Base 122: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
25 cycles2,420×(max) 20 nodes⮎ 0К → Й1 → З3 → Г7 → υF → εV → wΒ → 4Ж → Б9 → ρJ → Φd → gΣ → aΩ → mΜ → Oμ → Λn → Mξ → Οj → Uζ → yz ⮌
2,420×(max) 20 nodes⮎ 6Д → χD → ιR → Εt → AА → οL → Ρh → Yβ → qΘ → Gτ → γX → sΖ → Cψ → λP → Ιp → Iς → Ψb → kΞ → Sθ → Γv ⮌
1,210×10 nodes⮎ 2И → Е5 → ωB → νN → Νl → Qκ → Ηr → Eφ → ηT → Αx ⮌
1,210×10 nodes⮎ 8В → σH → αZ → oΚ → Kπ → Τf → cΧ → iΠ → Wδ → uΔ ⮌
121×(fixed) 1 node ⮎ eΥ ⮌
31 cycle 310,002×(fixed) (max) 1 node ⮎ yКz ⮌
415 cycles677,696×(max) 30 nodes⮎ gbΧΤ → kbΧΟ → kTζΟ → ΑTζy → Α1Иy → З1И4 → ЗВ74 → ГτF8 → υδVG → εvΒW → w5ДΓ → ω5ДC → ωμNC → νΜlO → ΝPκm → ΙPκq → ΙHςq → αHςa → αnΚa → oLξΛ → ΡLξi → ΡXβi → sXβΗ → sDφΗ → ιDφS → ιΔtS → Ε9Аu → ρ9АK → ρΥdK → ΦfΣe ⮌
673,314×(max) 30 nodes⮎ E5Дχ → ωθRC → νΔtO → Ν9Аm → ρPκK → ΦΘpe → gHςΤ → αbΧa → ojΞΛ → ULξη → Ρzxi → Y1Иγ → ЗrΖ4 → ГDφ8 → υθRG → εΔtW → w9АΓ → ρ5ДK → ωΥdC → νfΣO → ΝbΧm → kPκΟ → ΙTζq → ΑHςy → α1Иa → ЗnΚ4 → ГLξ8 → υΠhG → εXβW → wrΖΓ ⮌
672,762×(max) 30 nodes⮎ A1ИБ → ЗπJ4 → ГΥd8 → υfΣG → εbΧW → wjΞΓ → U5Дη → ωzxC → ν1ИO → ЗΜl4 → ГPκ8 → υΘpG → εHςW → αvΒa → o5ДΛ → ωLξC → νΠhO → ΝXβm → sPκΗ → ΙDφq → ιHςS → αΔta → o9АΛ → ρLξK → ΦΠhe → gXβΤ → sbΧΗ → kDφΟ → ιTζS → Εzxu ⮌
672,383×(max) 30 nodes⮎ MDφο → ιΠhS → ΕXβu → s9АΗ → ρDφK → ιΥdS → ΕfΣu → c9АΨ → ρjΞK → ΦTζe → ΑfΣy → c1ИΨ → ЗjΞ4 → ГTζ8 → υzxG → ε1ИW → ЗvΒ4 → Г5Д8 → ωτFC → νδVO → ΝvΒm → Q5Дλ → ωΘpC → νHςO → αΜla → oPκΛ → ΙLξq → ΡHςi → αXβa → snΚΗ ⮌
670,714×(max) 30 nodes⮎ QLξλ → ΡΘpi → YHςγ → αrΖa → oDφΛ → ιLξS → ΡΔti → Y9Аγ → ρrΖK → ΦDφe → ιfΣS → ΕbΧu → k9АΟ → ρTζK → Φzxe → g1ИΤ → ЗbΧ4 → ГjΞ8 → υTζG → εzxW → w1ИΓ → З5Д4 → ГψB8 → υμNG → εΜlW → wPκΓ → Ι5Дq → ωHςC → νΩZO → ΝnΚm ⮌
