Base 138: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

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

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)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
21 cycle 9,453×(max) 69 nodes0Ъ → Щ1 → Ч3 → У7 → ЛF → υV → ΝΒ → AР → ЕL → ιh → oβ → aπ → ΓΜ → 8Т → ЙH → ρZ → ΕΚ → 4Ц → С9 → ЗJ → νd → wΣ → KЖ → λf → sΧ → Sψ → Τv → MД → ηj → kζ → iθ → mδ → eμ → uΥ → OВ → γn → cξ → yΠ → GК → σX → ΙΖ → 2Ш → Х5 → ПB → ГN → εl → gκ → qΩ → Wτ → ΛΔ → 6Ф → НD → ωR → Φt → QА → Ψr → Uφ → Οz → EМ → χT → Ρx → IИ → οb → ΑΞ → CО → БP → αp → Yς → ΗΘ
31 cycle 447,442×(fixed) (max) 1 node ΗЪΘ
429 cycles644,206×(max) 22 nodesE5ФН → ПψRC → ГΥtO → εPАm → αfκq → sXςΨ → ΙTφΗ → Ρ1Шy → ЧHИ4 → УπZ8 → ЛΔΚG → υ5ФW → ПΜΒC → Г9РO → ЗδlK → νfκe → wrΧΤ → ULДχ → ιΠxi → oHИγ → ρbξa → ΕzΞΛ
642,106×(max) 22 nodesI1ШЙ → ЧπZ4 → УΔΚ8 → Л5ФG → ПτVC → ГΜΒO → ε9Рm → ЗfκK → νrΧe → wTφΤ → ΡLДy → ιHИi → ρnβa → ΕbξΛ → Α5ФΟ → ПDМC → ГψRO → εΥtm → gPАλ → αrΧq → YTφσ → ΡΘΖy
641,486×(max) 22 nodesA5ФС → ПЖJC → ГμdO → εvΣm → gLДλ → ιrΧi → oTφγ → Ρbξy → ΑHИΟ → ρDМa → ωΔΚS → Φ5Фu → ПPАC → ГΩpO → εXςm → ΙfκΗ → s1ШΨ → ЧTφ4 → УΠx8 → ЛHИG → υπZW → ΝΔΚΓ
640,635×(max) 22 nodesMHИЕ → ρθha → ΕnβΛ → c5Фο → ПzΞC → ГDМO → ωδlS → Φfκu → sPАΨ → αTφq → ΡXςy → ΙHИΗ → ρ1Шa → ЧΔΚ4 → У5Ф8 → ПКFC → ГτVO → εΜΒm → g9Рλ → ЗrΧK → νTφe → ΡvΣy
638,075×(max) 22 nodes61ШХ → ЧОB4 → УВN8 → ЛδlG → υfκW → ΝrΧΓ → U9Рχ → ЗΠxK → νHИe → ρvΣa → ΕLДΛ → ι5Фi → ПnβC → ГbξO → εzΞm → gDМλ → ωrΧS → ΦTφu → ΡPАy → αHИq → ρXςa → ΙΔΚΗ
637,078×(max) 22 nodesI9РЙ → ЗπZK → νΔΚe → w5ФΤ → ПLДC → ГθhO → εnβm → gbξλ → ΑrΧΟ → UDМχ → ωΠxS → ΦHИu → ρPАa → αΔΚq → Y5Фσ → ПΘΖC → Г1ШO → Чδl4 → Уfκ8 → ЛrΧG → υTφW → ΡΜΒy
