Base 61: 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 cycles600×(max) 5 nodes1x → v3 → r7 → jF → TV
600×(max) 5 nodes5t → nB → bN → Dl → XR
600×(max) 5 nodes9p → fJ → Ld → Hh → PZ
31 cycle 39,650×(max) 2 nodesTyV → UyU
415 cycles44,592×(max) 30 nodes74ts → pkDA → fWRK → L4te → pIfA → fMbK → LEje → VIfU → N0xc → xEj2 → vUT4 → r0x8 → xiF2 → vSV4 → r2v8 → tiF6 → nSVC → b2vO → tCl6 → nYPC → b8pO → hClI → ZOZQ → B8po → hcLI → PGha → RAnY → d6rM → lGhE → XQXS
44,484×(max) 30 nodes72vs → tkD6 → nWRC → b4tO → pClA → fYPK → L8pe → hIfI → PMba → FAnk → dUTM → H0xi → xQX2 → v6r4 → rkD8 → jWRG → T4tW → p2vA → teJ6 → nKdC → bIfO → NClc → ZEjQ → V8pU → h0xI → xOZ2 → vAn4 → rcL8 → jGhG → TQXW
44,320×(max) 30 nodes30xw → xs52 → vmB4 → raN8 → jClG → ZSVQ → 92vq → tgH6 → nOZC → bAnO → dClM → ZGhQ → R8pY → h6rI → lOZE → XAnS → d4tM → pGhA → fQXK → L6re → lIfE → XMbS → F4tk → pUTA → f0xK → xKd2 → vIf4 → rMb8 → jEjG → VSVU
44,250×(max) 30 nodesD8pm → hYPI → P8pa → hAnI → dOZM → HAni → dQXM → H6ri → lQXE → X6rS → l4tE → pWRA → f4tK → pKdA → fIfK → NKdc → JEjg → VMbU → F0xk → xUT2 → v0x4 → xq72 → viF4 → rSV8 → j2vG → tSV6 → n2vC → taN6 → nClC → bYPO
44,150×(max) 30 nodes96rq → lgHE → XOZS → B4to → pcLA → fGhK → RKdY → J6rg → lMbE → XEjS → V4tU → p0xA → xeJ2 → vKd4 → rIf8 → jMbG → TEjW → V2vU → t0x6 → xmB2 → vaN4 → rCl8 → jYPG → T8pW → h2vI → tOZ6 → nAnC → daNM → HCli → ZQXQ
44,087×(max) 30 nodesLIfe → NIfc → NEjc → VEjU → V0xU → x0x2 → xu32 → vq74 → riF8 → jSVG → T2vW → t2v6 → tmB6 → naNC → bClO → ZClQ → Z8pQ → h8pI → hOZI → PAna → dAnM → dGhM → RGhY → R6rY → l6rE → lWRE → X4tS → p4tA → peJA → fKdK
44,010×(max) 30 nodes70xs → xkD2 → vWR4 → r4t8 → piFA → fSVK → L2ve → tIf6 → nMbC → bEjO → VClU → Z0xQ → x8p2 → vgH4 → rOZ8 → jAnG → dSVM → H2vi → tQX6 → n6rC → laNE → XClS → Z4tQ → p8pA → heJI → PKda → JAng → dMbM → HEji → VQXU
43,894×(max) 30 nodesB2vo → tcL6 → nGhC → bQXO → D6rm → lYPE → X8pS → h4tI → pOZA → fAnK → dKdM → JGhg → RMbY → F6rk → lUTE → X0xS → x4t2 → vo94 → reJ8 → jKdG → TIfW → N2vc → tEj6 → nUTC → b0xO → xCl2 → vYP4 → r8p8 → jgHG → TOZW
