Base 132: 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---
25 cycles2,358×(max) 18 nodes⮎ 0Ф → У1 → С3 → Н7 → ЕF → οV → ΗΒ → 4Р → Л9 → БJ → ηd → qΣ → Qτ → Ρr → Oφ → Φn → Wξ → ΕΔ ⮌
2,358×(max) 18 nodes⮎ 2Т → П5 → ЙB → χN → Ψl → aκ → wΜ → EЖ → ρT → Λx → CИ → υP → Τp → Sς → Νv → GД → νX → ΓΖ ⮌
2,358×(max) 18 nodes⮎ 8М → ГH → λZ → yΚ → AК → ωL → γh → iβ → gδ → kΩ → cθ → sΠ → Mψ → αj → eζ → oΥ → Uπ → Ιz ⮌
1,179×9 nodes⮎ 6О → ЗD → σR → Οt → KА → εf → mΧ → Yμ → ΑΘ ⮌
393×3 nodes⮎ IВ → ιb → uΞ ⮌
31 cycle 391,952×(fixed) (max) 1 node ⮎ ΔФΕ ⮌
424 cycles720,464×(max) 5 nodes⮎ KBИБ → χζdO → ΨpΣm → aRςλ → ΟxΚu ⮌
690,565×(max) 5 nodes⮎ C3РЙ → НφN8 → ЕΧlG → οZκW → ΗxΚΓ ⮌
630,008×(max) 5 nodes⮎ K3РБ → Нζd8 → ЕpΣG → οRςW → ΟΖΒu ⮌
614,756×(max) 5 nodes⮎ a3Рλ → НxΚ8 → ЕBИG → χξVO → ΨΖΒm ⮌
591,500×(max) 5 nodes⮎ Η3РΓ → Н3Р8 → НДF8 → ЕξVG → οΖΒW ⮌
588,918×(max) 5 nodes⮎ S3Рσ → НΞt8 → ЕJАG → οζdW → ΗpΣΓ ⮌
584,384×(max) 5 nodes⮎ y3РΛ → НBИ8 → ЕφNG → οΧlW → ΗZκΓ ⮌
584,340×(max) 5 nodes⮎ aJАλ → ηxΚe → qBИΤ → χRςO → ΨΞtm ⮌
583,898×(max) 5 nodes⮎ qZκΤ → yRςΛ → ΟBИu → χJАO → ηΧle ⮌
582,730×(max) 5 nodes⮎ iBИγ → χhβO → Ψhβm → iZκγ → yhβΛ ⮌
582,350×(max) 5 nodes⮎ SBИσ → χΞtO → ΨJАm → ηZκe → ypΣΛ ⮌
582,200×(max) 5 nodes⮎ iJАγ → ηhβe → qhβΤ → iRςγ → Οhβu ⮌
580,866×(max) 5 nodes⮎ SJАσ → ηΞte → qJАΤ → ηRςe → ΟpΣu ⮌
486,196×(max) 5 nodes⮎ Ψ3Рm → НZκ8 → ЕxΚG → οBИW → χΖΒO ⮌
484,820×(max) 5 nodes⮎ ΗJАΓ → η3Рe → НpΣ8 → ЕRςG → οΞtW ⮌
484,196×(max) 5 nodes⮎ yJАΛ → ηBИe → χpΣO → ΨRςm → ΟZκu ⮌
484,100×(max) 5 nodes⮎ ΗBИΓ → χ3РO → НΧl8 → ЕZκG → οxΚW ⮌
482,820×(max) 5 nodes⮎ qRςΤ → ΟRςu → ΟJАu → ηJАe → ηpΣe ⮌
482,756×(max) 5 nodes⮎ i3Рγ → Нhβ8 → ЕhβG → οhβW → ΗhβΓ ⮌
482,724×(max) 5 nodes⮎ q3РΤ → НRς8 → ЕΞtG → οJАW → ηΖΒe ⮌
482,724×(max) 5 nodes⮎ ΗRςΓ → Ο3Рu → НJА8 → ЕζdG → οpΣW ⮌
482,628×(max) 5 nodes⮎ ο3РW → НΖΒ8 → Е3РG → НξV8 → ЕΖΒG ⮌
481,380×(max) 5 nodes⮎ yBИΛ → χBИO → χΧlO → ΨZκm → yZκΛ ⮌
481,380×(max) 5 nodes⮎ aBИλ → χxΚO → ΨBИm → χZκO → ΨxΚm ⮌
52 cycles359,915,426×(fixed) 1 node ⮎ γhФβi ⮌
17,554×(max) 2 nodes⮎ ΕΓФΕΕ → ΕФФФΔ ⮌
