Base 116: 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--
27 cycles12 nodesGξ → ΦX → mΖ → Iμ → Ρb → eΞ → YΥ → kΘ → Mθ → Ιj → Oζ → Εn
31 cycle (fixed) 1 node vДw
47 cycles14 nodesSJκγ → Οxte → a3АΤ → χhΚ8 → οRβG → ΨxtW → q3АΓ → χBς8 → οζNG → ΨΖlW → qJκΓ → ΟBςe → ηZΣO → ΗhΚm
52 cycles4 nodesΠbДΠd → ΡbДΠc → ΡdДΞc → ΠcДΟd
613 cycles108 nodesQ62Бψε → ωςΒpC6 → σζBςOC → θζΕmON → ΙΖHμmk → ΤOIλζa → ΡΖhΚmc → eSIλβΟ → ΡxZΣuc → ie2БΞΛ → ωZRβΤ6 → σyiΙtC → ηQ4ωδO → υΗΑqlA → λL9τιK → λΟΛgdK → ΟbTΩΡe → ufZΣΝy → iX3АΦΛ → χnRβΕ8 → οyGνtG → ΨΦ4ωXW → υqmΕΒA → λIAσμK → ιΣΞdaM → ΛhZΣΛi → iTRβαΛ → yvRβwu → y40ГАu → Гφ3А82 → БχνG74 → χπΥXE8 → οβlΖSG → ΨxJκuW → Οq2БΒe → ωaAσΣ6 → σιgΛLC → ηΜTΩgO → ΗuUΨxm → sK2БκΑ → ωΞ7φe6 → σοYΤFC → ηΩjΘUO → ΗtNζym → ΗK4ωκm → υΞJκeA → λΟYΤdK → ΟkaΡΘe → gaMηΣΝ → ΙhVΧΛk → qTNζαΓ → ΗvBςwm → ηK0ГκO → ГΞΖle2 → БZJκΤ4 → χΟiΙd8 → οbPδΡG → ΨΓeΝpW → qYCρΥΓ → εlBςΗQ → ηΓKιpO → ΝΗCρlg → εWKιΧQ → ΝΓoΓpg → WECρπΨ → εβpΒSQ → ΓxBςuq → ηC2БςO → ωζΖlO6 → σΖJκmC → ηΟIλdO → ΡΗaΡlc → geKιΞΝ → ΝZVΧΤg → qjVΧΙΓ → qPBςεΓ → ηΔBςoO → ηΗEοlO → αΗKιlU → ΝuKιxg → ΝW2БΧg → ωpVΧΓ6 → σqCρΒC → ηεAσPO → ιΗΓolM → ΛLDπιi → γΜRβgS → zxUΨut → s62БψΑ → ως7φC6 → σοεOFC → ηΩΔnUO → ΗtFξym → ΨK4ωκW → υΞpΒeA → λZBςΤK → ηΟiΙdO → ΗbPδΡm → ΓfJκΝq → ΟXBςΦe → ηnZΣΕO → ΗiGνΚm → ΦRJκγY → ΟzlΖse → aK6χκΤ → ρΞhΚeE → γZRβΤS → zxiΙut