Base 86: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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---
23 cycles2,380×(max) 28 nodes⮎ 0Ω → Ψ1 → Φ3 → Ρ7 → ΙF → sV → MΒ → ej → 4Υ → Ο9 → ΕJ → kd → 6Σ → ΛD → wR → Ut → Oz → an → CΜ → yP → Yp → GΘ → qX → IΖ → mb → AΞ → ΓL → gh ⮌
1,190×14 nodes⮎ 2Χ → Τ5 → ΝB → ΑN → cl → 8Π → ΗH → oZ → EΚ → uT → Qx → Wr → KΔ → if ⮌
85×(fixed) 1 node ⮎ Sv ⮌
31 cycle 109,650×(fixed) (max) 1 node ⮎ gΩh ⮌
430 cycles98,143×(max) 7 nodes⮎ 61ΧΤ → ΦΜB4 → ΡzN8 → ΙblG → s9ΞW → ΕLΒK → kfhe ⮌
93,904×(max) 7 nodes⮎ IDΚΗ → wnZS → UDΚu → wPxS → YTtq → QHΖy → oXpa ⮌
93,136×(max) 7 nodes⮎ A5ΣΟ → ΝΔJC → ΑjdO → c5Σm → Ν9ΞC → ΕzNK → kble ⮌
89,766×(max) 7 nodes⮎ cLΒm → g9Ξi → Ε1ΧK → Φjd4 → Ρ5Σ8 → ΝΘFC → ΑrVO ⮌
87,357×(max) 7 nodes⮎ g1Χi → Φ1Χ4 → ΦΠ74 → ΡΘF8 → ΙrVG → sLΒW → gLΒi ⮌
86,121×(max) 7 nodes⮎ Q9Ξy → ΕXpK → kHΖe → o5Σa → ΝDΚC → ΑvRO → cTtm ⮌
86,107×(max) 7 nodes⮎ MDΚΓ → wfhS → U1Χu → ΦPx4 → ΡXp8 → ΙHΖG → snZW ⮌
85,947×(max) 7 nodes⮎ M5ΣΓ → ΝfhC → Α1ΧO → Φbl4 → Ρ9Ξ8 → ΙΔJG → sjdW ⮌
85,947×(max) 7 nodes⮎ I9ΞΗ → ΕnZK → kDΚe → w5ΣS → ΝTtC → ΑPxO → cXpm ⮌
85,785×(max) 7 nodes⮎ UPxu → YPxq → YHΖq → oHΖa → oDΚa → wDΚS → wTtS ⮌
84,953×(max) 7 nodes⮎ ULΒu → gPxi → Y1Χq → ΦHΖ4 → ΡnZ8 → ΙDΚG → wrVS ⮌
83,737×(max) 7 nodes⮎ M9ΞΓ → ΕfhK → k1Χe → Φ5Σ4 → ΡΜB8 → ΙzNG → sblW ⮌
83,379×(max) 7 nodes⮎ E1ΧΛ → ΦvR4 → ΡTt8 → ΙPxG → sXpW → MHΖΓ → ofha ⮌
83,093×(max) 7 nodes⮎ E5ΣΛ → ΝvRC → ΑTtO → cPxm → Y9Ξq → ΕHΖK → ojda ⮌
83,085×(max) 7 nodes⮎ A1ΧΟ → ΦΔJ4 → Ρjd8 → Ι5ΣG → ΝrVC → ΑLΒO → gbli ⮌
83,049×(max) 7 nodes⮎ I1ΧΗ → ΦnZ4 → ΡDΚ8 → ΙvRG → sTtW → QLΒy → gXpi ⮌
83,049×(max) 7 nodes⮎ E9ΞΛ → ΕvRK → kTte → Q5Σy → ΝXpC → ΑHΖO → obla ⮌
76,278×(max) 7 nodes⮎ gDΚi → w1ΧS → ΦTt4 → ΡPx8 → ΙXpG → sHΖW → oLΒa ⮌
76,262×(max) 7 nodes⮎ k9Ξe → Ε5ΣK → ΝjdC → Α5ΣO → ΝblC → Α9ΞO → ΕblK ⮌
76,198×(max) 7 nodes⮎ s1ΧW → ΦLΒ4 → Ρfh8 → Ι1ΧG → ΦrV4 → ΡLΒ8 → ΙfhG ⮌
74,270×(max) 7 nodes⮎ U5Σu → ΝPxC → ΑXpO → cHΖm → o9Ξa → ΕDΚK → wjdS ⮌
74,270×(max) 7 nodes⮎ Y5Σq → ΝHΖC → ΑnZO → cDΚm → w9ΞS → ΕTtK → kPxe ⮌
74,238×(max) 7 nodes⮎ Q1Χy → ΦXp4 → ΡHΖ8 → ΙnZG → sDΚW → wLΒS → gTti ⮌
