Base 81: 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--
22 cycles10 nodes5Ξ → ΘB → vN → Xl → DΖ → rR → Pt → Tp → Lx → bh
31 cycle 2 nodesdΤf → eΤe
436 cycles27 nodesB0ΣΙ → ΣwL2 → Πah4 → Μ6Μ8 → ΖΓFE → rmVS → PGΒu → lUnY → JCΖΑ → tgbQ → T4Ξq → ΚMvA → zYjK → fAΘe → x0ΣM → Σah2 → Π6Μ4 → ΜΕD8 → ΔqRG → nOtW → VGΒo → lIzY → hCΖc → t4ΞQ → ΚSpA → zMvK → fYje
51 cycle (fixed) 1 node sQΤrR
62 cycles28 nodesHD5ΝΖΓ → ΘskXQC → vSCΖqO → tXNulQ → XTDΕpm → rMEΔwS → paOtiU → VL7Λxo → ΔcIzgG → nh3ΟbW → ΜH5ΝΒ8 → ΘΔjYFC → voAΘUO → xXJylM → fbDΕhe → r60ΣΝS → ΣΗOtC2 → ΠuUnO4 → ΜWIzm8 → ΔhFΓbG → om5ΝWV → ΘJFΓzC → vnfcVO → XI2ΠΑm → ΞiEΔa6 → Θp7ΛTC → ΔvLwNG → nbXkhW
73 cycles4 nodesxdIΤzfM → ΑdJΤyfJ → zhKΤxbK → yfLΤwdL