Base 112: 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--
24 cycles14 nodes8ς → ιH → ΟZ → eΚ → UΥ → oz → Aπ → εL → Ηh → Oβ → Αn → Cξ → αP → yp
31 cycle (fixed) 1 node tАu
41 cycle 3 nodesmFκΓ → ΤFκW → ΤlΒW
53 cycles4 nodesΝaАΝc → ΞZАΞb → ΟbАΜa → ΞcАΛb
63 cycles134 nodesI6ААσι → τθ9πI7 → νηΝaJE → ΨΜbΜcS → uaYΟΞu → gcААΛΙ → ΜΘ1ψgd → χYQΨΠ4 → σwgΗr8 → λQ4υΩG → ρΤwqVA → ηn5τΑK → οΛCνdC → γαWΡPO → ΓzjΔom → KGAοκη → εΣΚdWM → ΗlVΣΓi → mOGιβΓ → ΡΒFκmY → ΤiEλΖW → ΦmMγΒU → ΕqEλxk → ΦK6σζU → νΚpxeE → ΨV7ςΤS → λumΑtG → ΤE0ωμW → ωΧlΒS2 → χtFκu4 → σΤ0ωV8 → ωλmΑF2 → χΥDμU4 → σΨoyR8 → λv9πsG → ηΤ2χVK → υΛmΑd6 → οXDμΡC → γΨiΕRO → ΓvLδsm → ΗG2χκi → υΣNβW6 → οΓkΓlC → γIGιθO → ΡΞΒlaY → idFκΛΗ → ΤXNβΡW → ΓmiΕΒm → MGEλκε → ΦΣΖhWU → qlNβΓy → ΓH7ςιm → λΠFκYG → ΥΣgΗWV → olPΩΓΑ → yHBξιq → γΠ7ςYO → λΓgΗlG → ΤQGιΩW → ΡxlΒqY → iG6σκΗ → νΣNβWE → ΨΓkΓlS → uIGιθu → ΡΝААaY → ΠΞ3φaZ → σgcΛΘ8 → λYQΨΠG → ΤwgΗrW → mQ4υΩΓ → ρxFκqA → ηΤ6σVK → νΛmΑdE → ΨXDμΡS → ΨuiΕtS → uM0ωδu → ωΕААi2 → ψΖhΖi3 → υOMγβ6 → οΕΑmjC → γLDμεO → ΨΘΒlgS → uRFκΨu → ΤuААsW → ΣvNβsX → Γk2χΔm → υJFκη6 → οΤΛcVC → γnXΠΑO → ΓiCνΖm → αNFκγQ → ΤΔxpkW → mJ7ςηΓ → λΜFκcG → ΥΣYΟWV → olfΘΓΑ → SHBξιΨ → γΠttYO → ΓgААΗm → ΘΒ3φmh → σQEλΩ8 → λΦwqTG → Τr5τwW → οm4υΒC → ργEλNA → ηΦΓkTK → ΛrHθwe → ΟW4υΣa → ρldΚΓA → ηWGιΣK → ΡΛkΓdY → iXHθΡΗ → ΟjNβΕa → ΓeKεΚm → ΙVFκΤg → ΤnRΧΑW → umCνΒu → αEААλQ → μΩ9πQF → ηΦwqTK → Λr5τwe → οW4υΣC → ργkΓNA → ηΔHθkK → ΟΛIηda → ΝeWΡΚc → kaUΤΞΕ → odJζΛΑ → ΛXBξΡe → γjVΣΕO → ΓmKεΒm → ΙGEλκg → ΦΣRΧWU → uqkΓxu