74,238×(max) 7 nodes⮎ YLΒq → gHΖi → o1Χa → ΦDΚ4 → ΡvR8 → ΙTtG → sPxW ⮌
74,222×(max) 7 nodes⮎ c9Ξm → Ε9ΞK → ΕjdK → k5Σe → Ν5ΣC → ΝzNC → ΑblO ⮌
74,190×(max) 7 nodes⮎ g5Σi → Ν1ΧC → ΦzN4 → Ρbl8 → Ι9ΞG → ΕrVK → kLΒe ⮌
74,190×(max) 7 nodes⮎ c1Χm → Φ9Ξ4 → ΡΔJ8 → ΙjdG → s5ΣW → ΝLΒC → ΑfhO ⮌
72,278×(max) 7 nodes⮎ QDΚy → wXpS → UHΖu → oPxa → YDΚq → wHΖS → oTta ⮌
72,230×(max) 7 nodes⮎ I5ΣΗ → ΝnZC → ΑDΚO → wblS → U9Ξu → ΕPxK → kXpe ⮌
72,118×(max) 7 nodes⮎ M1ΧΓ → Φfh4 → Ρ1Χ8 → ΦΘF4 → ΡrV8 → ΙLΒG → sfhW ⮌
52 cycles43,941,702×(max) 4 nodes⮎ vRΩvT → wRΩvS → wTΩtS → vSΩuT ⮌
7,480×2 nodes⮎ hfΩhh → hΩΩΩg ⮌
67 cycles448,020,525×23 nodes⮎ cWCΛrm → yL9ΞΓQ → ΕhXpgK → kI0ΨΖe → Ψn5Σa2 → ΦΝCΛB4 → ΡΒxPM8 → ΙfXpiG → sI2ΦΖW → ΤnLΒa6 → ΝgCΛhC → Αy0ΨPO → ΨcYol2 → ΦG8ΟΘ4 → ΡΗqWH8 → ΙpJΔYG → skGΗdW → qM6ΡΒY → ΛfHΖiE → wo2ΦZS → ΤUEΙt6 → ΝuOyTC → ΑaQwnO ⮌
81,135,958×(max) 43 nodes⮎ SM0ΨΒw → ΨfTti2 → ΦQ2Φx4 → ΤΡWq76 → ΝΚJΔEC → ΑvjdSO → cT5Σum → ΝR9ΞwC → ΕΑUsNK → kdNzke → c75ΣΡm → ΝΚ9ΞEC → ΕΑuSNK → kdRvke → U75ΣΡu → ΝΚPxEC → ΑvXpSO → cTHΖum → oR9Ξwa → ΕVDΚsK → wkMΑdS → eU6Ρtk → ΛP5ΣyE → ΝwYoRC → ΑVFΘsO → scMΑlW → eM8ΟΒk → Ηf5ΣiI → Νo2ΦZC → ΤΑEΙN6 → ΝuckTC → ΑR7ΠwO → ΙcUslG → sO8ΟzW → ΗbLΒmI → ogAΝha → ΓE0ΨΚM → ΨvfhS2 → ΦT1Χu4 → ΦΡQw74 → ΡΚVrE8 → ΙvLΒSG → sgSuhW ⮌
62,662,927×13 nodes⮎ aE2ΦΚo → ΤvDΚS6 → ΝwSuRC → ΑVRvsO → cUMΑtm → eP9Ξyk → ΕZ5ΣoK → ΝkEΙdC → Αu6ΡTO → ΛcQwlE → wW8ΟrS → ΗUKΓtI → oiOyfa ⮌
42,670,154×27 nodes⮎ QG8ΟΘy → ΗrXpWI → oLHΖΓa → ohDΚga → wE0ΨΚS → ΨvTtS2 → ΦTPxu4 → ΡYQwp8 → ΙWGΗrG → sqKΓXW → iMIΕΒg → mf1Χic → ΦA2ΦΞ4 → ΤΡΓK76 → ΝΚhfEC → Αv1ΧSO → ΦcSul4 → ΡS8Οv8 → ΙΗSuHG → spRvYW → UMGΗΒu → qfPxiY → YI2ΦΖq → ΤnHΖa6 → ΝoCΛZC → ΑyEΙPO → ucYolU ⮌
31,345,859×7 nodes⮎ UIGΗΖu → qnPxaY → YICΛΖq → ynHΖaQ → oYCΛpa → yHDΚΗQ → wpXpYS ⮌
726,497×14 nodes⮎ wu0ΨTS → ΨUQwt2 → ΦWOyr4 → ΡaKΓn8 → ΙiCΛfG → ys2ΦVQ → ΤYMΑp6 → ΝeGΗjC → Αq4ΤXO → ΟcIΕlA → Εm8ΟbK → ΗkAΝdI → Γo6ΡZM → ΛgEΙhE ⮌
1,892×(fixed) 1 node ⮎ hgΩΩgh ⮌
71 cycle 8,760,554,002×(max) 4 nodes⮎ ΓgJΩΔhM → ΕhLΩΒgK → ΔjKΩΓeL → ΔiNΩzfL ⮌
8+---Not showing digit sets 8+ due to verbosity.