Base 115: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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 14 nodes3А → φ7 → ξF → ΧV → pΒ → Bς → ζN → Ζl → Jκ → Ξd → ZΣ → hΚ → Rβ → xt
31 cycle 2 nodesuГw → vГv
442 cycles44 nodesH4ψν → τΤXA → κkΖK → ΞKθe → ΜYΣg → jUΧΙ → rOδΑ → Δ8τo → μEξI → ΩΡZU → tgΚy → T4ψα → τuvA → κ0ВK → ВΝd2 → АYΣ4 → φiΘ8 → ξOδG → ΧΓnW → pEξΓ → ΩCπU → δsxQ → Β4ψq → τAςA → κηLK → ΞΙhe → ZQβΤ → ziΘs → P6φε → πΓnE → βEξS → ΩwtU → t2Аy → ψ4ψ6 → τρBA → κεNK → ΞΕle → ZIκΤ → ΠiΘc → dOδΟ → ΔaΠo → fEξΝ → ΩWΥU → tmΔy
52 cycles4 nodesΟbГΟd → ΠaГΠc → ΡcГΞb → ΠdГΝc
67 cycles88 nodesZCAςρΤ → θεiΘOM → ΚΕOδmi → ΔRHλβo → ΣyEξsa → Ωh5χΚU → ςtRαxC → ζx3ωtO → φΖ3ωl8 → φξJιF8 → ξΨΝdUG → ΧsYΣyW → pj5χΘΓ → ςOCπεC → ζδΔmPO → ΖΓGμom → ΥJDοκY → βΟkΖcS → xcKθΟu → Μc2АΟg → ψcUΧΟ6 → ςrbΟzC → ζd7υΞO → ξΖZΡlG → ΧhJιΚW → ΞpRαΒe → xZBρΣu → ζi2АΙO → ψΖPγl6 → ςΒJιpC → ζΞBρdO → ζΖZΡlO → ΖhJιΚm → ΞSIκαe → ΠwYΣuc → jd1БΞΙ → АaOδΡ4 → φΔfΛn8 → ξVFνΧG → ΨΦpΑWV → roAςΓΑ → θE8τοM → μαΙhSI → ΣwQβua → zh1БΚs → АS6φα4 → φπvuD8 → ξγ0ВQG → ВΧzqV2 → Аq8τΑ4 → φμ9σH8 → ξκΣYJG → ΧΟiΘcW → pcOδΟΓ → ΔcCπΟo → δcEξΟQ → ΩΒbΟpU → tdBρΞy → ζa4ψΡO → τΖfΛlA → κVJιΧK → ΟΝpΑed → bYAςΤΡ → θkeΜΗM → ΚXLηΥi → ΚmQβΕi → zRHλβs → Σy6φsa → πh5χΚE → ςβRαRC → ζywtsO → Ζ62Аχm → ψρIκC6 → ςεΟbOC → ζΕcΞmO → ΖbHλΠm → ΣeIκΝa → ΠhXΤΚc → ldRαΞΗ → xaKθΡu → Μg2АΛg → ψVTΨΧ6 → ςtpΑxC → ζB3ωςO → φηΕlM8 → ξΙIκiG → ΧΠPγbW → ΒpdΝΒq