Base 137: 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
СТУФХЦЧШЩЪЫЬЭЮЯа

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--
23 cycles22 nodes1Ш → Ц3 → Т7 → КF → τV → ΜΒ → 9Р → ЖJ → μd → vΣ → LД → θh → nβ → bξ → zΞ → DМ → ψR → Υt → PА → Ωp → Xς → ΘΖ
31 cycle 2 nodesΖЩΘ → ΗЩΗ
468 cycles34 nodesR4Фω → РΦrA → ЖSφK → μΡve → vKДΤ → κMВg → ζqΧk → jUτη → ΞkδΑ → hCМι → АoΩQ → ΩYπq → ΖWςΙ → Κ2ЦΕ → Ф4Ф6 → РНBA → ЖБNK → μγle → veκΤ → tMВΦ → ζQψk → Χiζs → lSφε → Σgθw → pKДα → κYπg → ΖqΧΙ → V2Цυ → ФΝz6 → ОCМC → ВωPO → δΨpm → fWςλ → ΚsΥΕ
51 cycle 4 nodesζiЩζk → ηiЩζj → ηkЩδj → ζjЩεk