668,623×(max) 30 nodes⮎ 61ИЕ → ЗψB4 → ГμN8 → υΜlG → εPκW → ΙvΒq → I5Дσ → ωΩZC → νnΚO → ΝLξm → ΡPκi → ΙXβq → sHςΗ → αDφa → ιnΚS → ΕLξu → Ρ9Аi → ρXβK → ΦrΖe → gDφΤ → ιbΧS → ΕjΞu → U9Аη → ρzxK → Φ1Иe → ЗfΣ4 → ГbΧ8 → υjΞG → εTζW → ΑvΒy ⮌
667,712×(max) 30 nodes⮎ E1Иχ → ЗθR4 → ГΔt8 → υ9АG → ρδVK → ΦvΒe → g5ДΤ → ωbΧC → νjΞO → ΝTζm → ΑPκy → Ι1Иq → ЗHς4 → ГΩZ8 → υnΚG → εLξW → ΡvΒi → Y5Дγ → ωrΖC → νDφO → ιΜlS → ΕPκu → Ι9Аq → ρHςK → αΥda → ofΣΛ → cLξΨ → ΡjΞi → YTζγ → ΑrΖy ⮌
667,218×(max) 30 nodes⮎ IDφσ → ιΩZS → ΕnΚu → M9Аο → ρΠhK → ΦXβe → sfΣΗ → cDφΨ → ιjΞS → ΕTζu → Α9Аy → ρ1ИK → ЗΥd4 → ГfΣ8 → υbΧG → εjΞW → wTζΓ → Α5Дy → ω1ИC → ЗμN4 → ГΜl8 → υPκG → εΘpW → wHςΓ → α5Дa → ωnΚC → νLξO → ΡΜli → YPκγ → ΙrΖq ⮌
667,082×(max) 30 nodes⮎ QHςλ → αΘpa → oHςΛ → αLξa → ΡnΚi → YLξγ → ΡrΖi → YDφγ → ιrΖS → ΕDφu → ι9АS → ρΔtK → Φ9Аe → ρfΣK → ΦbΧe → kfΣΟ → cTζΨ → ΑjΞy → U1Иη → Зzx4 → Г1И8 → ЗτF4 → ГδV8 → υvΒG → ε5ДW → ωvΒC → ν5ДO → ωΜlC → νPκO → ΝΘpm ⮌
666,706×(max) 30 nodes⮎ A5ДБ → ωπJC → νΥdO → ΝfΣm → cPκΨ → ΙjΞq → UHςη → αzxa → o1ИΛ → ЗLξ4 → ГΠh8 → υXβG → εrΖW → wDφΓ → ι5ДS → ωΔtC → ν9АO → ρΜlK → ΦPκe → ΙfΣq → cHςΨ → αjΞa → oTζΛ → ΑLξy → Ρ1Иi → ЗXβ4 → ГrΖ8 → υDφG → ιδVS → ΕvΒu ⮌
666,292×(max) 30 nodes⮎ I9Аσ → ρΩZK → ΦnΚe → gLξΤ → ΡbΧi → kXβΟ → sTζΗ → ΑDφy → ι1ИS → ЗΔt4 → Г9А8 → υπJG → εΥdW → wfΣΓ → c5ДΨ → ωjΞC → νTζO → Νzxm → Q1Иλ → ЗΘp4 → ГHς8 → υΩZG → εnΚW → wLξΓ → Ρ5Дi → ωXβC → νrΖO → ΝDφm → ιPκS → ΙΔtq ⮌
666,192×(max) 30 nodes⮎ M5Дο → ωΠhC → νXβO → ΝrΖm → QDφλ → ιΘpS → ΕHςu → α9Аa → ρnΚK → ΦLξe → ΡfΣi → cXβΨ → sjΞΗ → UDφη → ιzxS → Ε1Иu → З9А4 → ГπJ8 → υΥdG → εfΣW → wbΧΓ → k5ДΟ → ωTζC → νzxO → Ν1Иm → ЗPκ4 → ГΘp8 → υHςG → εΩZW → wnΚΓ ⮌