64 cycles7,330,210,572×(max) 192 nodes⮎ M42СРω → ПМβh86 → ЙДhβGC → χξhβWO → ΨΖhβΓm → ia2Сκγ → ПxhβΛ6 → ЙiCЗβC → χυgγPO → ΨΥjΩom → eaUοκη → ΙxpΣΛΑ → SD7МЗσ → ЕτΞtQG → οΣJАqW → ηΗQσΒe → Ρq4ПΣs → ЛRNφσA → БΨΟslK → ηbLψιe → γvpΣΝi → iSGГςγ → νΞhβuY → ΓiIБβΗ → ιh3Рγc → НuiαΞ8 → ЕgIБδG → οιkΨbW → ΗvbθΝΓ → uH3РГΟ → НμJАY8 → ЕηΑΗdG → οr5ОΡW → ЙΗOυΒC → χΦ4ПnO → ЛΨWνlA → БΕaιΔK → ηw0УΜe → УqEЕΣ2 → СρQσT4 → НΡΛwr8 → ЕPDЖυG → σοΤoVS → ΟΘTπΑu → ΛK6НАy → ЗζBИeE → χσoΤRO → ΨΠTπsm → ΛaMχκy → αxBИΛk → χeCЗζO → υΨoΤlQ → ΤbTπιq → ΛvRςΝy → ΟHBИГu → χμJАYO → ηΨΑΗle → qb5ОιΤ → ЙvRςΝC → χΟGГtO → νΨKωlY → εΓaιΖg → wm2СΧΝ → ПZFДλ6 → ЙοyΙVC → χΘ9КΑO → БΨ6НlK → ЗηaιdE → σwqΡΜS → ΟQEЕτu → ρΣJАqU → ηΛQσxe → ΡqCЗΣs → υRNφσQ → ΨΤΟspm → aTLψρλ → γΜxΚwi → iFBИЕγ → χπhβUO → ΨΚhβym → iaAЙκγ → ωxhβΛM → γiCЗβi → υigγβQ → ΤkgγΩq → kdRςηα → ΟrdζΡu → qPJАυΤ → ηΥRςoe → ΟqUοΣu → ΙRJАσΑ → ηΠ7Мse → ЕqMχΣG → οαQσjW → ΡΗeεΒs → oO4ПφΦ → ЛΧVξmA → БΗYλΒK → ηΑ4ПΘe → Лq6НΣA → ЗБQσJE → σθΠrcS → ΟtNφΟu → ΨLJАωm → ηδZκge → yqkΨΣΛ → cRBИσι → χΠtΞsO → ΨNJАχm → ηΩZκke → yqcηΣΛ → sRBИσΡ → χΠNφsO → ΩΧMχml → αcYλθk → ΑtdζΟΙ → qL7МωΤ → ЕδRςgG → οΟkΨtW → ΗcKωθΓ → εt3РΟg → НmKωΧ8 → ЕεYλfG → οΑmΦΘW → ΗY6НμΓ → ЗΒ3РΗE → Нσ4ПR8 → ЛЕΟsFA → БπLψUK → ηγΙyhe → qj9КαΤ → БfRςεK → ηΟmΦte → qYKωμΤ → εΒRςΗg → Οm4ПΧu → ЛZJАλA → БηyΙdK → ηr9КΡe → БqOυΣK → ηΦQσne → ΡqWνΣs → ΕRNφσΕ → ΨΟФФsm → ΧΠ7Мsn → ЕYMχμG → οαΑΗjW → Ηf5ОεΓ → Йn3РΦC → НχWνN8 → ЕΩΔΔkG → οcФФηW → ξθ7МcX → ЕΕsΟΔG → οM0УψW → УβΖΒi2 → Сh3Рγ4 → ОМiα87 → ЗДfδGE → σξlΧWS → ΟΖZκΓu → yK2САΛ → ПζBИe6 → ЙχoΤNC → χΩTπkO → ΨΛcηxm → saCЗκΡ → υxNφΛQ → ΨΤCЗpm → υaSρκQ → ΤΝwΛvq → SHDЖГσ → σμΞtYS → ΟΒJАΗu → ηK4ПАe → ЛζpΣeA → БpRςΤK → ηΟSρte → ΝqKωΣw → εRFДσg → οΠlΧsW → ΗaMχκΓ → αx3РΛk → НeCЗζ8 → ЕυoΤPG → οΥTπoW → ΛΗUοΒy → ΙC4ПИΑ → Лφ7МOA → ЕБΦmJG → οθXμcW → ΗΓsΟΖΓ ⮌
888,108,866×49 nodes⮎ ub1ТιΟ → СvJАΝ4 → НηGГd8 → ЕνqΡXG → οΔPτΕW → ΤΗ0УΒq → УS4Пς2 → СЛΝu94 → НВHВI8 → ЕλιaZG → οzvΜΙW → ΗG8ЛДΓ → Гξ3РWI → НλΕΓZ8 → Еz1ТΙG → Сο8ЛV4 → НГΗΑH8 → Еμ5ОYG → ЙοΑΗVC → χΘ5ОΑO → ЙΨ6НlC → ЗχaιNE → σΩvΜkS → ΟdFДηu → οrJАΡW → ηΗOυΒe → Φq4ПΣo → ЛWQσξA → БΡΕΓrK → ηP1Тυe → СΥpΣo4 → НVRςο8 → ЕΟΗΑtG → οL5ОωW → ЙδΖΒgC → χl3РΨO → НΨaιl8 → ЕwaιΜG → οwEЕΜW → ρΗEЕΒU → ρΛ4ПxU → ЛΛCЗxA → БυCЗPK → υηΤodQ → ΤrTπΡq → ΛSOυςy → ΦΞBИuo → χWIБξO → ιΨΕΓlc ⮌
148,732×(fixed) 1 node ⮎ ιuIБΞc ⮌
4,422×(fixed) 1 node ⮎ ΕΔФФΔΕ ⮌
7+---Not showing digit sets 7+ due to verbosity.