Base 69: 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---
23 cycles1,632×(max) 12 nodes⮎ 1Ζ → Δ3 → z7 → rF → bV → 5Β → vB → jN → Ll → Ph → Hp → XZ ⮌
408×3 nodes⮎ 9x → nJ → Td ⮌
272×2 nodes⮎ Dt → fR ⮌
31 cycle 57,086×(max) 2 nodes⮎ XΗZ → YΗY ⮌
429 cycles44,449×(max) 22 nodes⮎ PKli → RIng → VErc → d6zU → t8xE → peRI → XCta → h2ΔQ → ΒGp6 → vYXC → j0ΖO → ΖKl2 → ΔQf4 → zEr8 → rcTG → b8xW → p4ΒI → xWZA → n2ΔK → ΒSd6 → vAvC → liNM ⮌
41,938×(max) 22 nodes⮎ 96zy → toHE → fWZS → D2Δu → ΒgP6 → vGpC → jYXO → L0Ζm → ΖQf2 → ΔEr4 → zcT8 → r8xG → paVI → X4Βa → x2ΔA → ΒmJ6 → vSdC → jAvO → lKlM → ROhg → JEro → dUbU ⮌
41,780×(max) 22 nodes⮎ 72ΔΑ → ΒsD6 → veRC → jCtO → hKlQ → RGpg → ZErY → d0ΖU → Ζ8x2 → ΔoH4 → zWZ8 → r2ΔG → ΒaV6 → v4ΒC → xiNA → nKlK → TQfe → FAvs → lcTM → P8xi → pInI → XUba ⮌
41,674×(max) 22 nodes⮎ 94Βy → xoHA → nWZK → T2Δe → ΒAv6 → vkLC → jOhO → LInm → VQfc → F6zs → tcTE → f8xS → pCtI → hWZQ → H2Δq → ΒYX6 → v0ΖC → ΖiN2 → ΔKl4 → zQf8 → rErG → daVU ⮌
41,588×(max) 22 nodes⮎ 30ΖΕ → ΖΑ52 → ΔuB4 → ziN8 → rKlG → bQfW → F4Βs → xcTA → n8xK → pSdI → XAva → l2ΔM → ΒOh6 → vInC → jUbO → L6zm → tQfE → fErS → dCtU → h8xQ → pGpI → ZWZY ⮌
40,728×(max) 22 nodes⮎ 52ΔΓ → Βw96 → vmJC → jSdO → LAvm → lQfM → PEri → dInU → V8xc → p6zI → tWZE → f2ΔS → ΒCt6 → vgPC → jGpO → ZKlY → R0Ζg → ΖEr2 → ΔcT4 → z8x8 → roHG → bWZW ⮌
40,616×(max) 22 nodes⮎ 90Ζy → ΖoH2 → ΔWZ4 → z2Δ8 → ΒqF6 → vaVC → j4ΒO → xKlA → nQfK → TEre → dAvU → l8xM → pOhI → XIna → V2Δc → Β6z6 → vsDC → jeRO → LCtm → hQfQ → HErq → dYXU ⮌
40,538×(max) 22 nodes⮎ B2Δw → ΒkL6 → vOhC → jInO → VKlc → R6zg → tErE → fcTS → D8xu → pgPI → XGpa → Z2ΔY → Β0Ζ6 → ΖuB2 → ΔiN4 → zKl8 → rQfG → bErW → d4ΒU → x8xA → pmJI → XSda ⮌
40,379×(max) 22 nodes⮎ N0Ζk → ΖMj2 → ΔMj4 → zMj8 → rMjG → bMjW → N4Βk → xMjA → nMjK → TMje → NAvk → lMjM → PMji → NInk → VMjc → N6zk → tMjE → fMjS → NCtk → hMjQ → NGpk → ZMjY ⮌
40,245×(max) 22 nodes⮎ 70ΖΑ → ΖsD2 → ΔeR4 → zCt8 → rgPG → bGpW → Z4ΒY → x0ΖA → ΖmJ2 → ΔSd4 → zAv8 → rkLG → bOhW → J4Βo → xUbA → n6zK → tSdE → fAvS → lCtM → hOhQ → JGpo → ZUbY ⮌
40,215×(max) 22 nodes⮎ DAvu → lgPM → PGpi → ZInY → V0Ζc → Ζ6z2 → ΔsD4 → zeR8 → rCtG → haVQ → H4Βq → xYXA → n0ΖK → ΖSd2 → ΔAv4 → zkL8 → rOhG → bInW → V4Βc → x6zA → tmJE → fSdS ⮌
40,113×(max) 22 nodes⮎ 74ΒΑ → xsDA → neRK → TCte → hAvQ → lGpM → ZOhY → J0Ζo → ΖUb2 → Δ6z4 → zsD8 → reRG → bCtW → h4ΒQ → xGpA → nYXK → T0Ζe → ΖAv2 → ΔkL4 → zOh8 → rInG → bUbW ⮌
40,089×(max) 22 nodes⮎ B6zw → tkLE → fOhS → JCto → hUbQ → H6zq → tYXE → f0ΖS → ΖCt2 → ΔgP4 → zGp8 → rYXG → b0ΖW → Ζ4Β2 → Δw94 → zmJ8 → rSdG → bAvW → l4ΒM → xOhA → nInK → VSdc ⮌
