Base 78: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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 39 nodes0Π → Ο1 → Ν3 → Ι7 → ΑF → kV → EΒ → mT → Ix → eb → 2Ξ → Λ5 → ΕB → sN → Ul → Gz → iX → AΖ → uL → Yh → 8Θ → yH → gZ → 6Κ → ΓD → oR → Mt → Wj → CΔ → qP → Qp → Or → Sn → Kv → af → 4Μ → Η9 → wJ → cd
31 cycle (fixed) 1 node cΠd
417 cycles12 nodesM9Ζu → wXhK → c9Ζe → w1ΞK → Νbd4 → Ι1Ξ8 → ΝzF4 → ΙjV8 → ΑDΒG → ojVS → MDΒu → oXhS
52 cycles2 nodesdbΠdd → dΠΠΠc
65 cycles98 nodesEA0ΟΖΓ → ΟvnRK2 → ΝbLte4 → ΙY2Νh8 → ΛΑ8ΗF6 → ΕykUHC → shFzYO → kU8ΗlW → yHDΒyI → ohfZYS → M95ΚΗu → ΕxXhIC → sf9ΖaO → wU4ΛlK → ΗcGydA → wi0ΟXK → ΟcAΕd2 → Νu0ΟL4 → ΟΙYg72 → ΝΒ7ΘE4 → ΙΑmSF8 → ΑlJvUG → kcGydW → iE0ΟΒY → Οn9ΖS2 → ΝwKuJ4 → ΙdZfc8 → Α60ΟΚG → ΟΔjVC2 → ΝrDΒO4 → ΙoSmR8 → ΑNJvsG → kcUkdW → GE0ΟΒΑ → ΟnjVS2 → ΝLDΒu4 → ΙoYgR8 → ΑN7ΘsG → ΑkUkVG → kGEΑzW → mjDΒWU → oICΓxS → qfLtaQ → YQ4Λpi → ΗP9ΖqA → xvQoKJ → ebNrec → U31ΞΝm → ΝΚHx64 → ΙΔfZC8 → Αr5ΚOG → ΕkSmVC → sKEΑvO → mbTleU → JH2Νyx → ΛhdbY6 → Ε91ΞΗC → ΝxrNI4 → ΙfTla8 → ΑI4ΛxG → ΗkeaVA → wF3ΜΑK → ΙlbdU8 → ΑH1ΞyG → ΝkgYV4 → ΙF7ΘΑ8 → ΒzkUGF → mjFzWU → kICΓxW → qfDΒaQ → oQ4ΛpS → ΗPLtqA → wYQohK → cO8Ηre → yT1ΞmI → ΝgIwZ4 → Ιe6Ιb8 → ΓΑ2ΝFE → ΛokUR6 → ΕNFzsC → skUkVO → UGEΑzm → mjHxWU → gICΓxa → qf5ΚaQ → ΕQ4ΛpC → ΗsOqNA → wVRnkK → cMEΑte → mX1ΞiU → ΝIAΕx4 → ΙueaL8 → ΑZ3ΜgG → Ιk6ΙV8 → ΓΑEΑFE → omkUTS → MJFzwu → kdXhcW
71 cycle 4 nodeswcHΠxdK → ydJΠvcI → xfIΠwaJ → xeLΠtbJ