Base 121: 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 30 nodes1И → Ж3 → В7 → τF → δV → vΒ → 5Д → ψB → μN → Μl → Pκ → Θp → Hς → ΩZ → nΚ → Lξ → Πh → Xβ → rΖ → Dφ → θR → Δt → 9А → πJ → Υd → fΣ → bΧ → jΞ → Tζ → zx
31 cycle 2 nodesxЙz → yЙy
434 cycles55 nodesH8Аσ → ςαXI → ΩqΖa → nEτΛ → ζMμU → Ξyxk → T0Иη → ИΑv2 → Ж4Д4 → Вω98 → τοJG → δΤdW → veΣΓ → d6ВΦ → φgΠE → θYΩS → ΔoΘu → J8Аρ → ςΦbI → ΩiΞa → nUδΛ → xMμΑ → Ξ2Жk → ДSζ6 → ψΑvC → μ4ДO → АΛlA → πOκK → ΥΙne → fKξΤ → ΣcΥg → haΧΡ → lYΩΝ → pQθΙ → ΖIπs → ΧCφc → κiΞQ → ΘUδq → xGςΑ → β2ЖY → ДqΖ6 → ψEτC → μεTO → Μyxm → P0Иλ → ИΙn2 → ЖKξ4 → ВΡf8 → τaΧG → δkΜW → vQθΓ → Ζ6Вs → φCφE → κηRQ → ΘΓtq
52 cycles4 nodesΤdЙΤf → ΥcЙΥe → ΦeЙΣd → ΥfЙΡe
64 cycles283 nodesHD5Гφσ → ψιαXQC → μΗqΖqO → ΜGEτσm → ζγOκWU → ΚztΓxo → L91ЗАο → ЖρΡfI4 → ВΨaΧa8 → τmkΜΛG → δRNλθW → ΜΕuΒsm → PC6Вχλ → φλΙnOE → θΛKξmS → ΣΔNλtg → Μb9ωΧm → πkOκΝK → ΥΚRηne → ΔfLνΣu → Πc8АΦi → ςiWβΟI → ΩtVγΔa → vn9ωΚΓ → πM6ВνK → φΥΞidE → θgUδΡS → ΔxZΨzu → n91ЗАΛ → ЖρMμI4 → ВΨΝja8 → τmSζΛG → δΒNλvW → Μv5ГΒm → ψP5ГκC → ψμΘoNC → μΝIπkO → ΧΜRηlc → ΔjPιΞu → ΘU8Аεq → ςyGςyI → βΨЙЙZY → αΩ2ЖZZ → ДpnΙΘ6 → ψLHρξC → μΩΠgZO → ΜoYΩΙm → pPJοκΙ → ΥΙIπoe → ΧfJοΣc → ΥjbΦΞe → jfTεΣΟ → zcUδΦy → xi0ИΟΑ → ИW2Жγ2 → ЖДtΓ54 → Вω8АA8 → τςξKHG → δαΡfYW → vqaΧΗΓ → lG6ВσΝ → φγQθWE → θΖtΓrS → ΔE8Аυu → ςη8АSI → ςΩΒuZI → Ωo6ВΙa → φnJοΚE → θΥLνdS → ΠΔfΡti → bX9ωβΨ → πskΜΕK → ΥRBχθe → μΕeΣsO → ΜdBχΥm → μgOκΡO → ΜΚZΨnm → nPLνκΛ → ΠΙMμoi → ΞXJοβk → ΥsSζΕe → ΒfBχΣw → μc4ДΦO → АΜhΟlA → πXPιβK → ΥΘrΕpe → fICφρΤ → κΨcΥaQ → ΘmgΠΛq → ZOGςλα → βΛoΘmY → rOIπλΗ → ΧΛEτmc → ζjNλΞU → ΜzTεxm → zP1Зκy → ЖΙ0Иo4 → ИВJο72 → ЖυΤdE4 → ВηeΣS8 → τΓcΥuG → δh7БΠW → τvXαΒG → δr5ГΖW → ψvDυΒC → μθ5ГRO → ψΜΔslC → μQAψιO → ξΜΖqlM → ΠQEτιi → ζΗWβqU → ztFσΔy → δA0ИωW → ИοuΒK2 → ЖΤ6Вe4 → ВφdΤD8 → τιeΣQG → δΗcΥqW → vhFσΠΓ → δY6ВαW → φvpΗΒE → θH5ГςS → ψαΓtYC → μq8АΗO → ςΜFσlI → δΩPιZW → ΘvnΙΒq → LH5Гςο → ψαΡfYC → μqaΧΗO → ΜlFσΜm → δQOκιW → ΚΗuΒqo → LG6Вσο → φγΡfWE → θuaΧΓS → Δl7БΜu → τQ8АιG → ςδΖqVI → ΩwEτΑa → ζn3ЕΚU → ВzLνx8 → τΠ1ЗhG → ЖδXαV4 → ВwqΖΑ8 → τF3ЕτG → ВεγVU8 → τyuΒyG → δ6ЙЙВW → ГγNλW7 → φΜtΓlE → θQ8АιS → ςΗΓtqI → ΩG8Аσa → ςγmΚWI → ΩuMμΓa → Ξn7БΚk → τTLνζG → δΠzwhW → vY2ЖαΓ → Дq6ВΗ6 → ψφFσDC → μιγVQO → ΜΗuΒqm → PG6Вσλ → φγΙnWE → θuKξΓS → ΣΔ7Бtg → τb9ωΧG → πδjΝVK → ΥwSζΑe → Βf3ЕΣw → Вc4ДΦ8 → АτhΟFA → πεWβUK → ΥysΔye → fAЙЙψΤ → ωΣSζfB → ξΒbΦvM → Πj5ГΞi → ψXTεβC → μzrΕxO → ΜD1Зφm → ЖιOκQ4 → ВΚΖqn8 → τMEτνG → ζδΞiVU → zwUδΑy → x40ИЕΑ → ИБ2Ж82 → ЖДςG54 → ВωαXA8 → τοqΖKG → δΤEτeW → ζvdΤΒU → zf5ГΣy → ψc0ИΦC → ИμhΟN2 → ЖΝWβk4 → ВtRηΔ8 → τΔ9ωtG → πδ9ωVK → πΥvΑdK → Υg4ДΡe → АfZΨΣA → πnbΦΚK → ΥjLνΞe → ΠfTεΣi → zcWβΦy → ti0ИΟΕ → ИWAψγ2 → ЖξtΓL4 → ВΡ8Аg8 → τςZΨHG → δαmΚYW → vqMμΗΓ → ΞG6Вσk → φγSζWE → θΒtΓvS → Δ95ГАu → ψρ8АIC → ςμΧaNI → ΩΝkΜka → nSQθηΛ → ΖΓMμus → ΞD7Бφk → τιSζQG → δΗΑvqW → vG4ДσΓ → Аγ6ВWA → φπtΓJE → θΦ8АcS → ςΔhΟtI → ΩX9ωβa → πsmΚΕK → ΥNBχμe → μΝeΣkO → ΜdRηΥm → ΔgOκΡu → Κa8АΨo → ςmKξΛI → ΩΣNλfa → ΜnbΦΚm → jPLνκΟ → ΠΙUδoi → xXJοβΑ → Υs2ЖΕe → ДfBχΣ6 → ψμbΦNC → μΝiΞkO → ΜVRηδm → ΔwOκΑu → Κ93ЕАo → ВρKξI8 → τΨΡfaG → δmaΧΛW → vlNλΜΓ → ΜQ6Вιm → φΗOκqE → θΚFσnS → δΔLνtW → Πv9ωΒi → πX5ГβK → ψΥrΕdC → μgCφΡO → κΜZΨlQ → ΘnPιΚq → ΘMGςνq → βΟGςiY → βrVγΖY → vrDυΖΓ → θE6ВυS → φηΓtSE → θΓ8АuS → ςΔ7БtI → τΩ9ωZG → πδnΙVK → ΥwKξΑe → Σf3ЕΣg → ВcaΧΦ8 → τlhΟΜG → δXPιβW → ΘvrΕΒq