Base 116: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
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---
27 cycles1,380×(max) 12 nodes⮎ 0Д → Г1 → Б3 → χ7 → οF → ΨV → qΒ → Aτ → ιL → Λh → Sβ → wv ⮌
1,380×(max) 12 nodes⮎ 2В → ω5 → σB → ηN → Ηl → Kκ → Νf → WΧ → oΔ → Eπ → αT → ux ⮌
1,380×(max) 12 nodes⮎ 4А → υ9 → λJ → Οd → aΣ → gΜ → UΩ → sz → 6ψ → ρD → γR → yt ⮌
1,380×(max) 12 nodes⮎ Gξ → ΦX → mΖ → Iμ → Ρb → eΞ → YΥ → kΘ → Mθ → Ιj → Oζ → Εn ⮌
690×6 nodes⮎ 8φ → νH → ΤZ → iΚ → Qδ → Αr ⮌
345×3 nodes⮎ Cς → εP → Γp ⮌
115×(fixed) 1 node ⮎ cΠ ⮌
31 cycle 266,800×(fixed) (max) 1 node ⮎ vДw ⮌
47 cycles1,254,092×(max) 14 nodes⮎ KBςλ → ηΞdO → ΗZΣm → iJκΛ → ΟRβe → yZΣu → i3АΛ → χRβ8 → οxtG → Ψ3АW → χpΒ8 → οBςG → ηΧVO → ΗpΒm ⮌
1,240,955×(max) 14 nodes⮎ C3Аσ → χζN8 → οΖlG → ΨJκW → ΟpΒe → aBςΤ → ηhΚO → ΗRβm → yJκu → Ο3Аe → χZΣ8 → οhΚG → ΨRβW → ypΒu ⮌
1,214,074×(max) 14 nodes⮎ iRβΛ → yRβu → y3Аu → χ3А8 → χξF8 → οΧVG → ΨpΒW → qBςΓ → ηBςO → ηΖlO → ΗJκm → ΟJκe → ΟZΣe → iZΣΛ ⮌
1,211,490×(max) 14 nodes⮎ K3Аλ → χΞd8 → οZΣG → ΨhΚW → qRβΓ → yBςu → η3АO → χΖl8 → οJκG → ΨΞdW → qZΣΓ → iBςΛ → ηRβO → Ηxtm ⮌
1,207,742×(max) 14 nodes⮎ S3Аγ → χxt8 → ο3АG → χΧV8 → οpΒG → ΨBςW → ηpΒO → ΗBςm → ηJκO → ΟΖle → aJκΤ → ΟhΚe → aRβΤ → yhΚu ⮌
1,206,962×(max) 14 nodes⮎ SJκγ → Οxte → a3АΤ → χhΚ8 → οRβG → ΨxtW → q3АΓ → χBς8 → οζNG → ΨΖlW → qJκΓ → ΟBςe → ηZΣO → ΗhΚm ⮌
605,320×7 nodes⮎ SBςγ → ηxtO → Η3Аm → χJκ8 → οΞdG → ΨZΣW → qhΚΓ ⮌
52 cycles190,564,338×(max) 4 nodes⮎ ΠbДΠd → ΡbДΠc → ΡdДΞc → ΠcДΟd ⮌
13,570×2 nodes⮎ wuДww → wДДДv ⮌
613 cycles3,079,311,904×(max) 108 nodes⮎ Q62Бψε → ωςΒpC6 → σζBςOC → θζΕmON → ΙΖHμmk → ΤOIλζa → ΡΖhΚmc → eSIλβΟ → ΡxZΣuc → ie2БΞΛ → ωZRβΤ6 → σyiΙtC → ηQ4ωδO → υΗΑqlA → λL9τιK → λΟΛgdK → ΟbTΩΡe → ufZΣΝy → iX3АΦΛ → χnRβΕ8 → οyGνtG → ΨΦ4ωXW → υqmΕΒA → λIAσμK → ιΣΞdaM → ΛhZΣΛi → iTRβαΛ → yvRβwu → y40ГАu → Гφ3А82 → БχνG74 → χπΥXE8 → οβlΖSG → ΨxJκuW → Οq2БΒe → ωaAσΣ6 → σιgΛLC → ηΜTΩgO → ΗuUΨxm → sK2БκΑ → ωΞ7φe6 → σοYΤFC → ηΩjΘUO → ΗtNζym → ΗK4ωκm → υΞJκeA → λΟYΤdK → ΟkaΡΘe → gaMηΣΝ → ΙhVΧΛk → qTNζαΓ → ΗvBςwm → ηK0ГκO → ГΞΖle2 → БZJκΤ4 → χΟiΙd8 → οbPδΡG → ΨΓeΝpW → qYCρΥΓ → εlBςΗQ → ηΓKιpO → ΝΗCρlg → εWKιΧQ → ΝΓoΓpg → WECρπΨ → εβpΒSQ → ΓxBςuq → ηC2БςO → ωζΖlO6 → σΖJκmC → ηΟIλdO → ΡΗaΡlc → geKιΞΝ → ΝZVΧΤg → qjVΧΙΓ → qPBςεΓ → ηΔBςoO → ηΗEοlO → αΗKιlU → ΝuKιxg → ΝW2БΧg → ωpVΧΓ6 → σqCρΒC → ηεAσPO → ιΗΓolM → ΛLDπιi → γΜRβgS → zxUΨut → s62БψΑ → ως7φC6 → σοεOFC → ηΩΔnUO → ΗtFξym → ΨK4ωκW → υΞpΒeA → λZBςΤK → ηΟiΙdO → ΗbPδΡm → ΓfJκΝq → ΟXBςΦe → ηnZΣΕO → ΗiGνΚm → ΦRJκγY → ΟzlΖse → aK6χκΤ → ρΞhΚeE → γZRβΤS → zxiΙut ⮌
577,735,503×13 nodes⮎ wpJκΓw → ΟCДДρe → ςΞPδeD → εΓYΤpQ → ΓkCρΘq → εNBςηQ → ηΘΒpkO → ΗNBςηm → ηΘJκkO → ΟΗMηle → ΙaKιΣk → ΝhNζΛg → ΗWSαΧm ⮌
85,329,355×25 nodes⮎ GC2Бςο → ωζΧVO6 → σΖpΒmC → ηJBςλO → ηΠΖlcO → ΗdJκΟm → ΟbJκΡe → ΟfZΣΝe → iaWΦΣΛ → ohRβΛΕ → yTFξαu → Ψv3АwW → χq0ГΒ8 → ГοAσF2 → БιΨUL4 → χΜrzg8 → οV7φΨG → οΨqΑVG → Ψr9τΑW → λq8υΒK → νΟAσdI → ιΤaΡZM → ΛjfΜΙi → WSOεβΨ → ΕxpΒuo ⮌
51,130,914×12 nodes⮎ eL5ψιΟ → σΜZΣgC → ηiUΨΚO → ΗsQγzm → ΑK6χκs → ρΞ7φeE → ογYΤRG → ΨzjΘsW → qO6χζΓ → ρΖBςmE → ηγIλRO → ΡΗyslc ⮌
31,750,737×19 nodes⮎ igUΨΜΛ → sVRβΨΑ → yr7φΑu → ο93АυG → χμΧVI8 → οΣpΒaG → ΨhBςΛW → ηqSαΒO → ΗwAσvm → ιK0ГκM → ГΞΚhe2 → БZRβΤ4 → χyiΙt8 → οQ4ωδG → υΨΑqVA → λr9τΑK → λΟ8υdK → νΟaΡdI → ΤgaΡΜa ⮌
10,807,370×27 nodes⮎ iG0ГξΛ → ГΧRβW2 → БyoΓt4 → χE4ωπ8 → υοαSFA → λΩvvUK → ΟsДДye → ΞzFξsf → ΨY6χΥW → ρqkΗΒE → γMAσθS → ιΚxtiM → ΛR3Аγi → χzRβs8 → οy6χtG → ρΨ4ωVE → υγqΑRA → λz9τsK → λΟ6χdK → ρΟaΡdE → γgaΡΜS → ygUΨΜu → sV3АΨΑ → χr7φΑ8 → πξ8υGF → ναΦWTI → ΤvnΔwa ⮌
2,445,267×12 nodes⮎ ΡΟ0Гdc → ГeaΡΞ2 → БgYΤΜ4 → χkUΨΘ8 → οsMηzG → ΨΙ6χjW → ρqOεΒE → γΕAσnS → ιyGνtM → ΦΛ4ωhY → υmSαΖA → λwIλvK ⮌
2,315,832×3 nodes⮎ kKCρκΙ → εΞNζeQ → ΗΓYΤpm ⮌
1,425,984×12 nodes⮎ ΡΛ2Бhc → ωeSαΞ6 → σwYΤvC → ηk0ГΘO → ГΗMηl2 → БΙKιj4 → χΝOεf8 → οΕWΦnG → ΨoGνΔW → ΦqEοΒY → αmAσΖU → ιuIλxM ⮌
632,268×6 nodes⮎ ΤΝ2Бfa → ωiWΦΚ6 → σoQγΔC → ηΑEοrO → αΗ8υlU → νuKιxI ⮌
319,554×3 nodes⮎ ΤΑCρra → εi8υΚQ → νΓQγpI ⮌
115,258×(fixed) 1 node ⮎ εΓCρpQ ⮌
3,422×(fixed) 1 node ⮎ wvДДvw ⮌
7+---Not showing digit sets 7+ due to verbosity.