Base 114: 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---
23 cycles4,972×(max) 44 nodes⮎ 0В → Б1 → ω3 → υ7 → νF → ΦV → oΒ → Cπ → γP → Αp → Aς → ηL → Ιh → Qβ → yr → 6φ → οD → αR → wt → 2А → χ5 → ρB → εN → Εl → Iκ → Οb → cΞ → aΠ → eΜ → WΥ → mΔ → Gμ → ΤX → kΖ → Kθ → Λf → UΧ → qz → 8τ → λH → ΡZ → gΚ → SΩ → uv ⮌
1,243×11 nodes⮎ 4ψ → σ9 → ιJ → Νd → YΣ → iΘ → Oδ → Γn → Eξ → ΨT → sx ⮌
226×2 nodes⮎ Mζ → Ηj ⮌
31 cycle 253,346×(fixed) (max) 1 node ⮎ uВv ⮌
442 cycles206,993×(max) 9 nodes⮎ IDξλ → αΠZS → wfΚu → U1АΨ → ωrx4 → υ5φ8 → ρμFC → εΥVO → ΕnΒm ⮌
204,095×(max) 9 nodes⮎ 61Аχ → ωπB4 → υδN8 → νΔlG → ΦHκW → ΡnΒa → gDξΛ → αTΧS → wrxu ⮌
203,176×(max) 9 nodes⮎ I9ςλ → ιΠZK → ΝfΚe → YTΧΤ → sjΖy → M5φη → ρΘhC → εPβO → Εzpm ⮌
196,706×(max) 9 nodes⮎ A5φσ → ρθJC → εΜdO → ΕXΣm → kHκΗ → ΡLζa → ΙfΚi → UPβΨ → Αrxq ⮌
187,243×(max) 9 nodes⮎ oDξΓ → αDξS → αvtS → w1Аu → ω1А4 → ωτ74 → υμF8 → νΥVG → ΦnΒW ⮌
185,335×(max) 9 nodes⮎ c5φΟ → ρbΞC → εbΞO → ΕbΞm → cHκΟ → ΡbΞa → gbΞΛ → cTΧΟ → sbΞy ⮌
184,599×(max) 9 nodes⮎ UDξΨ → αrxS → w5φu → ρ1АC → ωδN4 → υΔl8 → νHκG → ΦΠZW → ofΚΓ ⮌
184,259×(max) 9 nodes⮎ I1Аλ → ωΠZ4 → υfΚ8 → νTΧG → ΦrxW → o5φΓ → ρDξC → εΩRO → Εvtm ⮌
184,241×(max) 9 nodes⮎ gXΣΛ → kTΧΗ → sLζy → Ι5φi → ρPβC → εzpO → Ε9ςm → ιHκK → ΡΜda ⮌
183,423×(max) 9 nodes⮎ MDξη → αΘhS → wPβu → Α1Аq → ω9ς4 → υθJ8 → νΜdG → ΦXΣW → ojΖΓ ⮌
183,351×(max) 9 nodes⮎ oHκΓ → ΡDξa → αfΚS → wTΧu → s1Аy → ω5φ4 → υπB8 → νδNG → ΦΔlW ⮌
183,199×(max) 9 nodes⮎ M9ςη → ιΘhK → ΝPβe → ΑXΣq → k9ςΗ → ιLζK → ΝΘhe → YPβΤ → ΑjΖq ⮌
183,187×(max) 9 nodes⮎ Q9ςγ → ιzpK → Ν9ςe → ιXΣK → ΝjΖe → YLζΤ → ΙjΖi → QLζγ → Ιzpi ⮌