665,382×(max) 30 nodes⮎ I1Иσ → ЗΩZ4 → ГnΚ8 → υLξG → εΠhW → wXβΓ → s5ДΗ → ωDφC → νθRO → ΝΔtm → Q9Аλ → ρΘpK → ΦHςe → αfΣa → obΧΛ → kLξΟ → ΡTζi → ΑXβy → s1ИΗ → ЗDφ4 → ГθR8 → υΔtG → ε9АW → ρvΒK → Φ5Дe → ωfΣC → νbΧO → ΝjΞm → UPκη → Ιzxq ⮌
658,192×(max) 30 nodes⮎ E9Аχ → ρθRK → ΦΔte → g9АΤ → ρbΧK → ΦjΞe → gTζΤ → ΑbΧy → k1ИΟ → ЗTζ4 → Гzx8 → υ1ИG → ЗδV4 → ГvΒ8 → υ5ДG → ωδVC → νvΒO → Ν5Дm → ωPκC → νΘpO → ΝHςm → αPκa → ΙnΚq → MHςο → αΠha → oXβΛ → sLξΗ → ΡDφi → ιXβS → ΕrΖu ⮌
330,985×15 nodes⮎ M1Иο → ЗΠh4 → ГXβ8 → υrΖG → εDφW → ιvΒS → Ε5Дu → ω9АC → ρμNK → ΦΜle → gPκΤ → ΙbΧq → kHςΟ → αTζa → ΑnΚy ⮌
52 cycles244,207,524×(max) 4 nodes⮎ ΥdКΥf → ΦdКΥe → ΦfКΣe → ΥeКΤf ⮌
15,004×2 nodes⮎ zxКzz → zКККy ⮌
69 cycles5,087,236,835×17 nodes⮎ ibXβΨΡ → slXβΝΗ → sRDφιΗ → ιΖDφsS → ιΕCχtS → λΕAωtQ → οΙAωpM → οΡIρhM → ΨΡYαhc → qkYαΞΙ → qTHςηΙ → αΒHςwa → αo4ЕΚa → БoKοΚA → ρΤKοfK → ΦΤcΦfe → igcΦΣΡ ⮌
60,412,940×5 nodes⮎ ΝxBψΑm → νQ2ЗκO → ЕΝΗql6 → ωRFτιC → νεΕsVO ⮌
10,463,524×(max) 25 nodes⮎ QE6Гφλ → χθΘpSE → ιΔHςuS → αΕ8Бta → σoAωΚI → οαKοZM → ΤΡoΙhg → cZJπαΨ → ΦpjΞΙe → gUIρζΤ → ΨzbΧyc → lj0ЙΟΞ → ЙVRθε2 → ЗΕwΑt4 → ГB3Жω8 → ГυνMF8 → υζΞjUG → εzTζyW → Αw0ЙΒy → Й51ИЕ2 → ИЖωA43 → ЕВξL86 → ωτΠhGC → νδXβWO → ΝvrΖΓm ⮌
5,405,732×16 nodes⮎ g60ЙДΤ → ЙψbΧC2 → ЗμjΞO4 → ГΜTζm8 → υΑOλxG → εΛ2ЗnW → ЕwMνΒ6 → ωΟ4ЕjC → БνUεNA → ρΞxzkK → ΦT1Иηe → ЗΒfΣw4 → Гc4ЕΧ8 → БυiΟFA → ρζVδUK → ΦzvΒye ⮌
2,027,579×3 nodes⮎ mLHςοΝ → αΣPκga → ΙoaΨΚq ⮌
1,538,137×10 nodes⮎ ΦΤ0Йfe → ЙgcΦΣ2 → ЗiaΨΠ4 → ГmWγΜ8 → υuOλΔG → εΛ8БnW → σwMνΒI → αΟ4Еja → БoUεΚA → ρyKοzK ⮌
1,251,320×10 nodes⮎ ΨΡ2Зhc → ЕkYαΞ6 → ωqSηΘC → νΓGσvO → γΝ6ГlY → χsQιΖE → ιΗCχrS → λΕEυtQ → ηΙAωpU → οΑIρxM ⮌
1,039,454×10 nodes⮎ YG8Бτγ → σδrΖWI → αvDφΓa → ιo6ГΚS → χΕKοtE → ιΤAωfS → οΕcΦtM → ΡiAωΠi → οYWγβM → ΡuqΗΔi ⮌
3,782×(fixed) 1 node ⮎ zyККyz ⮌
7+---Not showing digit sets 7+ due to verbosity.