Base 127: 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--
20 cycles--
31 cycle 2 nodesΑПΓ → ΒПΒ
4279 cycles7 nodesV0Оλ → ОΓz2 → М2М4 → КЗ76 → ДωFC → ςιVO → ΣΑΒm
52 cycles4 nodesΨfПΨh → ΩeПΩg → αgПΧf → ΩhПΦg
69 cycles31 nodesyvППΗΖ → ΘΕ0Оyw → ОB5ЙД2 → МДςMB4 → ИσΤjM8 → АΦYζiG → κvbγΘW → ΒpBГΞΓ → ςO0ОρO → ОΣΠml2 → МWSμι4 → ИΘzΓv8 → АC2МГG → КριVO6 → ДΡΑΒmC → ςU0ОλO → ОΣΔyl2 → МW4Кι4 → ИЖzΓ98 → Аχ2МIG → КκδaV6 → ДΓqΜΑC → ςL1НτO → МΨΡlg4 → ИgUκΨ8 → АΔfΨzG → κh3ЛΧW → ИΒdαΒ8 → АkППΣG → ωΤVιkH → θΒXηΒY