Base 107: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 cycles9 nodes3ς → ξ7 → ζF → ΞV → hΒ → Jβ → Ζd → RΣ → pt
31 cycle 2 nodesqυs → rυr
426 cycles53 nodesNIβΨ → Θyjc → VEζΟ → ΠizU → lGδy → ΜCθY → ΥcΖQ → tSΠq → n2ςw → π8μ6 → κγHC → ΧΙZO → xYΚm → bAκΙ → ΩWΜM → ΒeΔi → PIβΦ → Θunc → V6ξΟ → θizE → ΣGδS → ΜotY → d4πΗ → μSΠA → βmvK → Ζ8μe → δQΣI → Κqra → Z0τΛ → τaΘ2 → ςWΜ4 → ξeΔ8 → ζOΥG → ΞunW → h6ξΓ → θKΩE → ΣΓfS → pMΧu → z4πk → μEζA → βΟTK → Ζkxe → RCθΤ → ΥqrQ → t0τq → τ2ς2 → ςο54 → ξιB8 → ζΦNG → ΞwlW → hAκΓ → ΩKΩM → ΔΑhg
51 cycle 4 nodesΚYυΚa → ΛYυΚZ → ΛaυΘZ → ΚZυΙa
66 cycles90 nodesV2υυςΟ → σΞQΣV3 → πrhΑr6 → κIυυβC → ιγ7νID → ζΥΘaPG → ΞuWΜoW → hf5οΔΓ → κOKΩΦC → ΧΔvmfO → xO8μΦm → δwAκmI → ΩΚ9λZM → βΒZΙhK → ΖZJαΚe → ΖaQΣΙe → rYQΣΛs → rc0τΗs → τU0τΟ2 → τςjy32 → ςοEζ64 → ξιΟTC8 → ζΦkxOG → ΞwCθmW → Υh9λΒQ → βtJαpK → ΗΕ3ρed → ξTPΤΠ8 → ζtlwpG → ΞB3ρκW → ξΨgΒM8 → ζΑKΩiG → ΞΔHγfW → ΚhNΦΒa → xZJαΚm → ΖaAκΙe → ΩYQΣΛM → ΒrbΗri → VIυυβΟ → γΞAκVJ → ΩΘhΑbM → ΒWIβΝi → ΘgIβΓc → ΘVLΨΞc → ΒiUΞΑi → jJHγβΑ → ΚΗGδca → ΜZTΟΚY → ldZΙΖy → ZSCθΡΛ → ΥoaΘuQ → tX5οΜq → κe2ςΕC → πΧPΤN6 → κyspkC → ΧE2ςηO → πΡwlS6 → κoAκuC → ΩΧ5οNM → κΒxkhC → ΧKCθαO → ΥΕwleQ → tQAκΤq → Ωs2ςqM → πΒ1σh6 → ςκJαB4 → ξΨΕdM8 → ζΑQΣiG → ΞrHγrW → ΚgυυΒa → ΙΓ7νgb → ζXLΨΜG → ΞΒdΕhW → hRJαΣΓ → ΖqKΩse → ΔR1σΣg → ςqMΧs4 → ξz1σj8 → ςζFεF4 → ξΟΝVU8 → ζkgΒyG → ΞLDηΩW → ΣΓgΒgS → pMKΩΨu → ΔΑ4πig → μNHγΧA → βΚxkZK → ΖaCθΙe → ΥYQΣΛQ → trbΗrq