636,968×(max) 22 nodesM5ФЕ → ПθhC → ГnβO → εbξm → ΑfκΟ → sDМΨ → ωTφS → ΦΠxu → QHИБ → ρΩpa → ΕXςΛ → Ι5ФΗ → П1ШC → ЧВN4 → Уδl8 → ЛfκG → υrΧW → ΝTφΓ → Ρ9Рy → ЗHИK → ρμda → ΕvΣΛ
636,324×(max) 22 nodesU1Шχ → ЧΠx4 → УHИ8 → ЛπZG → υΔΚW → Ν5ФΓ → П9РC → ЗВNK → νδle → wfκΤ → sLДΨ → ιTφi → Ρnβy → cHИο → ρzΞa → ΕDМΛ → ω5ФS → ПΥtC → ГPАO → εΩpm → gXςλ → ΙrΧΗ
635,560×(max) 22 nodesIDМЙ → ωπZS → ΦΔΚu → Q5ФБ → ПΩpC → ГXςO → εΘΖm → g1Шλ → ЧrΧ4 → УTφ8 → ЛΠxG → υHИW → ρΜΒa → Ε9РΛ → З5ФK → ПμdC → ГvΣO → εLДm → ιfκi → snβΨ → cTφο → ΡzΞy
632,402×(max) 22 nodesUPАχ → αΠxq → YHИσ → ρΘΖa → Ε1ШΛ → Ч5Ф4 → УОB8 → ЛВNG → υδlW → ΝfκΓ → s9РΨ → ЗTφK → νΠxe → wHИΤ → ρLДa → ιΔΚi → o5Фγ → ПbξC → ГzΞO → εDМm → ωfκS → ΦrΧu
625,749×(max) 22 nodesofκγ → sbξΨ → ΑTφΟ → ΡDМy → ωHИS → ρΥta → ΕPАΛ → α5Фq → ПXςC → ГΘΖO → ε1Шm → Чfκ4 → УrΧ8 → ЛTφG → υΠxW → ΝHИΓ → ρ9Рa → ЗΔΚK → ν5Фe → ПvΣC → ГLДO → ιδli
618,047×(max) 22 nodesobξγ → ΑbξΟ → ΑDМΟ → ωDМS → ωΥtS → ΦPАu → αPАq → αXςq → ΙXςΗ → Ι1ШΗ → Ч1Ш4 → ЧТ74 → УКF8 → ЛτVG → υΜΒW → Ν9РΓ → З9РK → ЗμdK → νvΣe → wLДΤ → ιLДi → ιnβi
612,781×(max) 22 nodesk1Шη → Чjζ4 → Уjζ8 → ЛjζG → υjζW → ΝjζΓ → k9Рη → ЗjζK → νjζe → wjζΤ → kLДη → ιjζi → ojζγ → kbξη → ΑjζΟ → kDМη → ωjζS → Φjζu → kPАη → αjζq → kXςη → ΙjζΗ
612,381×(max) 22 nodesA1ШС → ЧЖJ4 → Уμd8 → ЛvΣG → υLДW → ιΜΒi → o9Рγ → ЗbξK → νzΞe → wDМΤ → ωLДS → ιΥti → oPАγ → αbξq → ΑXςΟ → ΙDМΗ → ω1ШS → ЧΥt4 → УPА8 → ЛΩpG → υXςW → ΝΘΖΓ
611,793×(max) 22 nodesQLДБ → ιΩpi → oXςγ → ΙbξΗ → Α1ШΟ → ЧDМ4 → УψR8 → ЛΥtG → υPАW → αΜΒq → Y9Рσ → ЗΘΖK → ν1Шe → ЧvΣ4 → УLД8 → ЛθhG → υnβW → ΝbξΓ → Α9РΟ → ЗDМK → ωμdS → ΦvΣu
611,649×(max) 22 nodesQDМБ → ωΩpS → ΦXςu → ΙPАΗ → α1Шq → ЧXς4 → УΘΖ8 → Л1ШG → ЧτV4 → УΜΒ8 → Л9РG → ЗτVK → νΜΒe → w9РΤ → ЗLДK → νθhe → wnβΤ → cLДο → ιzΞi → oDМγ → ωbξS → ΦzΞu
