Base 128: 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--
210 cycles7 nodesKφ → αf → iΧ → cδ → oΠ → Qπ → Νr
31 cycle (fixed) 1 node ΒРΓ
46 cycles9 nodes7РРЙ → Й6Й8 → ГАFE → οκVS → ΛΒΒu → FРРБ → БEБG → νκVU → ΗΒΒy
52 cycles4 nodesΩfРΩh → αfРΩg → αhРΧg → ΩgРΨh
6100 cycles48 nodesΤΙ2Нvm → ЛWCГκ6 → ЕρΑΓPC → σΠ1ОoO → НΤQοl4 → ЙΝWιr8 → БΑKυΔG → λα2НfW → ЛΓiΦΒ6 → Еc0ПδC → ПσoΟN2 → НΥPπk4 → ЙΟYηp8 → БwOρΘG → λΡAЕnW → υΓSνΒM → ΨΙ0Пvi → ПeCГβ2 → НρkΤP4 → ЙΠXθo8 → БyQοΖG → λΝ6ЙrW → ГΓKυΒE → οα0ПfS → ПΛiΦt2 → НcGωδ4 → ЙιoΟX8 → БzPπΕG → λΟ4ЛpW → ЗΓOρΒA → χΡ0ПnK → ПγSνd2 → НΙmΡv4 → ЙUCГμ8 → БρΕyPG → λΠ5КoW → ЕΓQοΒC → σΝ0ПrO → ПΤKυl2 → НαWιf4 → ЙΑiΦΔ8 → Бc2НδG → ЛλoΟV6 → ЕΔPπΑC → σΟ2НpO → ЛΤOρl6 → ЕΡWιnC → σΑSνΔO