΒ → 9φ → μJ → Πd → bΣ → fΞ → XΧ → nΖ → Hξ → ΥZ → jΚ → Pζ → Δp → Dς → δR → zt → 5А → τB → θN → Θl → Lκ → Μh → Tβ → vx
31 cycle 2 nodesvЕx → wЕw
4145 cycles12 nodesTEπγ → βwvU → v0Дy → Д2В2 → Вω54 → ψσB8 → πηNG → ΩΗlW → rKκΓ → ΞAτg → κWΧM → ΜoΔi
51 cycle (fixed) 1 node ΡcЕΠd
65 cycles278 nodesHD9υςο → μεΦXQK → ΠΓmΖqe → bJBσμΤ → θΡgΜcO → ΘeUΩΟm → taKκΤΑ → Ξi6ψΛg → ςXRγΧE → δznΕtS → zH5ωξu → τΦ4АYC → φθlΗNA → μΙKκkK → ΠΞNηfe → ΘbXΦΣm → ngKκΝΗ → ΞWIμΨg → ΣqWΧΓc → pfBσΞΕ → θYEπΦO → βΘlΗlU → vMKκιy → ΞΛ2Вig → АXRγΧ6 → τznΕtC → θH5ωξO → τΦΗlYC → θmKκΗO → ΞΘJλlg → ΠXLιΧe → ΜoaΣΕi → hTFοβΝ → ΩwUΩwW → tqЕЕΒΑ → Γz0Дtr → ДB5ωτ2 → ВτθMB4 → ψιΙjM8 → πΛOζiG → ΩΖRγnW → zrHνΒu → ΥA4Аυa → φλiΚKA → μΟQδeK → ΠΒZΤre → jb9υΣΛ → μgQδΝK → ΠΒVΨre → rb9υΣΓ → μgAτΝK → κΠVΨdM → ΜrbΡΒi → fT9υβΟ → μwYΥwK → ΠkЕЕΘe → ΟΙ7χkf → πZNηΥG → ΩΘjΙlW → rPLιζΓ → ΜΕAτoi → κTFοβM → ΩΜvwhW → rU0ДαΓ → ДuAτy2 → Вκ3БL4 → ωχΜg87 → ςοUΩGE → δΨszWS → zq6ψΓu → ςC4АσE → φηγROA → μΗytmK → ΠK4Аλe → φΟaΣeA → μhZΤΜK → ΠjTαΚe → vbPεΣy → Δg2ВΝq → АWCςΨ6 → τζpΓPC → θΕCςoO → ζΘFοlQ → ΩΔLιpW → ΜrDρΒi → δT9υβS → μzvwtK → Π60Дωe → ДσaΣC2 → ВηgΜO4 → ψΗUΩm8 → πtJλzG → ΩΠ5ωdW → τrbΡΒC → θf9υΞO → μΘXΦlK → ΠnLιΖe → ΜbHνΣi → ΥgSβΝa → xjVΨΚw → rQ0ДεΓ → ДΓAτq2 → ВκBσL4 → ψθΜgN8 → πΙUΩkG → ΩtNηzW → Θr5ωΒm → τL9υκC → μθΜgNK → ΠΙUΩke → tbNηΣΑ → Θg6ψΝm → ςWKκΨE → δΞpΓfS → zYCςΦu → ζm4АΗQ → φΔJλpA → μΠDρdK → δΠbΡdS → zfbΡΞu → fY4АΦΟ → φmYΥΗA → μlJλΘK → ΡΟLιed → ΜdZΤΠi → jcSβΡΛ → xeQδΟw → Βa0ДΤs → Дi8φΛ2 → ВξRγH4 → ψΦytY8 → πm4АΗG → φΩJλVA → μΠrΑdK → Πc8φΡe → ξeaΣΟI → ΥhZΤΜa → kiTαΛΚ → vSOζγy → Ζy2Вuo → АH3Бξ6 → ψτΥYB8 → πιkΘMG → ΩΛMθiW → ΚrRγΒk → zP9υζu → μΕ4АoK → φΠFοdA → μΩbΡVK → ΠseΞΑe → bZ7χΥΤ → πkgΜΙG → ΩVNηΩW → ΘsqΒΑm → LB7χτλ → πιΝfMG → ΩΛWΧiW → rpRγΔΓ → zEAτρu → κγ4АSM → φΜxuhA → μU2ВαK → АΠtyd6 → τc4АΡC → φθdΟNA → μΙaΣkK → ΠhNηΜe → ΘbTαΣm → vgKκΝy → ΞW2ВΨg → АqWΧΓ6 → τpBσΔC → ιηDρON → δΚΖmjS → zQIμεu → ΣΓ4Аqc → φfBσΞA → μθXΦNK → ΠΙmΖke → bOIμηΤ → ΣΗgΜmc → fVJλΩΟ → ΠsYΥΑe → lb7χΣΙ → πgMθΝG → ΩΚVΨjW → sqPεΓΒ → ΔC8φσq → ξηCςOI → ζΥΖmZQ → ΔkIμΙq → ΣOCςηc → ζΗeΞmQ → ΔZJλΥq → ΠkCςΙe → ζbNηΣQ → ΘΔfΝpm → XLDρκΨ → δΝoΔgS → zWEπΨu → βq4АΓU → φvBσxA → μθ1ГNK → ВΠΘkd4 → ψcMθΡ8 → πΚdΟjG → ΩbPεΣW → ΔrfΝΒq → XD9υςΨ → μεoΔQK → ΠΓEπqe → βbBσΣU → θvfΝxO → ΘX1ГΧm → ВoKκΕ4 → ψΞFοf8 → πΩXΦVG → ΩsmΖΑW → rJ7χμΓ → πΡAτcG → κΩdΟVM → ΜsaΣΑi → hT7χβΝ → πwUΩwG → ΩsЕЕzW → ΨΑNηsX → Θp7χΔm → πLDρκG → δΩΜgVS → zsUΩΑu → t84АχΑ → φο6ψGA → ςμΧWJE → δΡoΔcS → zeEπΟu → βa4АΤU → φvhΛxA → μT1ГβK → ВΠvwd4 → ψc0ДΡ8 → ДπdΟF2 → ВαaΣU4 → ψugΜy8 → πV3БΩG → ψΩrΑV8 → πs8φΑG → ξΩ7χVI → πΥrΑZG → Ωk8φΙW → ξrNηΒI → ΥΘ9υla → μjLιΚK → ΠΜPεhe → ΔbTαΣq → vgCςΝy → ζW2ВΨQ → АΔpΓp6 → τECςρC → θζβSPO → ΘΕwvom → LG0Дολ → ДΨΝfW2 → ВqWΧΓ4 → ψpBσΔ8 → πθDρNG → δΩΘkVS → zsMθΑu → Κ84Аχk → φοOζGA → μΨΕnWK → ΠqGξΓe → ΧbBσΣY → θnfΝΖO → ΘXHνΧm → ΥoKκΕa → ΞjFοΚg → ΩXPεΧW → ΔrnΕΒq