Base 125: 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 cycles6 nodesLς → Υh → bβ → nΞ → Pξ → Μp
31 cycle 2 nodeszНΒ → ΑНΑ
445 cycles50 nodesTIτλ → βΕvc → n8ДΟ → φQμI → δΙra → rGφΛ → ζIτY → βuΖc → nAВΟ → ςQμM → ΥΙri → bGφγ → ζoΜY → vMπΗ → ΣAВk → ςWζM → ΥwΔi → b6Жγ → АoΜE → μMπS → ΣΗtk → XCАη → ξwΔQ → Μ6Жq → АKςE → μΦfS → ΘeΧu → hCАΦ → ξcΩQ → ΜkΠq → VKςι → ΧΑzg → f0МΨ → МgΥ2 → КcΩ4 → ЖkΠ8 → ψUθG → θΑzW → z0МΓ → М2К2 → КЗ54 → ЖБB8 → ψοNG → θΟlW → zSκΓ → Ζ2Кw → И8Д6 → ВυHC → πγZO → ΠqΚm
51 cycle 4 nodesΧeНΧg → ΨeНΧf → ΨgНΥf → ΧfНΦg
630 cycles38 nodesJHBБφυ → πεαbYO → ΠumΞΗm → TRBБμλ → πΙΕvsO → ΠG8Дχm → φηSκWI → δΖxΓva → rA4ИГΛ → ДσIτKA → τβΧebK → ΩogΥΝe → jdNοΩΤ → ΠkYδΡm → tWSκηΙ → ΖyEψΓw → κ93ЙДU → ЖυΓxI8 → ψγ4ИaG → ДθpΛVA → τΑKςΑK → ΩΦННfe → ΨΧ2Кff → ИhfΦΥ6 → ВfbαΧC → πnfΦΞO → ΠfPνΧm → ΜgSκΦq → ΖeKςΨw → Χi8ДΤg → φfZγΧI → δrfΦΚa → rfHυΧΛ → δgIτΦa → βrdΨΚc → njHυΣΟ → δYQμεa → ΚuqΚΗs