43,840×(max) 30 nodes50xu → xo92 → veJ4 → rKd8 → jIfG → TMbW → F2vk → tUT6 → n0xC → xaN2 → vCl4 → rYP8 → j8pG → hSVI → P2va → tAn6 → ncLC → bGhO → RClY → Z6rQ → l8pE → hWRI → P4ta → pAnA → fcLK → LGhe → RIfY → N6rc → lEjE → XUTS
43,654×(max) 30 nodes90xq → xgH2 → vOZ4 → rAn8 → jcLG → TGhW → R2vY → t6r6 → nkDC → bWRO → D4tm → pYPA → f8pK → hKdI → PIfa → NAnc → dEjM → VGhU → R0xY → x6r2 → vkD4 → rWR8 → j4tG → pSVA → f2vK → tKd6 → nIfC → bMbO → FClk → ZUTQ
43,650×(max) 30 nodes52vu → to96 → neJC → bKdO → JClg → ZMbQ → F8pk → hUTI → P0xa → xAn2 → vcL4 → rGh8 → jQXG → T6rW → l2vE → tWR6 → n4tC → paNA → fClK → ZKdQ → J8pg → hMbI → PEja → VAnU → d0xM → xGh2 → vQX4 → r6r8 → liFE → XSVS
43,120×(max) 30 nodesB6ro → lcLE → XGhS → R4tY → p6rA → leJE → XKdS → J4tg → pMbA → fEjK → VKdU → J0xg → xMb2 → vEj4 → rUT8 → j0xG → xSV2 → v2v4 → tq76 → niFC → bSVO → D2vm → tYP6 → n8pC → haNI → PCla → ZAnQ → d8pM → hGhI → ROZY
43,060×(max) 30 nodesDAnm → dYPM → H8pi → hQXI → P6ra → lAnE → dWRM → H4ti → pQXA → f6rK → lKdE → XIfS → N4tc → pEjA → fUTK → L0xe → xIf2 → vMb4 → rEj8 → jUTG → T0xW → x2v2 → vs54 → rmB8 → jaNG → TClW → Z2vQ → t8p6 → ngHC → bOZO
43,038×(max) 30 nodes94tq → pgHA → fOZK → LAne → dIfM → NGhc → REjY → V6rU → l0xE → xWR2 → v4t4 → ro98 → jeJG → TKdW → J2vg → tMb6 → nEjC → bUTO → D0xm → xYP2 → v8p4 → rgH8 → jOZG → TAnW → d2vM → tGh6 → nQXC → b6rO → lClE → ZWRQ
21,166×15 nodesB0xo → xcL2 → vGh4 → rQX8 → j6rG → lSVE → X2vS → t4t6 → pmBA → faNK → LCle → ZIfQ → N8pc → hEjI → VOZU
52 cycles5,484,601×3 nodeseIyfL → gJyeJ → fMybK
2,775,226×(max) 4 nodeseJyeL → fIyfK → gKydJ → fLycK
69 cycles52,304,381×(max) 59 nodesFD3ulk → rYUTQ8 → j80xqG → xiSVG2 → vS2vW4 → tr3u76 → rnjEB8 → jcUTMG → TG0xiW → xS2vW2 → vt3u54 → sqnA87 → licLGE → XSGhWS → R53utY → ro6rA8 → ljdKFE → XUIfUS → N4yytc → ubGhN5 → pRDkXA → fX5sRK → nL5sdC → nbHgNC → bPDkZO → XD9olS → fY4tQK → pL7qdA → jfHgJG → TPLcZW → HA2voi → teQXK6 → nK6reC → lbJeNE → XLDkdS → XI4tgS → pO4taA → pfBmJA → fbLcNK → LHDkhe → XQIfYS → N84tqc → piEjGA → fVRWTK → L51wte → voIfA4 → reMbK8 → jKEjeG → VTJeVU → L20xwe → xuIf42 → vqMb84 → riEjG8 → jVRWTG → T51wtW → vo2vA4 → trdK76 → nkIfEC → bWMbSO
