Base 76: 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--
23 cycles30 nodes0Ξ → Ν1 → Λ3 → Η7 → yF → iV → CΒ → oP → Op → Qn → Mr → Uj → Ez → kT → Gx → gX → 8Ζ → wH → eZ → 4Κ → Ε9 → uJ → ad → 2Μ → Ι5 → ΓB → qN → Sl → Iv → cb
31 cycle (fixed) 1 node bΞc
44 cycles9 nodesC3ΚΓ → ΗpN8 → yRlG → iJtW → aBΒe → q3ΚO → ΗRl8 → yJtG → iZdW
53 cycles4 nodesoOΞoQ → pNΞpP → qPΞnO → pQΞmP
65 cycles62 nodesIGAΓxw → shdZWM → WB3ΚΓi → ΗrBΒM8 → yqUiNG → iTDzkW → mHBΒwS → qfJtYO → aS6Ηle → ΑJ3ΚuE → ΗmacR8 → yL1ΜsG → ΛiWgV4 → ΗD9ΔΑ8 → yumQJG → ibLrcW → WC0ΝΒi → ΝpBΒO2 → ΛqQmN4 → ΗTLrk8 → yWGwhG → igAΓXW → sC8ΕΒM → wpVhOI → eRBΒma → qL3ΚsO → ΗXRlg8 → yK8ΕtG → wiYeVI → eD5ΘΑa → Γn3ΚQC → ΗqMqN8 → yUSkjG → iIEyvW → kdBΒaU → qG2ΛxO → ΙhRlW6 → ΓKAΓtC → sqYeNM → WT5Θki → ΓHBΒwC → rpeYON → UR5Θmk → ΓLFxsC → qiWgVO → SD9ΔΑm → unJtQK → bZMqed → U51ΜΙk → ΛΔFxA4 → ΗthVK8 → yZBΒeG → qi4ΙVO → ΕSCΑlA → uoIuPK → caOodc → Q2ΞΞΛo → ΜnLrQ3 → ΙWMqh6 → ΓUAΓjC → sqEyNM → kWSkhU
72 cycles19 nodesuaHΞvdK → wbJΞtcI → vdHΞvaJ → wcKΞsbI → vcGΞwbJ → xdJΞtaH → weIΞuZI → veKΞsZJ → ubIΞucK → vaIΞudJ → vcJΞtbJ → ucHΞvbK → wbIΞucI → veIΞuZJ → vcKΞsbJ → ubGΞwcK → xcIΞubH → wfIΞuYI → veLΞrZJ