Base 72: 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 cycles639×(max) 9 nodes⮎ 0Κ → Ι1 → Η3 → Γ7 → uF → eV → 8Β → sH → aZ ⮌
639×(max) 9 nodes⮎ 2Θ → Ε5 → yB → mN → Ol → Mn → Qj → Ir → Yb ⮌
639×(max) 9 nodes⮎ 4Ζ → Α9 → qJ → Wd → 6Δ → wD → iR → Gt → cX ⮌
639×(max) 9 nodes⮎ Az → oL → Sh → Ev → gT → Cx → kP → Kp → Uf ⮌
31 cycle 64,752×(fixed) (max) 1 node ⮎ ZΚa ⮌
42 cycles699,900×(max) 3 nodes⮎ O7Βm → uNlG → eNlW ⮌
515,478×(max) 3 nodes⮎ e7ΒW → u7ΒG → udVG ⮌
52 cycles18,469,514×(fixed) 1 node ⮎ mNΚlO ⮌
5,254×(max) 2 nodes⮎ aYΚaa → aΚΚΚZ ⮌
68 cycles100,945,443×16 nodes⮎ QG8Αtk → sdJpWI → aW6Γda → w6ΚΚΓE → Δv5ΔE7 → ywgSDC → mjDvQO → iOIqlS → YNFtmc → eP3ΖkW → ΓL7Βo8 → vtSgGF → gdDvWU → iC6ΓxS → wlFtOE → ieMmVS ⮌
77,057,712×16 nodes⮎ E86ΓΒw → wthRGE → idFtWS → eG6ΓtW → wd7ΒWE → ui6ΓRG → weGsVE → ic8ΑXS → sG4ΕtI → ΑdZZWA → q6ΚΚΓK → ΔpBxK7 → wmUeNE → iP9zkS → qLFtoK → eWSgdW ⮌
35,242,079×18 nodes⮎ M80ΙΒo → ΙtRhG2 → ΗdFtW4 → Γe6ΓV8 → wu8ΑFE → sieURI → aH9zsa → qaΚΚYK → pbFtYL → eU2ΗfW → ΕB7Βy6 → yumMFC → mfPjUO → OKAypm → oVNleM → SO8Αli → sNFtmI → eaOkZW ⮌
22,795,493×(max) 47 nodes⮎ M2ΚΚΗo → ΘnHrM3 → ΕaQiZ6 → yI0ΙrC → ΙmYaN2 → ΗP1Θk4 → ΗΓKo74 → ΓvTfE8 → uhBxSG → meEuVO → gO8ΑlU → sNBxmI → maOkZO → OM0Ιnm → ΙRNli2 → ΗOGsl4 → ΓcMmX8 → uQ4ΕjG → ΑeIqVA → qY8ΑbK → sW2ΗdI → Εa6ΓZ6 → yw0ΙDC → ΙmiQN2 → ΗPHrk4 → ΓaKoZ8 → uU0ΙfG → ΙeAyV2 → Ηo8ΑL4 → ΓsSgH8 → ubDvYG → ie2ΗVS → ΕG8Αt6 → yscWHC → mb5ΔYO → yO2ΗlC → ΕmMmN6 → yQOkjC → mMIqnO → YRNlic → OH3Ζsm → ΓbNlY8 → uO2ΗlG → ΕeMmV6 → yQ8ΑjC → smIqNI → aYOkba ⮌
702,191×11 nodes⮎ OHBxsm → mbNlYO → PN2Ηml → ΕPLnk6 → ySKohC → mUEufO → gOAylU → oNBxmM → mSOkhO → OMEunm → gRNliU ⮌
284,146×9 nodes⮎ oa6ΓZM → wS0ΙhE → ΙiEuR2 → ΗgGsT4 → ΓcCwX8 → uk4ΕPG → ΑeKoVA → qU8ΑfK → sWAydI ⮌
65,312×3 nodes⮎ mQ2ΗjO → ΕOIql6 → yYMmbC ⮌
1,332×(fixed) 1 node ⮎ aZΚΚZa ⮌
72 cycles2,293,504,048×(max) 19 nodes⮎ rYGΚsbJ → tZIΚqaH → sbGΚsYI → taJΚpZH → saFΚtZI → ubIΚqYG → tcHΚrXH → scJΚpXI → rZHΚraJ → sYHΚrbI → saIΚqZI → raGΚsZJ → tZHΚraH → scHΚrXI → saJΚpZI → rZFΚtaJ → uaHΚrZG → tdHΚrWH → scKΚoXI ⮌
348,398,000×(fixed) 1 node ⮎ saHΚrZI ⮌
8+---Not showing digit sets 8+ due to verbosity.