Base 66: 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---
21 cycle 2,145×(max) 33 nodes⮎ 0Δ → 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 50,050×(fixed) (max) 1 node ⮎ WΔX ⮌
424 cycles46,225×(max) 5 nodes⮎ 61Βy → ΑrB4 → wfN8 → oHlG → YTZW ⮌
45,536×(max) 5 nodes⮎ A5xu → sjJC → gPdO → IDpm → cTZS ⮌
40,620×(max) 5 nodes⮎ I1Βm → ΑTZ4 → w5x8 → snFC → gXVO ⮌
40,095×(max) 5 nodes⮎ Y1ΒW → Α1Β4 → Αv74 → wnF8 → oXVG ⮌
38,931×(max) 5 nodes⮎ I9tm → kTZK → Q5xe → sDpC → gbRO ⮌
38,687×(max) 5 nodes⮎ M9ti → kLhK → QLhe → MDpi → cLhS ⮌
38,503×(max) 5 nodes⮎ U1Βa → Α5x4 → wrB8 → ofNG → YHlW ⮌
38,395×(max) 5 nodes⮎ E1Βq → ΑbR4 → w9t8 → ojJG → YPdW ⮌
37,993×(max) 5 nodes⮎ QHle → UDpa → c5xS → s9tC → kfNK ⮌
37,369×(max) 5 nodes⮎ E5xq → sbRC → g9tO → kHlK → UPda ⮌
37,219×(max) 5 nodes⮎ M5xi → sLhC → gLhO → MHli → ULha ⮌
37,075×(max) 5 nodes⮎ A1Βu → ΑjJ4 → wPd8 → oDpG → cXVS ⮌
36,625×(max) 5 nodes⮎ E9tq → kbRK → Q9te → kDpK → cPdS ⮌
32,646×(max) 5 nodes⮎ g1ΒO → ΑHl4 → wTZ8 → o5xG → sXVC ⮌
32,310×(max) 5 nodes⮎ Y9tW → k1ΒK → ΑPd4 → wDp8 → obRG ⮌
32,174×(max) 5 nodes⮎ U9ta → k5xK → sPdC → gDpO → cHlS ⮌
32,126×(max) 5 nodes⮎ Y5xW → s1ΒC → ΑfN4 → wHl8 → oTZG ⮌
31,838×(max) 5 nodes⮎ QDpe → cDpS → c9tS → k9tK → kPdK ⮌
31,806×(max) 5 nodes⮎ M1Βi → ΑLh4 → wLh8 → oLhG → YLhW ⮌
31,790×(max) 5 nodes⮎ Q1Βe → ΑDp4 → wbR8 → o9tG → kXVK ⮌
31,790×(max) 5 nodes⮎ YDpW → c1ΒS → Α9t4 → wjJ8 → oPdG ⮌
31,742×(max) 5 nodes⮎ o1ΒG → ΑXV4 → w1Β8 → ΑnF4 → wXV8 ⮌
31,470×(max) 5 nodes⮎ U5xa → s5xC → sfNC → gHlO → UHla ⮌
31,470×(max) 5 nodes⮎ I5xm → sTZC → g5xO → sHlC → gTZO ⮌
52 cycles12,098,528×(fixed) 1 node ⮎ iLΔhM ⮌
4,420×(max) 2 nodes⮎ XVΔXX → XΔΔΔW ⮌
68 cycles49,501,186×7 nodes⮎ cJ9tkS → kR9tcK → kQAsdK → iQCqdM → eMCqhQ → eLDpiQ → cNDpgS ⮌
35,798,030×(max) 34 nodes⮎ SI8ulc → 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 ⮌
25,394,863×23 nodes⮎ QKAsje → iPDpeM → cMEohS → aL9tiU → kN5xgK → sQIkdC → gSCqbO → eI8ulQ → mTDpaI → cU6wZS → qA4ytE → ujbRKA → kP9teK → kQEodK → aQCqdU → eD5xqQ → sdDpQC → gcCqRO → eIAslQ → iTDpaM → cM6whS → qL9tiE → kcMgRK ⮌
23,541,188×3 nodes⮎ cQCqdS → eD9tqQ → kdDpQK ⮌
7,642,135×5 nodes⮎ MJ9tki → kRLhcK → QMAshe → iLDpiM → cNLhgS ⮌
1,120,983×20 nodes⮎ A60Γxu → ΓrjJC2 → ΑfPdO4 → wHDpm8 → ocUYRG → YB3zsW → wh1ΒM8 → ΑoKiF4 → wZNfU8 → oI4ylG → uYSaVA → k82ΑvK → ynPdG6 → sXDpWC → gc0ΓRO → ΓIAsl2 → ΑiSaL4 → wN7vg8 → pnIkGF → aXRbWU ⮌
