Base 77: 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 cycles12 nodes1Ξ → Μ3 → Θ7 → zF → jV → DΒ → nR → Lt → Xh → 9Ζ → vJ → bd
31 cycle 2 nodesbΟd → cΟc
427 cycles30 nodesD2ΜΓ → ΚoP6 → ΔOpC → rQnO → TMrm → VIvk → dEzc → l0ΞU → ΞGx2 → ΜgX4 → Θ8Ζ8 → zwHG → jeZW → D4ΚΓ → ΖoPA → vOpK → bQne → N2Μs → ΚUj6 → ΔEzC → rkTO → TGxm → hIvY → d8Ζc → x0ΞI → ΞeZ2 → Μ4Κ4 → ΘΕ98 → zuJG → jadW
51 cycle 4 nodespOΟpQ → qOΟpP → qQΟnP → pPΟoQ
64 cycles172 nodes951ΝΚΗ → ΜΕwHA4 → ΘueZK8 → za4ΚeG → Ζj3ΛVA → ΘvDΑJ8 → znbcRG → jM0ΞsW → ΞWCΒi2 → ΜpBΓP4 → ΘrPoN8 → zUOpkG → jRFynW → jMCΒsW → pWCΒiQ → pPBΓpQ → rQOpoO → TRNqnm → TMIvsm → dWIvic → dC0ΞΓc → Ξq0ΞO2 → ΞΜRm32 → ΜΙKt64 → ΘΓYfC8 → zq6ΘOG → ΒjRmVE → nLDΑtS → nYKtgS → ZL7Ηtg → zY6ΘgG → Βj7ΗVE → znDΑRG → njLsVS → XLDΑti → nYAΔgS → tL7ΗtM → zYWhgG → jB7ΗΔW → zsCΒMG → pjViVQ → PECΒΑq → pmQnSQ → PNJurq → bUQnke → NG2Μys → ΚiUjW6 → ΔFBΓzC → sqjUON → VSEzmk → lKEzuU → laGxeU → hH3ΛxY → Θg8ΖY8 → zx7ΗHG → zjfYVG → jE6ΘΑW → ΒmCΒSE → pnJuRQ → bPLspe → XQ2Μoi → ΚOAΔq6 → ΔtRmLC → rYKtgO → ZT7Ηlg → zI6ΘwG → ΒjdaVE → nE2ΜΑS → ΚmKtS6 → ΔZJufC → rb5ΙdO → ΔT1ΝlC → ΜrHwN4 → ΘfTkZ8 → zH5ΙxG → ΔjfYVC → rE6ΘΑO → ΒmSlSE → nKIvuS → daKtec → Z40ΞΛg → ΞΗ6Θ82 → ΜΒxGD4 → ΘogXQ8 → zO8ΖqG → xjRmVI → fLDΑta → nY4ΚgS → ΖL7ΗtA → zvXgJG → jc8ΖcW → xCΟΟΒI → Γw3ΛID → ΘpdaP8 → zQ2ΜoG → ΚjNqV6 → ΔTDΑlC → rnHwRO → fTLsla → XI4Κwi → ΖeAΔaA → vt3ΛLK → ΘbXgd8 → z91ΝΖG → ΜwiVI4 → ΘeCΒa8 → zp3ΛPG → ΘjPoV8 → zPDΑpG → njPoVS → PLDΑtq → nYQngS → NL7Ηts → zYUjgG → jF7ΗzW → zkCΒUG → pjFyVQ → jPDΑpW → nQCΒoS → pOKtqQ → ZSOpmg → RK6Θuo → ΒaMreE → nV3ΛjS → ΘLDΑt8 → znXgRG → jM8ΖsW → xWCΒiI → pfBΓZQ → rP5ΙpO → ΔTPolC → rPHwpO → fTPola → PI4Κwq → ΖeQnaA → vN3ΛrK → ΘbTkd8 → zH1ΝxG → ΜjfYV4 → ΘE6ΘΑ8 → ΒzlSFE → nkIvUS → dLFytc → jY0ΞgW → ΞD7ΗΒ2 → ΜznQF4 → ΘkMrU8 → zVFyjG → kiDΑWV → nFBΓzS → rkKtUO → ZTFylg → jI6ΘwW → ΒeCΒaE → pn3ΛRQ → ΘPLsp8 → zXPohG → jP9ΕpW → vQCΒoK → pbNqdQ → TP1Νpm → ΜQIvo4 → ΘdNqb8 → zT1ΝlG → ΜjHwV4 → ΘfDΑZ8 → zn5ΙRG → ΔjLsVC → rXDΑhO → nT9ΕlS → vLHwtK → fbXgda
73 cycles4 nodesubHΟwdL → xbIΟvdI → wfJΟuZJ → vdKΟtbK