Base 66: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
21 cycle 33 nodes0Δ → Γ1 → Α3 → w7 → oF → YV → 2Β → y5 → sB → gN → Il → Sb → 8v → mH → UZ → 4z → u9 → kJ → Qd → Cr → eP → Ep → aT → 6x → qD → cR → At → iL → Mh → Kj → Of → Gn → WX
31 cycle (fixed) 1 node WΔX
424 cycles5 nodesI5xm → sTZC → g5xO → sHlC → gTZO
52 cycles2 nodesXVΔXX → XΔΔΔW
68 cycles34 nodesSI8ulc → mT9taI → kU6wZK → qQ4ydE → ucCqRA → keAsPK → iQEodM → aMCqhU → eL5xiQ → sNDpgC → gcIkRO → SIAslc → iT9taM → kM6whK → qQKidE → cOCqfS → eH9tmQ → kVDpYK → cQ2ΑdS → yD9tq6 → skcQJC → gRBrcO → gIAslO → iTHlaM → UM6wha → qL5xiE → scMgRC → gKAsjO → iPHleM → UMEoha → aL5xiU → sN5xgC → sgIkNC → gSIkbO
71 cycle 4 nodesnWEΔoXH → pXGΔmWF → oZFΔnUG → oYIΔkVG
817 cycles176 nodesOF95xuog → slZHlUIC → gUT4yaZO → uI74ywlA → upkSaJEA → kbR7vcSK → oQB8usdG → mhYCqVMI → eUL2ΑiZQ → yNE4ypg6 → usbIkSBA → khS8ubMK → mQL8uidI → mUNCqgZI → eUJ4ykZQ → uRE4ypcA → ukbAsSJA → kiR8ucLK → mQNAsgdI → iUJCqkZM → eRM4yhcQ → uLEAspiA → kibMgSLK → QNK8ujge → mPJDpkeI → cUREocZS → aBA4ytsU → ujh5xMKA → skPKieJC → gROEofcO → aIHAsmlU → iVT5xaYM → sM72ΑwhC → ypgKiNE6 → sbOIkfSC → gSH8umbO → mVI8ulYI → mUT2ΑaZI → yU74ywZ6 → usp4yEBA → ukhaSMJA → kRL7vicK → oQNAsgdG → iYJCqkVM → eRM2ΑhcQ → yLEAspi6 → sibMgSLC → gNK8ujgO → mPJHlkeI → VTREocaZ → aB73zwsU → wph5xME8 → sobKiSFC → gZO8ufUO → mIH4ymlI → uVUSaZYA → k852ΑyvK → ytnPdGA6 → sjXDpWKC → gcP0ΓeRO → ΓIFAsol2 → ΑiZSaUL4 → wN84yvg8 → uonIkGFA → kZXRbWUK → QA50Γyte → ΓtjDpKA2 → ΑjcOeRK4 → wPGAsne8 → oiXEoWLG → aYN0ΓgVU → ΓJ62Αxk2 → ΑyrQcC54 → wtfBrOA8 → ojgGmNKG → YWPIkeXW → SF20ΓΒoc → ΓzZ9tU42 → Αvk4yJ84 → wunQcG98 → olXBrWIG → gYT0ΓaVO → ΓI72Αwl2 → ΑypSaE54 → wtb7vSA8 → pnj8uKGF → maXOeWTI → UG70Γwna → ΓpX5xWE2 → Αsb0ΓSB4 → Γwh8uM72 → ΑpmKiHE4 → wbVNfYS8 → oI92ΑulG → ylYSaVI6 → sT82ΑvaC → yng6wNG6 → sqXIkWDC → gdS0ΓbQO → ΓID8uql2 → ΑmdSaQH4 → wVD7vqY8 → pnd2ΑQGF → yaXCqWT6 → se70ΓwPC → ΓpgEoNE2 → ΑbaIkTS4 → wS96wub8 → qol8uIFE → mcZSaURI → UB84yvsa → unh5xMGA → skXKiWJC → gRO0ΓfcO → ΓIHAsml2 → ΑiVSaYL4 → wN82Αvg8 → yonIkGF6 → sZXRbWUC → gA50ΓytO → ΓtjHlKA2 → ΑjUOeZK4 → wPG4yne8 → uoXEoWFA → kaZ0ΓUTK → ΓQ74ywd2 → ΑupCqE94 → wleaSPI8 → oTF7voaG → oZY6wVUG → qY52ΑyVE → ytc2ΑRA6 → ysjAsKB6 → sihOeMLC → gNLFnigO → YNJHlkgW → URJ1Βkca → ΑRB5xsc4 → wshAsMB8 → oihKiMLG → YONKigfW → OJH1Βmkg → ΑVRHlcY4 → wUB2ΑsZ8 → yoh4yMF6 → usZKiUBA → khO4yfMK → uQLGmidA → kWNCqgXK → eQJ0ΓkdQ → ΓRECqpc2 → ΑebAsSP4 → wiF8uoL8 → omZMgUHG → YVK4yjYW → uP31ΒΑeA → ΑxkEoJ64 → wraQcTC8 → ofC6wrOG → qfYGmVOE → cWH2ΑmXS → yVA0ΓtY6 → Γsj2ΑKB2 → ΑyhOeM54 → wtLFniA8 → ojYMgVKG → YPK2ΑjeW → yPF1Βoe6 → ΑsZEoUB4 → wha4yTM8 → uoL6wiFA → qkZMgUJE → cRK4yjcS → uPB9tseA → ljhEoMKJ → aSPKiebU