182,067×(max) 9 nodes⮎ Q1Аγ → ωzp4 → υ9ς8 → νθJG → ΦΜdW → oXΣΓ → kDξΗ → αLζS → Ιvti ⮌
180,627×(max) 9 nodes⮎ QHκγ → Ρzpa → g9ςΛ → ιTΧK → Νrxe → Y5φΤ → ρjΖC → εLζO → ΙΔli ⮌
180,393×(max) 9 nodes⮎ YHκΤ → ΡjΖa → gLζΛ → ΙTΧi → sPβy → Α5φq → ρ9ςC → ιδNK → ΝΔle ⮌
180,291×(max) 9 nodes⮎ E5φο → ρΩRC → εvtO → Ε1Аm → ωHκ4 → υΠZ8 → νfΚG → ΦTΧW → snΒy ⮌
180,177×(max) 9 nodes⮎ Q5φγ → ρzpC → ε9ςO → ιΔlK → ΝHκe → ΡXΣa → kfΚΗ → ULζΨ → Ιrxi ⮌
179,043×(max) 9 nodes⮎ MHκη → ΡΘha → gPβΛ → ΑTΧq → s9ςy → ι5φK → ρΜdC → εXΣO → ΕjΖm ⮌
178,665×(max) 9 nodes⮎ A1Аσ → ωθJ4 → υΜd8 → νXΣG → ΦjΖW → oLζΓ → ΙDξi → αPβS → Αvtq ⮌
178,547×(max) 9 nodes⮎ E1Аο → ωΩR4 → υvt8 → ν1АG → ωΥV4 → υnΒ8 → νDξG → αΥVS → wnΒu ⮌
178,163×(max) 9 nodes⮎ c9ςΟ → ιbΞK → ΝbΞe → cXΣΟ → kbΞΗ → cLζΟ → ΙbΞi → cPβΟ → ΑbΞq ⮌
176,625×(max) 9 nodes⮎ E9ςο → ιΩRK → Νvte → Y1АΤ → ωjΖ4 → υLζ8 → νΘhG → ΦPβW → ΑnΒq ⮌
170,646×(max) 9 nodes⮎ wHκu → Ρ1Аa → ωfΚ4 → υTΧ8 → νrxG → Φ5φW → ρnΒC → εDξO → αΔlS ⮌
168,870×(max) 9 nodes⮎ oPβΓ → ΑDξq → α9ςS → ιvtK → Ν1Аe → ωXΣ4 → υjΖ8 → νLζG → ΦΘhW ⮌
167,142×(max) 9 nodes⮎ U9ςΨ → ιrxK → Ν5φe → ρXΣC → εjΖO → ΕLζm → ΙHκi → ΡPβa → ΑfΚq ⮌
167,142×(max) 9 nodes⮎ k5φΗ → ρLζC → εΘhO → ΕPβm → ΑHκq → Ρ9ςa → ιfΚK → ΝTΧe → sXΣy ⮌
167,030×(max) 9 nodes⮎ oTΧΓ → sDξy → α5φS → ρvtC → ε1АO → ωΔl4 → υHκ8 → νΠZG → ΦfΚW ⮌
167,030×(max) 9 nodes⮎ g1АΛ → ωTΧ4 → υrx8 → ν5φG → ρΥVC → εnΒO → ΕDξm → αHκS → Ρvta ⮌
165,366×(max) 9 nodes⮎ kLζΗ → ΙLζi → ΙPβi → ΑPβq → Α9ςq → ι9ςK → ιΜdK → ΝXΣe → kXΣΗ ⮌
165,366×(max) 9 nodes⮎ Y9ςΤ → ιjΖK → ΝLζe → ΙXΣi → kPβΗ → ΑLζq → Ι9ςi → ιPβK → Νzpe ⮌
165,318×(max) 9 nodes⮎ c1АΟ → ωbΞ4 → υbΞ8 → νbΞG → ΦbΞW → obΞΓ → cDξΟ → αbΞS → wbΞu ⮌
