Base 51: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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 6 nodes3l → h7 → ZF → JV → Bd → RN
31 cycle 2 nodesOoQ → PoP
444 cycles8 nodesD0nc → nOP2 → l0n4 → ng72 → lYF4 → hIV8 → ZCbG → PIVQ
51 cycle (fixed) 1 node YGoXH
67 cycles26 nodesNI2lWS → jE4ja6 → fdLSBA → VS6hMK → bB5idE → dSMRMC → R64jiO → fc2lCA → jVPOJ6 → dC0ncC → nRPON2 → l40nk4 → nhf872 → laWHE4 → hMEZS8 → ZL5iTG → dJ7gVC → ZRBcNG → RJ3kVO → hC2lc8 → jZPOF6 → dK0nUC → nR9eN2 → lV3kJ4 → igBc87 → bYQNGE
71 cycle 8 nodescP9oePD → fRCobNA → eTDoaLB → dREoZNC → cPBocPD → dPCobPC → cRBocND → dPEoZPC
88 cycles8 nodesRMH1mXSO → lG62liY4 → jhcHWC76 → daQEZOEC → RML1mTSO → l862lig4 → jhcXGC76 → daQGXOEC
96 cycles9 nodeseVI7ogWJB → hVMCobSJ8 → gVI8ofWJ9 → gXNCobRH9 → fUK9oeUKA → fVK9oeUJA → fVLAodTJA → eVK9oeUJB → fTLAodTLA