Base 113: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
24 cycles9 nodes9ς → θJ → Μd → XΣ → jΖ → Lζ → Θh → Pβ → zp
31 cycle 2 nodestБv → uБu
4112 cycles14 nodesHEμλ → ΧΡXU → riΖy → N6τε → ξΕjE → ΩKζS → Κutg → T0АΨ → Аsv2 → ψ2ψ4 → φσ76 → πλFC → δΤVO → ΔmΒm
51 cycle 4 nodesΞaБΞc → ΟaБΞb → ΟcБΜb → ΞbБΝc
66 cycles198 nodesH73χτλ → τνΡXE8 → μΨiΖSG → ΥuMδuW → ΖmББΒk → ΕΓ3χml → τJFλθ8 → μΥΜcVG → ΥoYΠΑW → nhBοΘΓ → δQEμαO → ΧΔxqlU → rI6τιy → ξΟ6τaE → ξΩdΛRE → ΩwWΣsS → vl3χΔu → τI0Аι8 → АμΞaF2 → ψΦcΜU4 → τqYΠy8 → μh7σΘG → μΥPαVG → ΥznΑpW → nD9ρξΓ → θαEμQK → ΧΜxqdU → rY6τΡy → ξi6τΗE → ξΩNγRE → ΩΔvslS → vI2ψιu → φΟ0Аa6 → АπdΛB2 → ψεWΣM4 → τΗkΔi8 → μOIθγG → ΥΞΒmbW → ncEμΝΓ → ΧaEμΟU → ΧrdΛxU → rX5υΣy → πk6τΕC → ξδJηNE → ΩΜΔkdS → vYIθΡu → Ξi0АΗc → АbNγΞ2 → ψΔbΝl4 → τbHιΞ8 → μΠbΝZG → ΥgaΞΙW → ndRΨΜΓ → vYEμΡu → Χi0АΗU → АrNγx2 → ψΔ5υl4 → τπHιB8 → μεΟZMG → ΥΗeΚiW → nVNγΥΓ → ΔoEμΑm → ΧHBοκU → δΡqxYO → Δi6τΗm → ξOGκγE → ΩΣΒmXS → vkEμΕu → ΧK0АηU → АΛqxe2 → ψW6τΤ4 → τξlΓD8 → μαGκQG → ΥΣxqXW → nk6τΕΓ → ξKEμηE → ΩΧΚeTS → vsUΥwu → p40АχΑ → АσAπ82 → ψλεLG4 → τΤΗhW8 → μmOβΓG → ΥΒFλnW → ΥnDνΒW → ΩnDνΒS → ΩvDνtS → Ωv1ωtS → ψv1ωt4 → ψτ1ω74 → ψτμE74 → τνΦTE8 → μΨqxSG → Υu6τuW → ξmББΒE → νΓZΟmF → ΧfFλΚU → ΥrTΦxW → rn5υΒy → πE6τνC → ξδΧSNE → ΩΕsvkS → vK2ψηu → φΛ0Аe6 → АπVΤB2 → ψεmΒM4 → τΗEμi8 → μΧNγTG → ΥΔrwlW → nI4φιΓ → ςΟEμaA → θΧdΛTK → ΜsWΣwe → lX3χΣΕ → τkIθΕ8 → μΞJηbG → ΥΜbΝdW → nbXΡΞΓ → jcEμΝΗ → ΧaMδΟU → ΖrdΛxk → XL5υζΤ → πΙkΔgC → δSIθΨO → ΞΔtulc → bI0АιΟ → АΟcΜa2 → ψeYΠΛ4 → τhVΤΘ8 → μnPαΒG → ΥzDνpW → Ωn9ρΒS → θvDνtK → ΩΜ1ωdS → ψvXΡt4 → τj1ωΖ8 → ψμLεF4 → τΦΗhU8 → μqOβyG → ΥΒ7σnW → μnDνΒG → ΩΥDνVS → ΩvnΑtS → vD1ωξu → ψα0АQ4 → Аτxq72 → ψν6τE4 → τξΧSD8 → μαsvQG → Υy2ψqW → φn7σΒ6 → πμDνFC → δΩΥURO → Δwozsm → HB3χπλ → τεΡXM8 → μΗiΖiG → ΥOMδγW → ΖΓmΒmk → LGEμλη → ΧΤΙfWU → rmSΧΓy → tG6τλw → ξΤ2ψWE → φΩlΓR6 → πwGκsC → δΣ3χXO → τΔjΕl8 → μLHιζG → ΥΠΘgZW → ngQΩΙΓ → xSEμΨs → Χu4φuU → ςqББxA → ρyhΗqB → ζP7σβM → μΘzohG → ΥQAπαW → ζymΒqM → ΘF7σμi → μΦOβUG → ΥΒpynW → nE8ςνΓ → κΨEμSI → ΧΠtuZU → rg0АΙy → АS6τΨ2 → ψξtuD4 → τα0АQ8 → АμxqF2 → ψΦ6τU4 → τξpyD8 → μα8ςQG → κΥxqVI → Πo6τΑa → ξfBοΚE → δΩTΦRO → Δwqxsm