Base 87: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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--
21 cycle 5 nodes7Σ → ΚF → tV → NΒ → dl
31 cycle 2 nodesgαi → hαh
437 cycles28 nodesD6ΣΝ → ΜyPE → xYpS → VGΘu → rOzY → bIΖo → nCΜc → zAΞQ → ΔYpM → hGΘi → r0ΩY → ΩIΖ2 → Χmb4 → ΣAΞ8 → ΚΓLG → tghW → N0ΩΓ → Ωej2 → Χ4Υ4 → ΣΟ98 → ΚΕJG → tkdW → N6ΣΓ → ΜejE → x4ΥS → ΠUtA → ΖOzK → lane
51 cycle (fixed) 1 node wSαvT
65 cycles19 nodesJF3ΦΚΗ → ΣumbU8 → ΚQAΞyG → ΔtXqVM → hOIΖΑi → nc0Ωmc → ΩB9ΟΞ2 → ΧΖΒMJ4 → Σmejc8 → ΚA4ΥΟG → ΠΕsVKA → ΖkMΒeK → lf5Τje → Ξ73ΦΣC → ΣΛΑNE8 → ΚwclSG → tU8ΠuW → ΘQMΒyI → pfXqja
71 cycle 8 nodesΔhIαΖhM → ΗjLαΓfJ → ΖlMαΒdK → ΕjNαΑfL → ΔhKαΔhM → ΕhLαΓhL → ΔjKαΔfM → ΕhNαΑhL