Base 112: Cycles Sequences: All Cycle Counts

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)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
24 cycles1,554×(max) 14 nodes0А → ω1 → χ3 → σ7 → λF → ΤV → mΒ → Eμ → ΦT → qx → 6τ → νD → ΨR → ut
1,554×(max) 14 nodes2ψ → υ5 → οB → γN → Γl → Gκ → ΡX → iΖ → Mδ → Εj → Kζ → Ιf → SΧ → sv
1,554×(max) 14 nodes4φ → ρ9 → ηJ → Λd → WΣ → kΔ → Iθ → Νb → aΞ → cΜ → YΠ → gΘ → QΩ → wr
1,554×(max) 14 nodes8ς → ιH → ΟZ → eΚ → UΥ → oz → Aπ → εL → Ηh → Oβ → Αn → Cξ → αP → yp
31 cycle 240,352×(fixed) (max) 1 node tАu
41 cycle 6,913,228×(max) 3 nodesmFκΓ → ΤFκW → ΤlΒW
53 cycles106,845,798×3 nodesΝZАΞc → ΟaАΝa → ΞdАΚb
53,530,924×(max) 4 nodesΝaАΝc → ΞZАΞb → ΟbАΜa → ΞcАΛb
12,654×2 nodesusАuu → uАААt
63 cycles2,692,282,183×(max) 134 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
435,309,529×62 nodesOG0ωκγ → ωΣΒlW2 → χlFκΓ4 → σΤGιV8 → λΡmΑXG → ΤjDμΕW → ΨmKεΒS → ΙuEλtg → ΦS0ωΧU → ωtpxu2 → χ80ως4 → ωσιG72 → χμΠXE4 → σΧhΖS8 → λtNβuG → ΤΓ0ωlW → ωmGιΒ2 → χΡEλX4 → σΦiΕT8 → λrLδwG → ΤΗ4υhW → ρmOαΒA → ηΑEλnK → ΦΛCνdU → αqWΡxQ → yk6σΔq → νJ7ςηE → λΨΛcRG → ΤvXΠsW → mi2χΖΓ → υNFκγ6 → οΤΓkVC → γnHθΑO → ΟΓCνla → αeGιΚQ → ΡyUΤpY → oi8ρΖΑ → ιNBξγI → γΟΓkZO → ΓfHθΙm → ΟTFκΦa → ΤrdΚwW → mW4υΣΓ → ρlFκΓA → ηΤGιVK → ΡΛmΑdY → iXDμΡΗ → ΨjNβΕS → ΓuKεtm → ΙG0ωκg → ωΣRΧW2 → χukΓt4 → σI0ωθ8 → ωλΝaF2 → χΥbΜU4 → σpZΞy8 → λe8ρΚG → ιΤUΤVI → ΟomΑza → eEAομΛ → εΧVΣSM → ΗtlΒui
3,192×(fixed) 1 node utААtu
7+---Not showing digit sets 7+ due to verbosity.