Base 76: 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---
23 cycles2,250×(max) 30 nodes0Ξ → Ν1 → Λ3 → Η7 → yF → iV → CΒ → oP → Op → Qn → Mr → Uj → Ez → kT → Gx → gX → 8Ζ → wH → eZ → 4Κ → Ε9 → uJ → ad → 2Μ → Ι5 → ΓB → qN → Sl → Iv → cb
375×5 nodes6Θ → ΑD → mR → Kt → Yf
225×3 nodesAΔ → sL → Wh
31 cycle 76,000×(fixed) (max) 1 node bΞc
44 cycles389,796×(max) 9 nodesKBΒu → qZdO → S3Κm → ΗJt8 → yZdG → i3ΚW → ΗBΒ8 → ypNG → iRlW
373,184×(max) 9 nodesK3Κu → ΗZd8 → y3ΚG → ΗhV8 → yBΒG → qhVO → SBΒm → qJtO → aRle
371,086×(max) 9 nodesSJtm → aJte → a3Κe → Η3Κ8 → ΗxF8 → yhVG → iBΒW → qBΒO → qRlO
368,359×(max) 9 nodesC3ΚΓ → ΗpN8 → yRlG → iJtW → aBΒe → q3ΚO → ΗRl8 → yJtG → iZdW
53 cycles15,996,282×3 nodesoNΞpQ → qOΞoO → pRΞlP
8,037,808×(max) 4 nodesoOΞoQ → pNΞpP → qPΞnO → pQΞmP
5,850×2 nodescaΞcc → cΞΞΞb
65 cycles291,515,718×6 nodesgK2ΛtY → ΙZ7Ζe6 → Γy4ΙFC → ΕqiUNA → uTDzkK → maGwdS
32,779,808×(max) 62 nodesIGAΓxw → shdZWM → WB3ΚΓi → ΗrBΒM8 → yqUiNG → iTDzkW → mHBΒwS → qfJtYO → aS6Ηle → ΑJ3ΚuE → ΗmacR8 → yL1ΜsG → ΛiWgV4 → ΗD9ΔΑ8 → yumQJG → ibLrcW → WC0ΝΒi → ΝpBΒO2 → ΛqQmN4 → ΗTLrk8 → yWGwhG → igAΓXW → sC8ΕΒM → wpVhOI → eRBΒma → qL3ΚsO → ΗXRlg8 → yK8ΕtG → wiYeVI → eD5ΘΑa → Γn3ΚQC → ΗqMqN8 → yUSkjG → iIEyvW → kdBΒaU → qG2ΛxO → ΙhRlW6 → ΓKAΓtC → sqYeNM → WT5Θki → ΓHBΒwC → rpeYON → UR5Θmk → ΓLFxsC → qiWgVO → SD9ΔΑm → unJtQK → bZMqed → U51ΜΙk → ΛΔFxA4 → ΗthVK8 → yZBΒeG → qi4ΙVO → ΕSCΑlA → uoIuPK → caOodc → Q2ΞΞΛo → ΜnLrQ3 → ΙWMqh6 → ΓUAΓjC → sqEyNM → kWSkhU
213,608×6 nodescGAΓxc → sgΞΞWM → rhBΒWN → qUAΓjO → sSEylM → kWIuhU
29,524×(fixed) 1 node sWAΓhM
1,482×(fixed) 1 node cbΞΞbc
72 cycles3,285,714,436×(max) 19 nodesuaHΞvdK → wbJΞtcI → vdHΞvaJ → wcKΞsbI → vcGΞwbJ → xdJΞtaH → weIΞuZI → veKΞsZJ → ubIΞucK → vaIΞudJ → vcJΞtbJ → ucHΞvbK → wbIΞucI → veIΞuZJ → vcKΞsbJ → ubGΞwcK → xcIΞubH → wfIΞuYI → veLΞrZJ
516,042,304×(fixed) 1 node vcIΞubJ
8+---Not showing digit sets 8+ due to verbosity.