Base 78: 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---
21 cycle 3,003×(max) 39 nodes⮎ 0Π → Ο1 → Ν3 → Ι7 → ΑF → kV → EΒ → mT → Ix → eb → 2Ξ → Λ5 → ΕB → sN → Ul → Gz → iX → AΖ → uL → Yh → 8Θ → yH → gZ → 6Κ → ΓD → oR → Mt → Wj → CΔ → qP → Qp → Or → Sn → Kv → af → 4Μ → Η9 → wJ → cd ⮌
31 cycle 82,082×(fixed) (max) 1 node ⮎ cΠd ⮌
417 cycles125,661×(max) 12 nodes⮎ I1Ξy → ΝfZ4 → Ι5Κ8 → ΕzFC → sjVO → UDΒm → oHxS → gLta → Y5Κi → Ε9ΖC → wrNK → cTle ⮌
124,759×(max) 12 nodes⮎ 61ΞΛ → ΝΔB4 → ΙrN8 → ΑTlG → kHxW → gDΒa → o5ΚS → ΕLtC → sXhO → U9Ζm → wHxK → gbda ⮌
122,832×(max) 12 nodes⮎ E5ΚΓ → ΕnRC → sLtO → YTli → I9Ζy → wfZK → c5Κe → Ε1ΞC → ΝrN4 → ΙTl8 → ΑHxG → kfZW ⮌
122,462×(max) 12 nodes⮎ IDΒy → ofZS → M5Κu → ΕXhC → s9ΖO → wTlK → cHxe → g1Ξa → Ν5Κ4 → ΙΔB8 → ΑrNG → kTlW ⮌
121,974×(max) 12 nodes⮎ A5ΚΗ → ΕvJC → sbdO → U1Ξm → ΝHx4 → ΙfZ8 → Α5ΚG → ΕjVC → sDΒO → oTlS → MHxu → gXha ⮌
116,979×(max) 12 nodes⮎ ULtm → YHxi → g9Ζa → w5ΚK → ΕbdC → s1ΞO → ΝTl4 → ΙHx8 → ΑfZG → k5ΚW → ΕDΒC → snRO ⮌
116,701×(max) 12 nodes⮎ Y9Ζi → w9ΖK → wbdK → c1Ξe → Ν1Ξ4 → ΝΘ74 → ΙzF8 → ΑjVG → kDΒW → oDΒS → oLtS → YLti ⮌
113,801×(max) 12 nodes⮎ E1ΞΓ → ΝnR4 → ΙLt8 → ΑXhG → k9ΖW → wDΒK → obdS → M1Ξu → ΝXh4 → Ι9Ζ8 → ΑvJG → kbdW ⮌
113,771×(max) 12 nodes⮎ A1ΞΗ → ΝvJ4 → Ιbd8 → Α1ΞG → ΝjV4 → ΙDΒ8 → ΑnRG → kLtW → YDΒi → o9ΖS → wLtK → cXhe ⮌
113,175×(max) 12 nodes⮎ Q1Ξq → ΝPp4 → ΙPp8 → ΑPpG → kPpW → QDΒq → oPpS → QLtq → YPpi → Q9Ζq → wPpK → cPpe ⮌
113,057×(max) 12 nodes⮎ E9ΖΓ → wnRK → cLte → Y1Ξi → Ν9Ζ4 → ΙvJ8 → ΑbdG → k1ΞW → ΝDΒ4 → ΙnR8 → ΑLtG → kXhW ⮌
112,979×(max) 12 nodes⮎ M9Ζu → wXhK → c9Ζe → w1ΞK → Νbd4 → Ι1Ξ8 → ΝzF4 → ΙjV8 → ΑDΒG → ojVS → MDΒu → oXhS ⮌
61,597×6 nodes⮎ Q5Κq → ΕPpC → sPpO → UPpm → QHxq → gPpa ⮌
53,624×6 nodes⮎ cDΒe → o1ΞS → ΝLt4 → ΙXh8 → Α9ΖG → wjVK ⮌
52,116×6 nodes⮎ UHxm → gHxa → g5Κa → Ε5ΚC → ΕrNC → sTlO ⮌
52,116×6 nodes⮎ I5Κy → ΕfZC → s5ΚO → ΕTlC → sHxO → gTla ⮌
26,058×3 nodes⮎ U5Κm → ΕHxC → sfZO ⮌
52 cycles27,279,098×(fixed) 1 node ⮎ qPΠpQ ⮌
6,160×(max) 2 nodes⮎ dbΠdd → dΠΠΠc ⮌
