Base 148: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа
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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
21 cycle 10,878×(max) 74 nodes⮎ 0д → г1 → б3 → Э7 → ХF → ЕV → ΨΒ → KР → υf → ΓΧ → IТ → ωb → ΛΞ → 2в → Я5 → ЩB → НN → οl → qκ → gτ → ΑΩ → MО → ρj → uζ → YВ → ΡΘ → 8Ь → УH → БZ → ΟΚ → 4а → Ы9 → СJ → χd → ΗΣ → AЪ → ПL → σh → yβ → QК → ιr → eφ → ΕΥ → EЦ → ЗT → γx → SИ → εv → WД → ΦΔ → GФ → ГX → ΤΖ → CШ → ЛP → λp → iς → wδ → UЖ → αz → OМ → νn → mξ → oμ → kπ → sθ → cψ → ΙΠ → 6Ю → ЧD → ЙR → ηt → aА → ΝΜ ⮌
31 cycle 551,152×(fixed) (max) 1 node ⮎ ΜдΝ ⮌
49 cycles2,487,640×(max) 18 nodes⮎ aJРБ → χΞΚe → Η3аΤ → ЭBШ8 → ХМNG → ЕξlW → ΨpκΓ → iJРσ → χxβe → ΗRИΤ → ηBШu → НZАO → οΞΚm → q3аλ → Эhς8 → ХxβG → ЕRИW → ηΧΒu ⮌
2,474,146×(max) 18 nodes⮎ KBШС → НφdO → οΖΣm → qBШλ → НhςO → οxβm → qRИλ → ηhςu → yZАγ → ΟRИΛ → η3аu → ЭZА8 → ХΞΚG → Е3аW → ЭΧΒ8 → ХJРG → ЕφdW → ΨΖΣΓ ⮌
2,469,382×(max) 18 nodes⮎ SBШЙ → НζtO → οZАm → ΟpκΛ → i3аσ → Эxβ8 → ХRИG → ЕζtW → ΨZАΓ → ΟJРΛ → χ3аe → ЭΖΣ8 → ХBШG → НДVO → οΧΒm → qJРλ → χhςe → ΗxβΤ ⮌
2,445,910×(max) 18 nodes⮎ qhςλ → yhςγ → yRИγ → ηRИu → ηZАu → ΟZАΛ → Ο3аΛ → Э3а8 → ЭФF8 → ХДVG → ЕΧΒW → ΨJРΓ → χJРe → χΖΣe → ΗBШΤ → НBШO → НξlO → οpκm ⮌
2,437,406×(max) 18 nodes⮎ K3аС → Эφd8 → ХΖΣG → ЕBШW → НΧΒO → οJРm → χpκe → ΗhςΤ → yBШγ → НRИO → οζtm → qZАλ → ΟhςΛ → y3аγ → ЭRИ8 → ХζtG → ЕZАW → ΨΞΚΓ ⮌
2,429,670×(max) 18 nodes⮎ a3аБ → ЭΞΚ8 → Х3аG → ЭДV8 → ХΧΒG → ЕJРW → χΧΒe → ΗJРΤ → χBШe → НΖΣO → οBШm → НpκO → οhςm → ypκγ → iRИσ → ηxβu → aRИБ → ηΞΚu ⮌
2,428,653×(max) 18 nodes⮎ C3аЩ → ЭМN8 → ХξlG → ЕpκW → ΨhςΓ → yJРγ → χRИe → ηΖΣu → aBШБ → НΞΚO → ο3аm → Эpκ8 → ХhςG → ЕxβW → ΨRИΓ → ηJРu → χZАe → ΟΖΣΛ ⮌
2,426,608×(max) 18 nodes⮎ S3аЙ → Эζt8 → ХZАG → ЕΞΚW → Ψ3аΓ → ЭJР8 → ХφdG → ЕΖΣW → ΨBШΓ → НJРO → χξle → ΗpκΤ → iBШσ → НxβO → οRИm → ηpκu → iZАσ → ΟxβΛ ⮌
1,212,012×9 nodes⮎ SJРЙ → χζte → ΗZАΤ → ΟBШΛ → Н3аO → Эξl8 → ХpκG → ЕhςW → ΨxβΓ ⮌
53 cycles421,586,466×3 nodes⮎ νlдξo → οmдνm → ξpдκn ⮌
211,063,216×(max) 4 nodes⮎ νmдνo → ξlдξn → οnдμm → ξoдλn ⮌
22,050×2 nodes⮎ ΝΛдΝΝ → ΝдддΜ ⮌
6+---Not showing digit sets 6+ due to verbosity.