Base 65: 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---
24 cycles640×(max) 5 nodes⮎ 1Β → z3 → v7 → nF → XV ⮌
640×(max) 5 nodes⮎ 5x → rB → fN → Hl → TZ ⮌
640×(max) 5 nodes⮎ 9t → jJ → Pd → Dp → bR ⮌
128×(fixed) 1 node ⮎ Lh ⮌
31 cycle 47,840×(max) 2 nodes⮎ VΓX → WΓW ⮌
486 cycles11,137×(max) 6 nodes⮎ NIjg → RIjc → RArc → hArM → hKhM → NKhg ⮌
11,134×(max) 6 nodes⮎ XArW → h0ΒM → ΒKh2 → zMf4 → vIj8 → nQbG ⮌
11,110×(max) 6 nodes⮎ j0ΒK → ΒOd2 → zEn4 → vYT8 → n4xG → tWVA ⮌
10,910×(max) 6 nodes⮎ Z8tU → l4xI → tSZA → j6vK → pOdE → bEnS ⮌
10,900×(max) 6 nodes⮎ 52zy → xs96 → riJC → fOdO → HEnm → ZUXU ⮌
10,838×(max) 6 nodes⮎ n2zG → xWV6 → r0ΒC → ΒeN2 → zGl4 → vUX8 ⮌
10,797×(max) 6 nodes⮎ FAro → hYTM → L4xi → tMfA → jIjK → ROdc ⮌
10,673×(max) 6 nodes⮎ D8tq → lcPI → TCpa → d6vQ → pCpE → daRQ ⮌
10,550×(max) 6 nodes⮎ 30ΒΑ → Βw52 → zqB4 → veN8 → nGlG → XUXW ⮌
10,477×(max) 6 nodes⮎ J2zk → xQb6 → rArC → heNM → LGli → VMfY ⮌
10,406×(max) 6 nodes⮎ RGlc → VArY → h2zM → xKh6 → rMfC → fIjO ⮌
10,398×(max) 6 nodes⮎ VCpY → d2zQ → xCp6 → rcPC → fCpO → dGlQ ⮌
10,398×(max) 6 nodes⮎ TEna → Z6vU → p4xE → taRA → j8tK → lOdI ⮌
10,398×(max) 6 nodes⮎ T6va → p6vE → paRE → b8tS → l8tI → lSZI ⮌
10,398×(max) 6 nodes⮎ T8ta → l6vI → pSZE → b6vS → p8tE → laRI ⮌
10,387×(max) 6 nodes⮎ NEng → ZIjU → R4xc → tArA → jgLK → PKhe ⮌
10,387×(max) 6 nodes⮎ JArk → hQbM → LAri → hMfM → LIji → RMfc ⮌
10,382×(max) 6 nodes⮎ V8tY → l2zI → xSZ6 → r6vC → peNE → bGlS ⮌
10,382×(max) 6 nodes⮎ P2ze → xEn6 → rYTC → f4xO → tGlA → jUXK ⮌
10,366×(max) 6 nodes⮎ L0Βi → ΒMf2 → zIj4 → vQb8 → nArG → hWVM ⮌
10,361×(max) 6 nodes⮎ D4xq → tcPA → jCpK → dOdQ → FCpo → dYTQ ⮌
10,358×(max) 6 nodes⮎ XCpW → d0ΒQ → ΒCp2 → zcP4 → vCp8 → ncPG ⮌
10,357×(max) 6 nodes⮎ B2zs → xgL6 → rKhC → fMfO → JGlk → VQbY ⮌
10,342×(max) 6 nodes⮎ X4xW → t0ΒA → ΒiJ2 → zOd4 → vEn8 → nYTG ⮌
10,342×(max) 6 nodes⮎ b0ΒS → Β8t2 → zkH4 → vSZ8 → n6vG → pWVE ⮌
10,333×(max) 6 nodes⮎ B8ts → lgLI → TKha → N6vg → pIjE → bQbS ⮌
10,326×(max) 6 nodes⮎ f0ΒO → ΒGl2 → zUX4 → v2z8 → xmF6 → rWVC ⮌
10,249×(max) 6 nodes⮎ F6vo → pYTE → b4xS → t8tA → liJI → TOda ⮌
10,243×(max) 6 nodes⮎ B6vs → pgLE → bKhS → N8tg → lIjI → TQba ⮌
10,153×(max) 6 nodes⮎ 72zw → xoD6 → raRC → f8tO → lGlI → VSZY ⮌
10,150×(max) 6 nodes⮎ N2zg → xIj6 → rQbC → fArO → hGlM → VKhY ⮌
10,126×(max) 6 nodes⮎ V4xY → t2zA → xiJ6 → rOdC → fEnO → ZGlU ⮌
10,110×(max) 6 nodes⮎ R0Βc → ΒAr2 → zgL4 → vKh8 → nMfG → XIjW ⮌
10,086×(max) 6 nodes⮎ X6vW → p0ΒE → ΒaR2 → z8t4 → vkH8 → nSZG ⮌
9,971×(max) 6 nodes⮎ 94xu → tkHA → jSZK → P6ve → pEnE → bYTS ⮌
9,910×(max) 6 nodes⮎ PIje → REnc → ZArU → h4xM → tKhA → jMfK ⮌
9,902×(max) 6 nodes⮎ PCpe → dEnQ → ZCpU → d4xQ → tCpA → jcPK ⮌
9,870×(max) 6 nodes⮎ TGla → V6vY → p2zE → xaR6 → r8tC → leNI ⮌
9,870×(max) 6 nodes⮎ H4xm → tUXA → j2zK → xOd6 → rEnC → fYTO ⮌
9,859×(max) 6 nodes⮎ DArq → hcPM → LCpi → dMfQ → JCpk → dQbQ ⮌
9,854×(max) 6 nodes⮎ N0Βg → ΒIj2 → zQb4 → vAr8 → ngLG → XKhW ⮌
9,830×(max) 6 nodes⮎ X8tW → l0ΒI → ΒSZ2 → z6v4 → voD8 → naRG ⮌
9,807×(max) 6 nodes⮎ B4xs → tgLA → jKhK → PMfe → JEnk → ZQbU ⮌
9,799×(max) 6 nodes⮎ D2zq → xcP6 → rCpC → fcPO → HCpm → dUXQ ⮌
9,729×(max) 6 nodes⮎ 74xw → toDA → jaRK → P8te → lEnI → ZSZU ⮌
9,697×(max) 6 nodes⮎ PGle → VEnY → Z2zU → x4x6 → tqBA → jeNK ⮌
9,670×(max) 6 nodes⮎ NCpg → dIjQ → RCpc → dArQ → hCpM → dKhQ ⮌
9,654×(max) 6 nodes⮎ N4xg → tIjA → jQbK → PAre → hEnM → ZKhU ⮌
9,654×(max) 6 nodes⮎ J6vk → pQbE → bArS → h8tM → lKhI → TMfa ⮌
9,654×(max) 6 nodes⮎ L6vi → pMfE → bIjS → R8tc → lArI → hSZM ⮌
9,654×(max) 6 nodes⮎ J8tk → lQbI → TAra → h6vM → pKhE → bMfS ⮌
9,630×(max) 6 nodes⮎ PEne → ZEnU → Z4xU → t4xA → tiJA → jOdK ⮌
9,630×(max) 6 nodes⮎ F4xo → tYTA → j4xK → tOdA → jEnK → ZOdU ⮌
9,598×(max) 6 nodes⮎ J0Βk → ΒQb2 → zAr4 → vgL8 → nKhG → XMfW ⮌
9,598×(max) 6 nodes⮎ H2zm → xUX6 → r2zC → xeN6 → rGlC → fUXO ⮌
9,587×(max) 6 nodes⮎ H8tm → lUXI → T2za → x6v6 → roDC → faRO ⮌
9,574×(max) 6 nodes⮎ P0Βe → ΒEn2 → zYT4 → v4x8 → tmFA → jWVK ⮌
9,574×(max) 6 nodes⮎ T0Βa → Β6v2 → zoD4 → vaR8 → n8tG → lWVI ⮌
9,558×(max) 6 nodes⮎ X2zW → x0Β6 → ΒqB2 → zeN4 → vGl8 → nUXG ⮌
9,477×(max) 6 nodes⮎ 50Βy → Βs92 → ziJ4 → vOd8 → nEnG → ZWVU ⮌
9,173×(max) 6 nodes⮎ 90Βu → ΒkH2 → zSZ4 → v6v8 → pmFE → bWVS ⮌
9,142×(max) 6 nodes⮎ J4xk → tQbA → jArK → hOdM → LEni → ZMfU ⮌
9,142×(max) 6 nodes⮎ L8ti → lMfI → TIja → R6vc → pArE → haRM ⮌
9,134×(max) 6 nodes⮎ D6vq → pcPE → bCpS → d8tQ → lCpI → dSZQ ⮌
9,126×(max) 6 nodes⮎ HArm → hUXM → L2zi → xMf6 → rIjC → fQbO ⮌
9,126×(max) 6 nodes⮎ NGlg → VIjY → R2zc → xAr6 → rgLC → fKhO ⮌