65 cycles202,312,980×48 nodes⮎ MF7ΘΑu → ΑlXhUG → kH9ΖyW → whDΒYK → oc8ΗdS → yM0ΟtI → ΟgWiZ2 → ΝC6ΙΔ4 → ΙΓqOD8 → ΑpRnQG → kPLtqW → YRDΒoi → oN9ΖsS → wVLtkK → cYEΑhe → m91ΞΗU → ΝxHxI4 → ΙgeaZ8 → Α73ΜΙG → ΙΒjVE8 → ΑnDΒSG → okKuVS → aMEΑtg → mX5ΚiU → ΕIAΕxC → useaNM → YV3Μki → ΙF9ΖΑ8 → ΑwkUJG → kdFzcW → kE0ΟΒW → ΟnDΒS2 → ΝoKuR4 → ΙaMsf8 → ΑW4ΛjG → ΗkCΓVA → wqEΑPK → mcQodU → OI0Οxs → ΟfTla2 → ΝI4Λx4 → ΙΗea98 → Αx3ΜIG → ΙkeaV8 → ΑF3ΜΑG → ΙljVU8 → ΑHDΒyG → okgYVS ⮌
117,824,470×(max) 98 nodes⮎ EA0ΟΖΓ → ΟvnRK2 → ΝbLte4 → ΙY2Νh8 → ΛΑ8ΗF6 → ΕykUHC → shFzYO → kU8ΗlW → yHDΒyI → ohfZYS → M95ΚΗu → ΕxXhIC → sf9ΖaO → wU4ΛlK → ΗcGydA → wi0ΟXK → ΟcAΕd2 → Νu0ΟL4 → ΟΙYg72 → ΝΒ7ΘE4 → ΙΑmSF8 → ΑlJvUG → kcGydW → iE0ΟΒY → Οn9ΖS2 → ΝwKuJ4 → ΙdZfc8 → Α60ΟΚG → ΟΔjVC2 → ΝrDΒO4 → ΙoSmR8 → ΑNJvsG → kcUkdW → GE0ΟΒΑ → ΟnjVS2 → ΝLDΒu4 → ΙoYgR8 → ΑN7ΘsG → ΑkUkVG → kGEΑzW → mjDΒWU → oICΓxS → qfLtaQ → YQ4Λpi → ΗP9ΖqA → xvQoKJ → ebNrec → U31ΞΝm → ΝΚHx64 → ΙΔfZC8 → Αr5ΚOG → ΕkSmVC → sKEΑvO → mbTleU → JH2Νyx → ΛhdbY6 → Ε91ΞΗC → ΝxrNI4 → ΙfTla8 → ΑI4ΛxG → ΗkeaVA → wF3ΜΑK → ΙlbdU8 → ΑH1ΞyG → ΝkgYV4 → ΙF7ΘΑ8 → ΒzkUGF → mjFzWU → kICΓxW → qfDΒaQ → oQ4ΛpS → ΗPLtqA → wYQohK → cO8Ηre → yT1ΞmI → ΝgIwZ4 → Ιe6Ιb8 → ΓΑ2ΝFE → ΛokUR6 → ΕNFzsC → skUkVO → UGEΑzm → mjHxWU → gICΓxa → qf5ΚaQ → ΕQ4ΛpC → ΗsOqNA → wVRnkK → cMEΑte → mX1ΞiU → ΝIAΕx4 → ΙueaL8 → ΑZ3ΜgG → Ιk6ΙV8 → ΓΑEΑFE → omkUTS → MJFzwu → kdXhcW ⮌
57,057,052×78 nodes⮎ MA8ΗΖu → yvXhKI → gb9Ζea → w62ΝΚK → ΛΔbdC6 → Εr1ΞOC → ΝsSmN4 → ΙVJvk8 → ΑcEΑdG → mk0ΟVU → ΟIEΑx2 → ΝmeaT4 → ΙJ3Μw8 → ΙΑccF8 → ΑkΠΠUG → zlFzUH → kiGyXW → iEAΕΒY → un9ΖSM → wYKuhK → ca8Ηfe → y51ΞΛI → ΝΖfZA4 → Ιv5ΚK8 → ΕΑaeFC → sl3ΜUO → ΙUGyl8 → ΑiGyXG → kiAΕXW → uEAΕΒM → unXhSM → YL9Ζui → wZ9ΖgK → wc6ΙdK → Γc0ΟdE → Οo0ΟR2 → ΟΝMs32 → ΝΚVj64 → ΙΔDΒC8 → ΑrnROG → kTLtmW → YJDΒwi → od9ΖcS → wM0ΟtK → ΟcWid2 → ΝC0ΟΔ4 → ΟΙqO72 → ΝΒRnE4 → ΙnLtS8 → ΑYKuhG → ka8ΗfW → yE4ΛΒI → ΗnfZSA → wL5ΚuK → ΕcYgdC → s80ΟΘO → ΟzTlG2 → ΝjHxW4 → ΙgCΓZ8 → Αq6ΙPG → ΓkQoVE → oOEΑrS → mTLtmU → YJHxwi → gd9Ζca → w60ΟΚK → ΟΔbdC2 → Νr1ΞO4 → ΝΙSm74 → ΙΒJvE8 → ΑnbdSG → kL1ΞuW → ΝZDΒg4 → Ιo6ΙR8 → ΓΑMsFE → olVjUS → MHDΒyu → ohXhYS ⮌
251,008×5 nodes⮎ kW0ΟjW → ΟECΓΒ2 → ΝqmSP4 → ΙRJvo8 → ΑcMsdG ⮌
1,560×(fixed) 1 node ⮎ dcΠΠcd ⮌
71 cycle 4,529,365,698×(max) 4 nodes⮎ wcHΠxdK → ydJΠvcI → xfIΠwaJ → xeLΠtbJ ⮌
8+---Not showing digit sets 8+ due to verbosity.