Base 54: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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 cycles1,060×(max) 20 nodes⮎ 0r → q1 → o3 → k7 → cF → MV → 8j → aH → IZ → Gb → KX → Cf → SP → 2p → m5 → gB → UN → 6l → eD → QR ⮌
265×5 nodes⮎ 4n → i9 → YJ → Ed → OT ⮌
106×2 nodes⮎ Ah → WL ⮌
31 cycle 27,666×(fixed) (max) 1 node ⮎ QrR ⮌
410 cycles49,521×(max) 9 nodes⮎ A5li → gXJC → UDdO → Q5lS → g1pC → oTN4 → k5l8 → gbFC → ULVO ⮌
49,343×(max) 9 nodes⮎ 61pm → ofB4 → kTN8 → c5lG → gLVC → U9hO → Y5lK → gDdC → UPRO ⮌
47,894×(max) 9 nodes⮎ I1pa → oHZ4 → kHZ8 → cHZG → MHZW → I9ha → YHZK → IDda → QHZS ⮌
47,880×(max) 9 nodes⮎ E5le → gPRC → U1pO → o5l4 → kfB8 → cTNG → M5lW → g9hC → YTNK ⮌
44,609×(max) 9 nodes⮎ M9hW → Y9hK → YDdK → QDdS → Q1pS → o1p4 → oj74 → kbF8 → cLVG ⮌
44,391×(max) 9 nodes⮎ MDdW → Q9hS → Y1pK → oDd4 → kPR8 → c1pG → oLV4 → k9h8 → cXJG ⮌
42,837×(max) 9 nodes⮎ E1pe → oPR4 → k1p8 → obF4 → kLV8 → c9hG → YLVK → E9he → YPRK ⮌
42,765×(max) 9 nodes⮎ A1pi → oXJ4 → kDd8 → cPRG → M1pW → o9h4 → kXJ8 → cDdG → QLVS ⮌
13,062×3 nodes⮎ U5lO → g5lC → gTNC ⮌
12,654×3 nodes⮎ I5la → gHZC → UHZO ⮌
52 cycles4,579,094×(fixed) 1 node ⮎ aHrZI ⮌
2,968×(max) 2 nodes⮎ RPrRR → RrrrQ ⮌
65 cycles38,146,322×(max) 101 nodes⮎ E73nke → kdPRE8 → cP1pSG → oM2oV4 → mk8i76 → gdZHEC → UPHZSO → I62ola → mfHZC6 → gTHZOC → UI4mZO → iH5laA → gYIYJC → UGEcbO → OL5lWU → gB5lgC → gVTNMC → U95liO → gZ5lIC → gUGaNC → UK6kXO → eD5leE → gRPRQC → U20qpO → qn5l42 → ojfB84 → kbTNG8 → cL5lWG → gMAgVC → WU8iNM → aA6khI → eXHZKE → QICeZS → SH1paQ → oJ1pY4 → okEc74 → kdNTE8 → cP5lSG → gM2oVC → mU8iN6 → ga6kHC → eUIYNE → QG6kbS → eL1pWE → oQAgR4 → kW0qL8 → qcAgF2 → oWMUL4 → kB7jg8 → dbUMGF → OL7jWU → cB5lgG → gVLVMC → UA8ihO → aX5lKI → gICeZC → USGaPO → K62olY → mfDdC6 → gTPROC → U51pmO → oh5lA4 → kgWKB8 → cVBfMG → UM8iVO → a95liI → gZHZIC → UIGaZO → KH5laY → gJDdYC → UQEcRO → O60qlU → qf5lC2 → ogSOB4 → kV3nM8 → kc8iF8 → caMUHG → MJ7jYW → cF9hcG → YNLVUK → EA6khe → eXPRKE → QD1peS → oR1pQ4 → ok0q74 → qkcE72 → odNTE4 → kP5lS8 → gc2oFC → mUMUN6 → g86kjC → ebTNGE → QL5lWS → gB1pgC → oVTNM4 → k95li8 → gcYIFC → UNFbUO → M75lkW → gd9hEC → YUOSNK ⮌