9,102×(max) 6 nodes⮎ F2zo → xYT6 → r4xC → teNA → jGlK → VOdY ⮌
9,102×(max) 6 nodes⮎ H6vm → pUXE → b2zS → x8t6 → rkHC → fSZO ⮌
9,086×(max) 6 nodes⮎ B0Βs → ΒgL2 → zKh4 → vMf8 → nIjG → XQbW ⮌
9,086×(max) 6 nodes⮎ V2zY → x2z6 → xqB6 → reNC → fGlO → VGlY ⮌
9,078×(max) 6 nodes⮎ D0Βq → ΒcP2 → zCp4 → vcP8 → nCpG → dWVQ ⮌
9,062×(max) 6 nodes⮎ XEnW → Z0ΒU → Β4x2 → zs94 → viJ8 → nOdG ⮌
9,006×(max) 6 nodes⮎ n0ΒG → ΒWV2 → z0Β4 → Βu72 → zmF4 → vWV8 ⮌
9,002×(max) 6 nodes⮎ X0ΒW → Β0Β2 → Βy32 → zu74 → vmF8 → nWVG ⮌
8,791×(max) 6 nodes⮎ 70Βw → ΒoD2 → zaR4 → v8t8 → nkHG → XSZW ⮌
8,735×(max) 6 nodes⮎ F0Βo → ΒYT2 → z4x4 → vs98 → niJG → XOdW ⮌
8,606×(max) 6 nodes⮎ F8to → lYTI → T4xa → t6vA → piJE → bOdS ⮌
8,590×(max) 6 nodes⮎ 92zu → xkH6 → rSZC → f6vO → pGlE → bUXS ⮌
8,557×(max) 6 nodes⮎ H0Βm → ΒUX2 → z2z4 → xu76 → rmFC → fWVO ⮌
8,387×(max) 6 nodes⮎ V0ΒY → Β2z2 → zw54 → vqB8 → neNG → XGlW ⮌
5,567×3 nodes⮎ f2zO → xGl6 → rUXC ⮌
5,464×3 nodes⮎ 96vu → pkHE → bSZS ⮌
4,815×3 nodes⮎ P4xe → tEnA → jYTK ⮌
4,759×3 nodes⮎ v0Β8 → ΒmF2 → zWV4 ⮌
4,327×3 nodes⮎ NArg → hIjM → RKhc ⮌
1,781×(fixed) 1 node ⮎ dCpQ ⮌
51 cycle 11,238,448×(max) 4 nodes⮎ hKΓhM → iKΓhL → iMΓfL → hLΓgM ⮌
66 cycles34,801,126×(max) 21 nodes⮎ nL1ΑhG → zXLgV4 → vL1Αh8 → znLgF4 → vYKhU8 → nN3yfG → vXHkV8 → nT1ΑZG → zX5wV4 → vr1ΑB8 → znfMF4 → vYIjU8 → nR3ybG → vX9sV8 → nj1ΑJG → zXPcV4 → vD1Αp8 → znbQF4 → vYArU8 → nh3yLG → vXLgV8 ⮌
23,081,521×5 nodes⮎ jX5wVK → rP1ΑdC → zfDoN4 → vbHkR8 → nT9sZG ⮌
21,606,741×5 nodes⮎ jf1ΑNK → zPHkd4 → vTDoZ8 → nb5wRG → rX9sVC ⮌
19,939,023×5 nodes⮎ nT5wZG → rX5wVC → rf1ΑNC → zfHkN4 → vTHkZ8 ⮌
18,773,236×5 nodes⮎ jP1ΑdK → zPDod4 → vbDoR8 → nb9sRG → jX9sVK ⮌
12,914,273×7 nodes⮎ nb1ΑRG → zX9sV4 → vj1ΑJ8 → znPcF4 → vYCpU8 → nd3yPG → vXDoV8 ⮌
73 cycles1,096,738,216×2 nodes⮎ mXFΓmVH → nVGΓlXG ⮌
119,065,537×2 nodes⮎ nXEΓnVG → oXHΓkVF ⮌
114,086,887×(max) 4 nodes⮎ lVEΓnXI → oVFΓmXF → nZGΓlTG → mXHΓkVH ⮌
82 cycles10,429,778,393×(fixed) 1 node ⮎ vnY3yUF8 ⮌
1,539,237,887×(max) 19 nodes⮎ XI84xukW → tmS0ΒaGA → ΒjW7uWJ2 → znPΓΓcF4 → ynaArSF5 → thY7uULA → njM3ygJG → vXQJicV8 → nPC1ΑqdG → zeXDoVO4 → vbG1ΑmR8 → znW9sWF4 → vjXΓΓUJ8 → ujRBqbJ9 → lfQ9scNI → jTIBqkZK → fSP5wdaO → rHE7uolC → nfaTYSNG ⮌
9+---Not showing digit sets 9+ due to verbosity.