Base 156: 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---
23 cycles4,030×(max) 26 nodes⮎ 0м → л1 → й3 → е7 → ЭF → НV → ηΒ → SР → νv → eД → ΝΥ → 6ж → ЯD → СR → οt → iА → Εδ → MЦ → ωj → Γζ → QТ → ρr → mφ → wμ → cЖ → ΡΠ ⮌
4,030×(max) 26 nodes⮎ 2к → з5 → бB → ХN → χl → yκ → YК → αΘ → GЬ → ЛX → γΖ → KШ → Гf → ΛΧ → Aв → ЧL → Бh → Ηβ → IЪ → Зb → ΤΞ → 4и → г9 → ЩJ → Еd → ΟΣ ⮌
4,030×(max) 26 nodes⮎ 8д → ЫH → ЙZ → ΨΚ → Cа → УP → σp → qς → oτ → sπ → kψ → Αθ → UО → ιz → WМ → εΔ → OФ → υn → uξ → gВ → ΙΩ → EЮ → ПT → λx → aИ → ΦΜ ⮌
31 cycle 644,800×(fixed) (max) 1 node ⮎ ΠмΡ ⮌
417 cycles1,928,740×(max) 12 nodes⮎ KBаЩ → ХДdO → χΞΣm → y3иλ → еZИ8 → ЭΧΚG → НBаW → ХζΒO → χRРm → οxκu → iZИБ → ΨΖβΛ ⮌
1,923,914×(max) 12 nodes⮎ a3иЙ → еΧΚ8 → ЭBаG → ХМVO → χζΒm → yRРλ → οZИu → ΨhАΛ → ΗBаγ → ХJШO → Еφle → ΟxκΤ ⮌
1,896,385×(max) 12 nodes⮎ C3иб → еФN8 → ЭφlG → НxκW → ηZИΓ → ΨRРΛ → οBаu → ХhАO → χΖβm → yJШλ → ЕZИe → ΨΞΣΛ ⮌
1,890,964×(max) 12 nodes⮎ SBаС → ХξtO → χhАm → Ηxκγ → aJШЙ → ЕΧΚe → ΟBаΤ → Х3иO → еφl8 → ЭxκG → НZИW → ηΧΚΓ ⮌
1,887,436×(max) 12 nodes⮎ aRРЙ → οΧΚu → iBаБ → ХΖβO → χJШm → Еxκe → ΟZИΤ → Ψ3иΛ → еBа8 → ЭФNG → НφlW → ηxκΓ ⮌
1,809,288×(max) 12 nodes⮎ iJШБ → ЕΖβe → ΟJШΤ → Е3иe → еΞΣ8 → Э3иG → еМV8 → ЭζΒG → НRРW → οζΒu → iRРБ → οΖβu ⮌
1,765,658×(max) 12 nodes⮎ yhАλ → ΗZИγ → ΨJШΛ → ЕBаe → ХΞΣO → χ3иm → еxκ8 → ЭZИG → НΧΚW → ηBаΓ → ХRРO → χξtm ⮌
1,762,208×(max) 12 nodes⮎ ΗJШγ → ЕJШe → ЕΞΣe → Ο3иΤ → е3и8 → еЬF8 → ЭМVG → НζΒW → ηRРΓ → οRРu → οhАu → ΗhАγ ⮌
1,753,962×(max) 12 nodes⮎ SJШС → Еξte → ΟhАΤ → Η3иγ → еJШ8 → ЭДdG → НΞΣW → η3иΓ → еRР8 → ЭξtG → НhАW → ηΖβΓ ⮌
1,753,902×(max) 12 nodes⮎ K3иЩ → еДd8 → ЭΞΣG → Н3иW → еζΒ8 → ЭRРG → НξtW → ηhАΓ → ΗRРγ → οJШu → ЕhАe → ΟΖβΤ ⮌
1,753,734×(max) 12 nodes⮎ S3иС → еξt8 → ЭhАG → НΖβW → ηJШΓ → ЕRРe → οΞΣu → i3иБ → еΖβ8 → ЭJШG → НДdW → ηΞΣΓ ⮌
1,743,548×(max) 12 nodes⮎ q3иσ → еpς8 → ЭpςG → НpςW → ηpςΓ → qRРσ → οpςu → qhАσ → Ηpςγ → qJШσ → Еpςe → ΟpςΤ ⮌
952,262×6 nodes⮎ qBаσ → ХpςO → χpςm → ypςλ → qZИσ → ΨpςΛ ⮌
808,624×6 nodes⮎ ΟRРΤ → ο3иu → еhА8 → ЭΖβG → НJШW → ЕζΒe ⮌
802,488×6 nodes⮎ yZИλ → ΨZИΛ → ΨBаΛ → ХBаO → ХφlO → χxκm ⮌
802,488×6 nodes⮎ aBаЙ → ХΧΚO → χBаm → ХxκO → χZИm → ΨxκΛ ⮌
401,244×3 nodes⮎ yBаλ → ХZИO → χΧΚm ⮌
52 cycles820,359,386×(fixed) 1 node ⮎ σpмςq ⮌
24,490×(max) 2 nodes⮎ ΡΟмΡΡ → ΡмммΠ ⮌
6+---Not showing digit sets 6+ due to verbosity.