610,233×(max) 22 nodesM9РЕ → ЗθhK → νnβe → wbξΤ → ΑLДΟ → ιDМi → ωnβS → Φbξu → ΑPАΟ → αDМq → ωXςS → ΦΘΖu → Q1ШБ → ЧΩp4 → УXς8 → ЛΘΖG → υ1ШW → ЧΜΒ4 → У9Р8 → ЛЖJG → υμdW → ΝvΣΓ
605,607×(max) 22 nodesY1Шσ → ЧΘΖ4 → У1Ш8 → ЧКF4 → УτV8 → ЛΜΒG → υ9РW → ЗΜΒK → ν9Рe → ЗvΣK → νLДe → ιvΣi → oLДγ → ιbξi → ΑnβΟ → cDМο → ωzΞS → ΦDМu → ωPАS → αΥtq → YPАσ → αΘΖq
605,349×(max) 22 nodesM1ШЕ → Чθh4 → Уnβ8 → ЛbξG → υzΞW → ΝDМΓ → ω9РS → ЗΥtK → νPАe → αvΣq → YLДσ → ιΘΖi → o1Шγ → Чbξ4 → УzΞ8 → ЛDМG → ωτVS → ΦΜΒu → Q9РБ → ЗΩpK → νXςe → ΙvΣΗ
605,181×(max) 22 nodesMDМЕ → ωθhS → Φnβu → cPАο → αzΞq → YDМσ → ωΘΖS → Φ1Шu → ЧPА4 → УΩp8 → ЛXςG → υΘΖW → Ν1ШΓ → Ч9Р4 → УЖJ8 → ЛμdG → υvΣW → ΝLДΓ → ι9Рi → ЗnβK → νbξe → ΑvΣΟ
604,071×(max) 22 nodesE1ШН → ЧψR4 → УΥt8 → ЛPАG → υΩpW → ΝXςΓ → Ι9РΗ → З1ШK → Чμd4 → УvΣ8 → ЛLДG → υθhW → ΝnβΓ → c9Рο → ЗzΞK → νDМe → ωvΣS → ΦLДu → ιPАi → αnβq → cXςο → ΙzΞΗ
602,277×(max) 22 nodesE9РН → ЗψRK → νΥte → wPАΤ → αLДq → ιXςi → ΙnβΗ → c1Шο → ЧzΞ4 → УDМ8 → ЛψRG → υΥtW → ΝPАΓ → α9Рq → ЗXςK → νΘΖe → w1ШΤ → ЧLД4 → Уθh8 → ЛnβG → υbξW → ΝzΞΓ
314,315×11 nodesk5Фη → ПjζC → ГjζO → εjζm → kfκη → sjζΨ → kTφη → Ρjζy → kHИη → ρjζa → ΕjζΛ
300,454×11 nodeswXςΤ → ΙLДΗ → ι1Шi → Чnβ4 → Уbξ8 → ЛzΞG → υDМW → ωΜΒS → Φ9Рu → ЗPАK → νΩpe
290,466×11 nodessTφΨ → ΡTφy → ΡHИy → ρHИa → ρΔΚa → Ε5ФΛ → П5ФC → ПВNC → ГδlO → εfκm → sfκΨ
290,466×11 nodesI5ФЙ → ПπZC → ГΔΚO → ε5Фm → ПfκC → ГrΧO → εTφm → Ρfκy → sHИΨ → ρTφa → ΡΔΚy
290,466×11 nodesUHИχ → ρΠxa → ΕHИΛ → ρ5Фa → ПΔΚC → Г5ФO → ПδlC → ГfκO → εrΧm → gTφλ → ΡrΧy
290,466×11 nodesU5Фχ → ПΠxC → ГHИO → ρδla → ΕfκΛ → s5ФΨ → ПTφC → ГΠxO → εHИm → ρfκa → ΕrΧΛ
290,466×11 nodesg5Фλ → ПrΧC → ГTφO → εΠxm → gHИλ → ρrΧa → ΕTφΛ → Ρ5Фy → ПHИC → ГπZO → εΔΚm
52 cycles448,053,020×(fixed) 1 node ηjЪζk
19,180×(max) 2 nodesΘΖЪΘΘ → ΘЪЪЪΗ
6+---Not showing digit sets 6+ due to verbosity.