Base 80: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
24 cycles2,133×(max) 27 nodes⮎ 0Σ → Ρ1 → Ο3 → Λ7 → ΓF → mV → GΒ → kX → CΖ → sP → Sp → Mv → Yj → AΘ → wL → ah → 6Μ → ΕD → qR → Ot → Un → Iz → gb → 4Ξ → Ι9 → yJ → ed ⮌
711×9 nodes⮎ 2Π → Ν5 → ΗB → uN → Wl → EΔ → oT → Kx → cf ⮌
237×3 nodes⮎ 8Κ → ΑH → iZ ⮌
79×(fixed) 1 node ⮎ Qr ⮌
31 cycle 88,480×(fixed) (max) 1 node ⮎ dΣe ⮌
42 cycles1,685,156×(fixed) 1 node ⮎ mFΒW ⮌
152,384×(max) 5 nodes⮎ FΣΣΓ → ΓEΓG → olVU → KFΒy → mddW ⮌
52 cycles30,865,458×(max) 4 nodes⮎ rPΣrR → sPΣrQ → sRΣpQ → rQΣqR ⮌
6,478×2 nodes⮎ ecΣee → eΣΣΣd ⮌
67 cycles355,948,472×(max) 182 nodes⮎ KE0ΡΔy → ΡpddS2 → ΟMΣΣu4 → ΞvJxM5 → ΙeYidA → yA0ΡΘK → ΡxddK2 → ΟcΣΣe4 → ΞfZhc5 → Ι82ΟΚA → ΝΒxJG6 → ΗlddWC → uEΣΣΓO → Δt7ΚOF → ΓoUmTG → mLHzwW → ibFΒga → m84ΝΚW → ΙΒFΒGA → ymkWVK → eHDΔΑe → qiΣΣYS → pj7ΚYT → ΓMAΗvG → wmYiVM → aH9ΘΑi → yj7ΚYK → ΓeAΗdG → wm0ΡVM → ΡaGΑh2 → Οk6ΛX4 → ΛΕCΕD8 → ΓsqQPG → mTProW → SLFΒwq → mbNtgW → WG4ΝΒm → ΙlFΒWA → ymEΓVK → oeGΑdU → kK0ΡxY → ΡdBΖe2 → Οu0ΡN4 → ΡΛWk72 → ΟΔDΔE4 → ΛqoSR8 → ΓPLvsG → maSohW → MG6ΛΒw → ΕlZhWE → qF7ΚΓS → ΓnNtUG → mWIylW → gGEΓΒc → ol3ΞWU → ΛKEΓx8 → ΓoceTG → mL1ΠwW → ΟbFΒg4 → Λm4ΝV8 → ΙΓGΑFA → ynjXUK → eJBΖye → ueΣΣcO → tfFΒcP → mU2ΟnW → ΝJFΒy6 → ΗmecVC → uH1ΠΑO → ΟjVlY4 → ΛGAΗΒ8 → ΓwkWLG → mbDΔgW → qG4ΝΒS → ΙlNtWA → yWEΓlK → oeEΓdU → oK0ΡxU → ΡdJxe2 → Οe0Ρd4 → ΡΛ0Ρ72 → ΡΟΓE32 → ΟΜnT64 → ΛΖJxC8 → ΓtddOG → mUΣΣmW → nkΣΣWV → ml2ΟWW → ΝGEΓΒ6 → ΗokWTC → uLDΔwO → qbVlgS → OG4ΝΒu → ΙlVlWA → yGEΓΒK → olddWU → KEΣΣΓy → Δx3ΞKF → ΛoceT8 → ΓL1ΠwG → ΟmagV4 → ΛH5ΜΑ8 → ΗΓiYFC → un9ΘUO → yWIylK → geEΓdc → o40ΡΞU → ΡΚJx82 → ΟΒddG4 → ΛkΣΣW8 → ΚlPrW9 → ΑSEΓpI → oiMuZU → YK8Ιxk → ΑdBΖeI → ui0ΡZO → ΡW8Ιl2 → ΟΑEΓH4 → ΛoiYT8 → ΓL9ΘwG → ymagVK → eH5ΜΑe → ΗiΣΣYC → ΖjNtYD → sWAΗlQ → wSEΓpM → oaMuhU → YK6Λxk → ΕdBΖeE → uq0ΡRO → ΡWOsl2 → ΟUEΓn4 → ΛoIyT8 → ΓgKwbG → mc4ΝfW → ΙG2ΟΒA → ΝykWJ6 → ΗfDΔcC → uq2ΟRO → ΝWOsl6 → ΗUEΓnC → uoIyTO → gWKwlc → cF3ΞΓg → Λn3ΞU8 → ΛΓIyF8 → ΓnfbUG → mJ3ΞyW → ΛfFΒc8 → Γm2ΟVG → ΝmGΑV6 → ΗkGΑXC → ukCΕXO → sWCΕlQ → sSEΓpQ → oSMupU → YNJxuk → eXBΖke → uCΣΣΕO → Ζt9ΘOD → ysUmPK → eTHzoe → iKΣΣwa → xhDΔaL → qc6ΛfS → ΕO2ΟtE → ΝqUmR6 → ΗPHzsC → uiSoZO → WM8Ιvm → ΑZFΒiI → mi8ΙZW → ΑG8ΙΒI → ΑlhZWI → iF7ΚΓa → Γn7ΚUG → ΓmIyVG → mgGΑbW → kG4ΝΒY → ΙlBΖWA → yuEΓNK → oeWkdU ⮌
62,034,222×36 nodes⮎ GEAΗΔΓ → wplVSM → aNFΒui → mX7ΚkW → ΓGCΕΒG → smkWVQ → SHDΔΑq → qjNtYS → WOAΗtm → wVFΒmM → maGΑhW → kG6ΛΒY → ΕlBΖWE → uqEΓRO → oWOslU → UKEΓxo → odJxeU → eK0Ρxe → ΡcΣΣe2 → Πfbfc3 → Ν42ΟΞ6 → ΝΚΖB86 → ΗΒtNGC → ulVlWO → WGEΓΒm → olFΒWU → mKEΓxW → odFΒeU → mK0ΡxW → ΡdFΒe2 → Οm0ΡV4 → ΡΛGΑ72 → ΟΔjXE4 → ΛpBΖS8 → ΓuMuNG → mYWkjW ⮌
18,843,110×19 nodes⮎ WPHzsm → iTFΒoa → mL7ΚwW → ΓbFΒgG → nl4ΝWV → ΙIEΓzA → yogaTK → eL5Μwe → ΗaΣΣgC → ΖhPraD → sS6ΛpQ → ΕSMupE → qYMujS → YOAΗtk → wVBΖmM → uaGΑhO → kW6ΛlY → ΕFBΖΓE → uqmURO ⮌
382,396×9 nodes⮎ sq0ΡRQ → ΡSOsp2 → ΟUMun4 → ΛYIyj8 → ΓgAΗbG → wm4ΝVM → ΙaGΑhA → yk6ΛXK → ΕeCΕdE ⮌
104,922×3 nodes⮎ uo2ΟTO → ΝWKwl6 → ΗcEΓfC ⮌
38,718×(fixed) 1 node ⮎ Αi8ΙZI ⮌
1,640×(fixed) 1 node ⮎ edΣΣde ⮌
72 cycles4,695,949,756×(max) 19 nodes⮎ xcIΣyfL → zdKΣweJ → yfIΣycK → zeLΣvdJ → yeHΣzdK → ΑfKΣwcI → zgJΣxbJ → ygLΣvbK → xdJΣxeL → ycJΣxfK → yeKΣwdK → xeIΣydL → zdJΣxeJ → ygJΣxbK → yeLΣvdK → xdHΣzeL → ΑeJΣxdI → zhJΣxaJ → ygMΣubK ⮌
677,251,044×(fixed) 1 node ⮎ yeJΣxdK ⮌
8+---Not showing digit sets 8+ due to verbosity.