Base 84: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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---
27 cycles664×(max) 8 nodes⮎ 0Χ → Φ1 → Τ3 → Ο7 → ΗF → qV → KΒ → gf ⮌
664×(max) 8 nodes⮎ 2Υ → Ρ5 → ΛB → yN → al → AΜ → ΑL → eh ⮌
664×(max) 8 nodes⮎ 6Π → ΙD → uR → St → Qv → Ur → Mz → cj ⮌
664×(max) 8 nodes⮎ 8Ξ → ΕH → mZ → CΚ → wP → Wp → IΔ → kb ⮌
332×4 nodes⮎ 4Σ → Ν9 → ΓJ → id ⮌
332×4 nodes⮎ EΘ → sT → Ox → Yn ⮌
166×2 nodes⮎ GΖ → oX ⮌
31 cycle 102,256×(fixed) (max) 1 node ⮎ fΧg ⮌
49 cycles338,164×(max) 6 nodes⮎ KBΚΓ → yhdO → a3Σm → ΟBΚ8 → ΗxNG → qZlW ⮌
323,473×(max) 6 nodes⮎ C3ΣΛ → ΟxN8 → ΗZlG → qBΚW → yJΒO → iZle ⮌
299,458×(max) 6 nodes⮎ S3Σu → ΟRt8 → ΗRtG → qRtW → SJΒu → iRte ⮌
294,600×(max) 6 nodes⮎ aJΒm → iBΚe → y3ΣO → ΟZl8 → ΗBΚG → ypVO ⮌
285,614×(max) 6 nodes⮎ i3Σe → Ο3Σ8 → ΟΖF8 → ΗpVG → qJΒW → iJΒe ⮌
282,312×(max) 6 nodes⮎ K3ΣΓ → Οhd8 → Η3ΣG → ΟpV8 → ΗJΒG → qhdW ⮌
162,974×3 nodes⮎ SBΚu → yRtO → aRtm ⮌
119,924×3 nodes⮎ q3ΣW → ΟJΒ8 → ΗhdG ⮌
119,292×3 nodes⮎ aBΚm → yBΚO → yZlO ⮌
52 cycles39,168,530×(fixed) 1 node ⮎ uRΧtS ⮌
7,138×(max) 2 nodes⮎ geΧgg → gΧΧΧf ⮌
612 cycles572,946,287×(max) 140 nodes⮎ 851ΥΡΟ → ΤΜΖFA4 → ΟΒpVK8 → ΗhJΒeG → qi2ΤdW → ΡK4ΡΒ6 → ΝΛgeBA → Γz1ΥMK → Τicid4 → Ο64ΡΠ8 → ΝΚΖFCA → ΓxpVOK → iZJΒme → iD3ΣΙe → Οv3ΣQ8 → ΟΗUqF8 → ΗrLzUG → qeMyhW → cK2ΤΒk → Ρh7Ξe6 → ΛΗ2ΤFC → ΡyqUN6 → ΛbLzkC → ye8ΝhO → Εa2ΤlI → ΡmAΛZ6 → ΛΑCΙLC → ywegPO → aX1Υom → ΤHBΚΕ4 → ΟymYN8 → ΗbDΘkG → uq8ΝVS → ΕSKΑtI → mgQufa → UC0ΦΚs → ΦxNxO2 → ΤaYml4 → ΟEAΛΘ8 → ΗΑsSLG → qfPvgW → WK0ΦΒq → ΦhJΒe2 → Τi2Τd4 → ΡΟ4Ρ76 → ΝΛΗEBA → ΓzrTMK → idNxie → a53ΣΡm → ΟΜBΚA8 → ΗΒxNKG → qhZleW → KC2ΤΚΓ → ΡxhdO6 → ΛZ3ΣmC → ΟyCΙN8 → ΗwakPG → qX9ΜoW → ΓKGΕΒK → oigedY → G51ΥΡΗ → ΤΜpVA4 → ΟΒJΒK8 → ΗigedG → q51ΥΡW → ΤΜJΒA4 → ΟΒhdK8 → Ηh3ΣeG → Οq2ΤV8 → ΡΗKΑF6 → ΛrffUC → yMΧΧyO → zwΧΧON → yx2ΤOO → ΡaYml6 → ΛEAΛΘC → ΑysSNM → ebPvki → W93ΣΝq → ΟΔJΒI8 → ΗlhdaG → qB3ΣΛW → ΟzJΒM8 → ΗicidG → q64ΡΠW → ΝΚJΒCA → ΓxhdOK → iZ3Σme → ΟD3ΣΙ8 → ΟΗuQF8 → ΗrTrUG → qOMyxW → cZJΒmk → iD7ΞΙe → Ηv3ΣQG → ΟqUqV8 → ΗMKΑzG → qgcifW → K60ΦΠΓ → ΦΚhdC2 → Τx3ΣO4 → ΠΞYm87 → ΙΖDΘGE → vtoWSR → URHΔus → mTNxsa → aPBΚwm → yXBΚoO → yaGΕlO → oaAΛlY → ΑGAΛΖM → ΑpdhWM → eJ3ΣΓi → Οj3Σc8 → ΟΗ6ΟF8 → ΙΗqUFE → urLzUS → eSMyti → cR3Σuk → ΟT7Ξs8 → ΘΖOwGF → spXnWU → OJFΖΓy → qjZlcW → KC6ΟΚΓ → ΙxhdOE → uZ3ΣmS → ΟSCΙt8 → ΗwQuPG → qXTroW → OKGΕΒy → ohZleY → GC2ΤΚΗ → ΡxpVO6 → ΛZJΒmC → yiCΙdO → wa4ΡlQ → ΝWAΛpA → ΓΑIΓLK → kiegdc ⮌
5,988,112×6 nodes⮎ eXJΒoi → iH3ΣΕe → Οn3ΣY8 → ΟΗEΗF8 → ΗsqUTG → qPLzwW ⮌
609,743×8 nodes⮎ wW2ΤpQ → ΡWIΓp6 → ΛkIΓbC → yk8ΝbO → Εa8ΝlI → ΕmAΛZI → ΑmCΙZM → weCΙhQ ⮌
397,918×8 nodes⮎ ugCΙfS → wS0ΦtQ → ΦWQup2 → ΤUIΓr4 → ΟkMyb8 → Ηc8ΝjG → Εq6ΟVI → ΙmKΑZE ⮌
283,652×8 nodes⮎ uU2ΤrS → ΡSMyt6 → ΛcQujC → yU6ΟrO → ΙaMylE → ucAΛjS → ΑS6ΟtM → ΙeQuhE ⮌
167,788×4 nodes⮎ wi8ΝdQ → ΕW4ΡpI → ΝmIΓZA → ΓkCΙbK ⮌
164,450×4 nodes⮎ ΓY4ΡnK → ΝiEΗdA → Γs4ΡTK → ΝiOwdA ⮌
157,970×4 nodes⮎ Ηo0ΦXG → ΦqGΕV2 → ΤoKΑX4 → ΟgGΕf8 ⮌
153,344×4 nodes⮎ Ηs0ΦTG → ΦqOwV2 → ΤYKΑn4 → ΟgEΗf8 ⮌
149,504×4 nodes⮎ ΗY0ΦnG → ΦqEΗV2 → ΤsKΑT4 → ΟgOwf8 ⮌
86,330×2 nodes⮎ Γo4ΡXK → ΝiGΕdA ⮌
1,806×(fixed) 1 node ⮎ gfΧΧfg ⮌
72 cycles6,523,734,518×(max) 19 nodes⮎ ΑeJΧΒhM → ΓfLΧzgK → ΒhJΧΒeL → ΓgMΧyfK → ΒgIΧΓfL → ΔhLΧzeJ → ΓiKΧΑdK → ΒiMΧydL → ΑfKΧΑgM → ΒeKΧΑhL → ΒgLΧzfL → ΑgJΧΒfM → ΓfKΧΑgK → ΒiKΧΑdL → ΒgMΧyfL → ΑfIΧΓgM → ΔgKΧΑfJ → ΓjKΧΑcK → ΒiNΧxdL ⮌
947,640,958×(fixed) 1 node ⮎ ΒgKΧΑfL ⮌
8+---Not showing digit sets 8+ due to verbosity.