219,426×5 nodes⮎ MJ5xki → sRLhcC → gMAshO → iLHliM → UNLhga ⮌
1,122×(fixed) 1 node ⮎ XWΔΔWX ⮌
71 cycle 1,473,109,638×(max) 4 nodes⮎ nWEΔoXH → pXGΔmWF → oZFΔnUG → oYIΔkVG ⮌
817 cycles7,805,274,559×(max) 176 nodes⮎ OF95xuog → 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 ⮌
1,365,242,950×6 nodes⮎ YSJ2ΑkbW → yR91Βuc6 → ΑslAsIB4 → wihSaML8 → oNL7vigG → oYNIkgVG ⮌
1,283,871,719×6 nodes⮎ YSJ0ΓkbW → ΓR91Βuc2 → ΒzlAsI43 → yviSaL86 → snN7vgGC → ogXIkWNG ⮌
895,732,428×6 nodes⮎ eUL4yiZQ → uNE4ypgA → ukbIkSJA → kSR8ucbK → mQB8usdI → mhUCqZMI ⮌
856,846,847×35 nodes⮎ SLJ9tkic → kRN9tgcK → kQJAskdK → iRQCqdcM → eMDAsqhQ → idLDpiQM → cNMCqhgS → eLJ9tkiQ → kRNDpgcK → cQJAskdS → iRD9tqcM → kdMAshQK → iQLCqidM → eNMCqhgQ → eLJDpkiQ → cRNDpgcS → cJB9tskS → khR9tcMK → kQLAsidK → iQNCqgdM → eMJCqkhQ → eRLDpicQ → cNEAspgS → ibJ9tkSM → kRM8uhcK → mQLAsidI → iUNCqgZM → eMJ4ykhQ → uRLDpicA → kcNAsgRK → iQJAskdM → iRMCqhcM → eMLAsihQ → iNLDpigM → cNMIkhgS ⮌
662,557,173×11 nodes⮎ SMJ8ukhc → mRL9ticI → kUNAsgZK → iQJ4ykdM → uRMCqhcA → keLAsiPK → iQNEogdM → aMJCqkhU → eRL5xicQ → sNEAspgC → igbIkSNM ⮌
171,269,757×6 nodes⮎ oJC2ΑrkG → yfYQcVO6 → sHC2ΑrmC → ygfUYON6 → sJH3zmkC → wgVQcYN8 ⮌
121,618,963×23 nodes⮎ MD95xuqi → sldLhQIC → gTMCqhaO → eLI6wliQ → qTNDpgaE → dbJ6wkSR → qRC8urcE → mfcAsROI → iUHAsmZM → iVM4yhYM → uML2ΑihA → ykNKigJ6 → sROIkfcC → gSHAsmbO → iVI8ulYM → mTM2ΑhaI → yUL6wiZ6 → sqN4ygDC → ugdIkQNA → kSJCqkbK → eRQ8udcQ → mEDAsqpI → idbTZSQM ⮌
116,402,072×6 nodes⮎ aM74ywhU → upL5xiEA → skbMgSJC → gRK8ujcO → mPIAsleI → iUTEoaZM ⮌
59,439,319×18 nodes⮎ aL75xwiU → spN5xgEC → sgbIkSNC → gSJ8ukbO → mRI8ulcI → mUTAsaZI → iU74ywZM → upM4yhEA → ukbKiSJA → kRO8ufcK → mQHAsmdI → iVUCqZYM → eM52ΑyhQ → ytLDpiA6 → sjcMgRKC → gPKAsjeO → iPIEoleM → aTMEohaU ⮌
51,262,737×5 nodes⮎ QMJAskhe → iRLDpicM → cNMAshgS → iLJ9tkiM → kRNLhgcK ⮌
27,694,364×12 nodes⮎ aQN4ygdU → uJD5xqkA → skdQcQJC → gRDBrqcO → gdIAslQO → iTICqlaM → eTM6whaQ → qLE6wpiE → qcbMgSRE → cKB8usjS → mhP9teMI → kULEoiZK ⮌
18,949,853×6 nodes⮎ cQLCqidS → eND9tqgQ → kdJDpkQK → cRQCqdcS → eDB9tsqQ → khdDpQMK ⮌
3,014,399×5 nodes⮎ UNMAshga → iLJ5xkiM → sRNLhgcC → gMJAskhO → iRLHlicM ⮌
2,023,654×6 nodes⮎ eZM4yhUQ → uLE4ypiA → ukbMgSJA → kRK8ujcK → mQPAsedI → iUFCqoZM ⮌
838,363×6 nodes⮎ cXO6wfWS → qHA0ΓtmE → ΓjcUYRK2 → ΑPB3zse4 → xvhEoM87 → qnaKiTGE ⮌
86,826×(fixed) 1 node ⮎ ihLΔΔhMM ⮌
9+---Not showing digit sets 9+ due to verbosity.