18,538,826×5 nodesjW0xSG → xT3uV2 → vr1w74 → vrjE74 → rkUTE8
14,213,720×5 nodesD91wpm → vgYPI4 → rO8pa8 → jhBmHG → bTPYVO
2,716,171×24 nodesD42vum → tqYP86 → ni8pGC → hbRWNI → PE4tka → pWAnSA → fd3uLK → rLHgd8 → jPHgZG → TP9oZW → fA2voK → teKdK6 → nKIfeC → bNJebO → LEClke → ZWIfSQ → N93upc → rgEjI8 → jVNaTG → TD1wlW → vY2vQ4 → tr7q76 → nkiFEC → bWSVSO
917,413×5 nodesfT5sVK → nL1wdC → vbHgN4 → rPDkZ8 → jX9oRG
818,548×5 nodesfb1wNK → vLDkd4 → rXHgR8 → jP5sZG → nT9oVC
562,992×5 nodesjX5sRG → nT5sVC → nb1wNC → vbDkN4 → rXDkR8
553,460×5 nodesfL1wdK → vLHgd4 → rPHgZ8 → jP9oZG → fT9oVK
233,196×2 nodesnE2vkC → tbVSN6
73 cycles717,845,445×2 nodesjVEyjTG → kTFyiVF
76,296,854×(max) 4 nodesiTDykVH → lTEyjVE → kXFyiRF → jVGyhTG
75,505,848×2 nodeskVDykTF → lVGyhTE
810 cycles6,518,765,657×(max) 111 nodesLC62vsme → tmaIfOC6 → naNBmbOC → caEBmkON → bWFBmjSO → bUD3ulUO → rYCyylQ8 → qmRClXC9 → haZ5sPOI → nPC9omZC → fba9oONK → fLEBmkdK → bWLHgdSO → PID3ulga → rYOAnaQ8 → jdC7qmLG → jaTHgVOG → TPC1wmZW → vaA2voO4 → treBmK76 → nkbJeNEC → bWLDkdSO → XID3ulgS → rYO4taQ8 → pjC7qmFA → jfaTUOJG → TMC0xmcW → xaG2viO2 → vtSBmW54 → rob3uNA8 → rjeDkKF8 → jXUJeURG → TL5yysdW → tdP6rZL6 → nlI9ogDC → fbYNaQNK → LED7qlke → jYWIfSQG → TN83uqbW → riE2vkG8 → tjWRWSF6 → nU53utUC → roayyNA8 → qoUDkUA9 → heWyyRKI → geG7qiKJ → jSNJebWG → TLE3ukdW → rWI2vgS8 → tjO3uaF6 → rnUBmUB8 → jcayyNMG → icM1wcMH → vRGFiiX4 → rTS5sWV8 → nj41wuFC → vqbTUN84 → riE0xkG8 → xjWRWSF2 → vU53utU4 → sqnyyA87 → rqi2vG88 → tjiRWGF6 → nUS4tWUC → pb3yyuNA → voXDkRA4 → reX5sRK8 → njK5seFC → nbUJeUNC → bLDyykdO → ldM1wcLE → vXIFigR4 → rTO5saV8 → njC1wmFC → vbaTUON4 → rEC0xmk8 → xjaVSOF2 → vUC2vmU4 → trZyyO76 → srVHgT77 → lkP1wZEE → vXW9oSR4 → rf63usJ8 → rmjLcFC8 → jaUGhUOG → TRByymXW → nXJ0xfRC → xbM5scN2 → vnGDkiB4 → rcXRWRM8 → jG64tsiG → pmTRWVCA → fa51wtOK → voLBmdA4 → rebHgNK8 → jPKDkeZG → XTK9oeVS → fK51wteK → voLJedA4 → reLHgdK8 → jPKHgeZG → TPK9oeZW → fKA2voeK → teLJedK6 → nLKHgedC → bPKHgeZO → PKD9olea → fYKAneQK → dLK7qedM → jKIGhgeG → TROJeaXW