4,741,653×30 nodes⮎ KHDdaY → QJDdYS → QF1pcS → oN1pU4 → ok6k74 → kecED8 → cRNTQG → M60qlW → qf9hC2 → oYSOJ4 → kF3nc8 → kcMUF8 → cN7jUG → cM6kVG → eM8iVE → aQ8iRI → aI0qZI → qIGaZ2 → oKGaX4 → kKCeX8 → cSCePG → SM2oVQ → m91pi6 → ogYIB4 → kVFbM8 → cM8iVG → aM8iVI → aI8iZI → aIGaZI → KIGaZY ⮌
2,035,206×18 nodes⮎ OD1peU → oR5lQ4 → kg0qB8 → qcUMF2 → oN7jU4 → kc6kF8 → ecMUFE → QN7jUS → c71pkG → odLVE4 → kP9hS8 → cY2oJG → mMEcV6 → gO8iTC → aU4mNI → iI6kZA → eYGaJE → QKEcXS ⮌
133,483×4 nodes⮎ UP1pSO → o62ol4 → mkeC76 → gdRPEC ⮌
756×(fixed) 1 node ⮎ RQrrQR ⮌
71 cycle 386,206,866×(max) 4 nodes⮎ eQBrfRE → gRDrdQC → fTCreOD → fSFrbPD ⮌
84 cycles2,932,100,358×(max) 261 nodes⮎ E630qole → qlfPRC62 → ofT1pOC4 → okT4mO74 → kid4mE98 → icZOSIFA → YNH3naUK → kJE6kdY8 → ecPEcSFE → QON2oUTS → m751pmk6 → ohgcEBA4 → kXVNTMK8 → cD95lieG → gZRLVQIC → UHA0qhaO → qXJ5lYK2 → ogFCecB4 → kVSMUPM8 → c982ojiG → mbZLVIG6 → gLH9haWC → YUJAgYNK → WFE6kdcM → ePN9hUSE → YQ72okRK → mdE0qdE6 → qgPOSSB2 → oV42onM4 → mkj8i876 → gdbZHGEC → UPLHZWSO → IB62olga → mfVHZMC6 → gTI8iZOC → aUH4maNI → iJI6kZYA → eYHEcaJE → QOJEcYTS → OF51pmcU → ohN5lUA4 → kgX6kKB8 → ecVCeMFE → SQN8iURQ → a720qpkI → qndHZE42 → ojPHZS84 → kbI2oZG8 → mcLGaWF6 → gNKAgXUC → WUD6keNM → eRA6khQE → eXQ0qRKE → qQD0qeR2 → qoR0qQ32 → qol0q632 → qoleC632 → olfRPC64 → kfT1pOC8 → ocT4mOF4 → kiN4mU98 → icZ6kIFA → eYNGaUJE → QKF6kcXS → eND1peUE → oRQ6kRQ4 → ke10qqD8 → qpcQQF22 → onMrrU44 → nnSIYP45 → jiG2ob99 → maZKWIH6 → gJHBfaYC → VTJEcYON → OF84mjcU → ibN5lUGA → gYL6kWJC → eUFAgcNE → WQN6kURM → eA70qkhE → qdXPRKE2 → oPD1peS4 → okR2oQ74 → mkd0qE76 → qgdOSEB2 → oVP3nSM4 → lj92oi87 → mebYIGD6 → gRLFbWQC → UMB0qgVO → qV95liM2 → ogZ8iIB4 → kaVGaMH8 → cKJ8iYXG → aMFCecVI → SNI8iZUQ → aH71pkaI → odJHZYE4 → kPIEcZS8 → cOH2oaTG → mMJ4mYV6 → igF8icBA → aYVMUMJI → IF97jica → cZNHZUIG → MIH6kaZW → eJH9haYE → YQJEcYRK → OFE0qdcU → qPN5lUS2 → og72okB4 → mkdUME76 → gdP7jSEC → cUP2oSNG → mM72okV6 → mgd8iEB6 → gaVOSMHC → UJ93niYO → kZF5lcI8 → gcNGaUFC → UNK6kXUO → eD75lkeE → gdRPRQEC → UP20qpSO → qn62ol42 → omjeC854 → khbRPGA8 → cXL1pWKG → oMDAgeV4 → kWR8iQL8 → caB0qgHG → qVMIYVM2 → oG98iib4 → kaZKWIH8 → cJHBfaYG → UMJEcYVO → OF95licU → gZN5lUIC → gUH6kaNC → eUJ6kYNE → eQF6kcRE → eQN0qURE → qQ70qkR2 → qod0qE32 → qolOS632 → olf3nC64 → ljfSOC87 → ebT3nOGE → kQL4mWR8 → icB0qgFA → qYVMUMJ2 → oF97jic4 → kcZMUIF8 → cNH7jaUG → cMJ6kYVG → eMF8icVE → aQN8iURI → aI70qkZI → qdIGaZE2 → oPKGaXS4 → kKD2oeX8 → mcRCeQF6 → gSN0qUPC → qU72okN2 → omd6kE54 → kheOSDA8 → cXR3nQKG → kMD0qeV8 → qcR8iQF2 → oaN0qUH4 → qkJ6kY72 → oedEcED4 → kRPNTSQ8 → c630qolG → qlfLVC62 → ofT9hOC4 → kYT4mOJ8 → icF4mcFA → iYNMUUJA → YF86kjcK → ebNDdUGE → RPL6kWSR → eB2rrogE → pga1pHB3 → omVIYM54 → khG8ibA8 → caXKWKHG → MJDBfeYW → URF9hcQO → YN60qlUK → qfE6kdC2 → oeTOSOD4 → kR53nmQ8 → khc0qFA8 → qcXMUKF2 → oND7jeU4 → kcR6kQF8 → ecN0qUFE → qQN6kUR2 → oe70qkD4 → qkdQQE72 → odOrrSE4 → ndQAgRE5 → iWP0qSLA → qYB2ogJ2 → omVEcM54 → khO8iTA8 → caX4mKHG → iMJCeYVA → YSF8icPK → aNE2odUI → mPI6kZS6 → geH2oaDC → mURIYQN6 → gG70qkbC → qdUKWNE2 → oPC6kfS4 → keT2oOD8 → mcR4mQF6 → igN0qUBA → qYV6kMJ2 → oeF8icD4 → kaRMUQH8 → cJ80qjYG → qbMEcVG2 → oOL8iWT4 → kaB4mgH8 → icVIYMFA → YNG8ibUK → aLE6kdWI → ePIAgZSE → WQH2oaRM → mJA0qhY6 → qgXEcKB2 → oVOCeTM4 → kS94miP8 → icZ2oIFA → mYNGaUJ6 → gKF6kcXC → eUNCeUNE → SQ76kkRQ → ed20qpEE → qnQOSR42 → oj40qn84 → qkjaG872 → odbJXGE4 → kPLDdWS8 → cQB2ogRG → mVM0qVM6 → qg98iiB2 → oaZUMIH4 → kJH7jaY8 → dbJEcYGF → PNLEcWUT → OB73nkgU → kdV5lME8 → gcP8iSFC → aUN2oUNI → mI76kkZ6 → gedGaEDC → URPJXSQO ⮌
7,232,422×11 nodes⮎ aRM6kVQI → eI90qiZE → qZQGaRI2 → oKH0qaX4 → qkJCeY72 → odSEcPE4 → kPO2oTS8 → mc52omF6 → mhgMUBA6 → gXV7jMKC → cUD8ieNG ⮌
5,447,217×11 nodes⮎ SE30qodQ → qlP1pS62 → pnf2oC43 → nljSO865 → ifb3nGCA → kYTKWOJ8 → cFC4mfcG → iTNLVUOA → YA74mkhK → idXDdKEA → YQPCeSRK ⮌
47,714×(fixed) 1 node ⮎ aZHrrZII ⮌
9+---Not showing digit sets 9+ due to verbosity.