165,254×(max) 9 nodes⮎ QDξγ → αzpS → w9ςu → ι1АK → ωΜd4 → υXΣ8 → νjΖG → ΦLζW → ΙnΒi ⮌
165,254×(max) 9 nodes⮎ M1Аη → ωΘh4 → υPβ8 → νzpG → Φ9ςW → ιnΒK → ΝDξe → αXΣS → wjΖu ⮌
165,254×(max) 9 nodes⮎ YDξΤ → αjΖS → wLζu → Ι1Аi → ωPβ4 → υzp8 → ν9ςG → ιΥVK → ΝnΒe ⮌
165,254×(max) 9 nodes⮎ k1АΗ → ωLζ4 → υΘh8 → νPβG → ΦzpW → o9ςΓ → ιDξK → αΜdS → wXΣu ⮌
165,142×(max) 9 nodes⮎ wDξu → α1АS → ωvt4 → υ1А8 → ωμF4 → υΥV8 → νnΒG → ΦDξW → αnΒS ⮌
165,142×(max) 9 nodes⮎ o1АΓ → ωDξ4 → υΩR8 → νvtG → Φ1АW → ωnΒ4 → υDξ8 → νΩRG → ΦvtW ⮌
163,494×(max) 9 nodes⮎ gTΧΛ → sTΧy → s5φy → ρ5φC → ρδNC → εΔlO → ΕHκm → ΡHκa → ΡfΚa ⮌
163,494×(max) 9 nodes⮎ I5φλ → ρΠZC → εfΚO → ΕTΧm → sHκy → Ρ5φa → ρfΚC → εTΧO → Εrxm ⮌
163,494×(max) 9 nodes⮎ U5φΨ → ρrxC → ε5φO → ρΔlC → εHκO → ΡΔla → gHκΛ → ΡTΧa → sfΚy ⮌
163,494×(max) 9 nodes⮎ UHκΨ → Ρrxa → g5φΛ → ρTΧC → εrxO → Ε5φm → ρHκC → εΠZO → ΕfΚm ⮌
52 cycles174,950,216×(fixed) 1 node ⮎ ΟbВΞc ⮌
13,108×(max) 2 nodes⮎ vtВvv → vВВВu ⮌
67 cycles2,919,534,763×(max) 127 nodes⮎ A64χφσ → σπθJCA → ιδΜdOK → ΝΔXΣme → kYGλΣΗ → ΤjLζΗY → ΙkMεΖi → ΗQKηβk → ΛzLζqg → ΙU8σΧi → λrPβyI → ΡΑ6υpa → οgAρΚE → ηαSΨRM → Ιxtvsi → Q51Аχγ → ωςzpA4 → υθ9ςK8 → νιΛeJG → ΦΞVΥcW → pnaΟΓΒ → eFBπνΝ → εΧXΣUO → ΕrjΖym → MI6υκη → οΠΘhaE → αfPβΛS → ΑwUΦtq → qA2ωςΑ → χθ9ςK6 → ριΛeJC → εΞVΥcO → ΕoaΟΒm → eICοκΝ → γΠXΣaQ → ΑkeΛΖq → WL9ςηΦ → ιΚnΒgK → ΝTDξΨe → αtXΣwS → wk2ωΖu → χL1Аη6 → ωρΙgB4 → υζRΩM8 → νΘvtiG → ΦP1АγW → ωΒnΒo4 → υECοξ8 → νγΨSPG → ΦΒtvoW → oD1АοΓ → ωβDξQ4 → υαyqR8 → νx7τsG → νΦ4χVG → σΦoΑVA → ιpBπΑK → εΝAρdO → ηΕYΡlM → ΙiIιΘi → ΟQOγβc → ΓzbΞqo → cE8σξΟ → λΩbΞSI → ΡvbΞua → gc0БΞΛ → БbTΧΟ2 → ωscΝx4 → υa4χΠ8 → σνeΛFA → ιΧVΥUK → ΝrnΒye → YE6υξΤ → οΩjΖSE → αvLζuS → Ιw0Бti → БQ2ωβ2 → ωχyq54 → υς7τA8 → ξμηKGF → ΨΥΚfWU → snTΧΓy → sF5φνy → ρΧ5φUC → ρεqyNC → εΖ7τkO → νΕKηlG → ΦΛIιfW → ΟoUΦΒc → qcCοΞΑ → γb9ςΟQ → ιΑcΝpK → ΝaAρΠe → ηfXΣΛM → ΙkUΦΖi → qQKηβΑ → Λz9ςqg → ιU8σΧK → λΝqydI → ΡZ7τΡa → νhfΚΙG → ΦUQαΧW → yrnΒys → E75φυο → ρξΩREC → εΩvtSO → Εv1Аum → ωI0Бκ4 → БυΟa72 → ωξdΜE4 → υΩXΣS8 → νvjΖuG → ΦM0БζW → БΘnΒi2 → ωPDξγ4 → υαΑoR8 → νxBπsG → εΦ4χVO → σΕoΑlA → ιJBπιK → εΞΜdcO → ΕbXΣΟm → kdHκΝΗ → ΡZLζΡa → ΙhfΚΙi → URPβαΨ → Αxrxsq ⮌
479,715,360×65 nodes⮎ KHBπλι → εΣΜdYO → ΕjXΣΗm → kNHκεΗ → ΡΖLζka → ΙgKηΚi → ΛTPβΨg → ΑtTΧwq → sA2ωςy → χθ5φK6 → ςπΛeCB → ηδVΥOM → ΙΔnΒmi → QHDξλγ → αΣzpYS → wj9ςΗu → ιN1АεK → ωΝΕkd4 → υZJθΡ8 → νΝgΙdG → ΦZRΩΡW → wogΙΒu → SD1Аοα → ωβvtQ4 → υz1Аq8 → ων8σF4 → υλΦUH8 → νΣpzYG → Φj9ςΗW → ιoMεΒK → ΝΗCοje → γYMεΣQ → ΗΑiΗpk → OMAρζε → ηΘΔliM → ΙPHκγi → ΡΒPβoa → ΑgCοΚq → γT9ςΨQ → ιΑswpK → ΝB3ψρe → υζXΣM8 → νΘjΖiG → ΦPLζγW → ΙΒnΒoi → QECοξγ → γΩzpSQ → Αv9ςuq → ιA0БςK → БθΜdK2 → ωΜXΣe4 → υkWΤΖ8 → νmKηΔG → ΦΛGλfW → ΤoUΦΒY → qkCοΖΑ → γL9ςηQ → ιΚzpgK → ΝT9ςΨe → ιtXΣwK → Νk2ωΖe → χYKηΣ6 → ρΛiΗfC → εVNδΦO → ΖΔoΑml ⮌
44,920,629×17 nodes⮎ pnCοΓΒ → γFBπνQ → εΧzpUO → Εr9ςym → ιI6υκK → οΠΜdaE → αfXΣΛS → wkUΦΖu → qL1АηΑ → ωΚ9ςg4 → υιSΨJ8 → νΞtvcG → Φb1АΟW → ωocΝΒ4 → υaCοΠ8 → νγeΛPG → ΦΒVΥoW ⮌
16,674,649×15 nodes⮎ oT5φΨΓ → ρtDξwC → εα2ωRO → χΕwsl6 → ρJ3ψιC → υεΝcN8 → νΖZΠkG → ΦgKηΚW → ΛoSΨΒg → uUCοΧw → γr1АyQ → ωΑ6υp4 → υοAρD8 → νηαQLG → ΦΚxrgW ⮌
8,454,617×3 nodes⮎ Ιp7τΑi → νQAρβG → ηΦyqVM ⮌
804,749×6 nodes⮎ iYUΦΣΙ → qjPβΗΑ → ΑN9ςεq → ιΖ9ςkK → ιΝKηdK → ΝΛYΡfe ⮌
3,306×(fixed) 1 node ⮎ vuВВuv ⮌
7+---Not showing digit sets 7+ due to verbosity.