511,797,944×75 nodesFC40xumk → xqaUTO82 → viC0xmG4 → xraRWO72 → vkC4tmE4 → rpaVSO98 → jgC2vmIG → taTNaVO6 → nDC1wmlC → vbaXQON4 → rEC6rmk8 → ljaVSOFE → XUC2vmUS → ta4yytO6 → usVIfT65 → pmN1wbCA → vfaDkOJ4 → rXMBmcR8 → jbG5siNG → nTSDkWVC → bX41wuRO → vqD5sl84 → rniXQGB8 → jcS6rWMG → lTG3uiVE → rXS1wWR8 → vj63usF4 → sqmTUC87 → lia0xOGE → xXSBmWR2 → vb63usN4 → sqmDkC87 → liaWROGE → XSC4tmWS → pa53utOA → rofBmJA8 → jebLcNKG → TKHDkheW → XQK2veYS → tK84tqe6 → pniJeGBA → fcSKdWMK → LJG3uife → rSMIfcW8 → jNG3uibG → rTSDkWV8 → jX41wuRG → vqT5sV84 → rni1wGB8 → vjcRWMF4 → rUG4tiU8 → pjRyyWFA → ojOClaFB → dZUBmUPM → bH9yyohO → phQ5sYHA → nfQ7qYJC → jbM7qcNG → jTGDkiVG → XTS1wWVS → v541wut4 → vrqnA874 → rkicLGE8 → jWSGhWSG → TR43uuXW → rq62vs88 → tmjhGFC6 → naUQXUOC → bC6yyrmO → smTAnVC7 → lda1wOLE → vXIBmgR4 → rbO5saN8 → njEBmkFC → caWTUSON
156,462,069×58 nodesLEDBmlke → bYWIfSQO → ND83uqlc → riYEjQG8 → jVS7qWTG → jT41wuVG → vqT1wV84 → vri1wG74 → vrkRWE74 → rkW4tSE8 → pjW3uSFA → rfU3uUJ8 → rjLyycF8 → qjW6rSF9 → lhU3uUHE → rXPyyYR8 → qZQ0xYP9 → xhA7qoH2 → vjePYKF4 → rUK8peU8 → jhJyyeHG → ihQ2vYHH → tRQ7qYX6 → nj85sqFC → nibTUNGC → bSE0xkWO → xWD3ulS2 → vrY3uQ74 → sqk7qE87 → ljiVSGFE → XUS2vWUS → t53yyut6 → vtnyyA54 → utl5sD55 → ponXQBAA → fec6rMKK → lLKFiedE → XTKHgeVS → PK51wtea → voKAneA4 → redJeLK8 → jLKHgedG → TPKHgeZW → PKA2voea → teKAneK6 → ndKJeeLC → bLKHgedO → PKIClgea → ZOKAneaQ → dKC8pmeM → haKGheOI → RPKBmeZY → bKA6roeO → leKCleKE → ZXKJeeRQ → LK95spee → ngKIfeIC → bONJebaO
58,551,131×11 nodesT864tsqW → pmi2vGCA → tfaRWOJ6 → nMC4tmcC → pbaFiONA → fTEBmkVK → bWL1wdSO → vID3ulg4 → sqYNaQ87 → liD7qlGE → jYXRWRQG
53,201,721×5 nodesfTK5seVK → nLK1wedC → vbKHgeN4 → rPKDkeZ8 → jXK9oeRG
41,610,060×17 nodesTP85sqZW → niA2voGC → tebRWNK6 → nKE4tkeC → pbWJeSNA → fLE3ukdK → rWLHgdS8 → jPI3ugZG → rTO9oaV8 → jfC1wmJG → vaTLcVO4 → rHC1wmh8 → vjaPYOF4 → rUC8pmU8 → jhZyyOHG → ihL7qdHH → jRQHgYXG
24,441,379×5 nodesfLK1wedK → vLKHged4 → rPKHgeZ8 → jPK9oeZG → fTK9oeVK
14,729,453×5 nodesjXK5seRG → nTK5seVC → nbK1weNC → vbKDkeN4 → rXKDkeR8
10,674,679×5 nodesfbK1weNK → vLKDked4 → rXKHgeR8 → jPK5seZG → nTK9oeVC
1,775,614×2 nodesnEC2vmkC → tbaVSON6
9+---Not showing digit sets 9+ due to verbosity.