40,064×(max) 22 nodes⮎ B8xw → pkLI → XOha → J2Δo → ΒUb6 → v6zC → tiNE → fKlS → RCtg → hErQ → dGpU → Z8xY → p0ΖI → ΖWZ2 → Δ2Δ4 → Βy76 → vqFC → jaVO → L4Βm → xQfA → nErK → dSdU ⮌
39,926×(max) 22 nodes⮎ FCts → hcTQ → H8xq → pYXI → X0Ζa → Ζ2Δ2 → ΔΑ54 → zuB8 → riNG → bKlW → R4Βg → xErA → ncTK → T8xe → pAvI → lWZM → P2Δi → ΒIn6 → vUbC → j6zO → tKlE → fQfS ⮌
39,903×(max) 22 nodes⮎ 50ΖΓ → Ζw92 → ΔmJ4 → zSd8 → rAvG → laVM → P4Βi → xInA → nUbK → T6ze → tAvE → leRM → PCti → hInQ → VGpc → Z6zY → t0ΖE → ΖeR2 → ΔCt4 → zgP8 → rGpG → bYXW ⮌
39,758×(max) 22 nodes⮎ F0Ζs → ΖcT2 → Δ8x4 → zoH8 → rWZG → b2ΔW → Β4Β6 → xuBA → niNK → TKle → RAvg → lErM → dOhU → J8xo → pUbI → X6za → t2ΔE → ΒeR6 → vCtC → jgPO → LGpm → ZQfY ⮌
39,645×(max) 22 nodes⮎ H0Ζq → ΖYX2 → Δ0Ζ4 → Ζy72 → ΔqF4 → zaV8 → r4ΒG → xaVA → n4ΒK → xSdA → nAvK → lSdM → PAvi → lInM → VOhc → J6zo → tUbE → f6zS → tCtE → heRQ → HCtq → hYXQ ⮌
39,390×(max) 22 nodes⮎ PIni → VInc → V6zc → t6zE → teRE → fCtS → hCtQ → hGpQ → ZGpY → Z0ΖY → Ζ0Ζ2 → ΖΓ32 → Δy74 → zqF8 → raVG → b4ΒW → x4ΒA → xmJA → nSdK → TAve → lAvM → lOhM ⮌
39,315×(max) 22 nodes⮎ D6zu → tgPE → fGpS → ZCtY → h0ΖQ → ΖGp2 → ΔYX4 → z0Ζ8 → ΖqF2 → ΔaV4 → z4Β8 → xqFA → naVK → T4Βe → xAvA → nkLK → TOhe → JAvo → lUbM → P6zi → tInE → fUbS ⮌
38,913×(max) 22 nodes⮎ B0Ζw → ΖkL2 → ΔOh4 → zIn8 → rUbG → b6zW → t4ΒE → xeRA → nCtK → hSdQ → HAvq → lYXM → P0Ζi → ΖIn2 → ΔUb4 → z6z8 → tqFE → faVS → D4Βu → xgPA → nGpK → ZSdY ⮌
38,439×(max) 22 nodes⮎ B4Βw → xkLA → nOhK → TIne → VAvc → l6zM → tOhE → fInS → VCtc → h6zQ → tGpE → fYXS → D0Ζu → ΖgP2 → ΔGp4 → zYX8 → r0ΖG → ΖaV2 → Δ4Β4 → zw98 → rmJG → bSdW ⮌
21,703×11 nodes⮎ TGpe → ZAvY → l0ΖM → ΖOh2 → ΔIn4 → zUb8 → r6zG → taVE → f4ΒS → xCtA → ngPK ⮌
21,118×11 nodes⮎ N2Δk → ΒMj6 → vMjC → jMjO → NKlk → RMjg → NErk → dMjU → N8xk → pMjI → XMja ⮌
19,239×11 nodes⮎ RErg → dErU → d8xU → p8xI → pWZI → X2Δa → Β2Δ6 → ΒuB6 → viNC → jKlO → RKlg ⮌
19,239×11 nodes⮎ 92Δy → ΒoH6 → vWZC → j2ΔO → ΒKl6 → vQfC → jErO → dKlU → R8xg → pErI → dWZU ⮌
19,239×11 nodes⮎ F8xs → pcTI → X8xa → p2ΔI → ΒWZ6 → v2ΔC → ΒiN6 → vKlC → jQfO → LErm → dQfU ⮌
19,239×11 nodes⮎ F2Δs → ΒcT6 → v8xC → piNI → XKla → R2Δg → ΒEr6 → vcTC → j8xO → pKlI → XQfa ⮌
19,239×11 nodes⮎ L2Δm → ΒQf6 → vErC → jcTO → L8xm → pQfI → XEra → d2ΔU → Β8x6 → voHC → jWZO ⮌
51 cycle 15,020,265×(fixed) (max) 1 node ⮎ kMΗjN ⮌
63 cycles184,924,027×(max) 39 nodes⮎ F4ΗΗΒs → Γr8xF5 → xpbUHA → nY6zYK → tSΗΗdE → seFqSF → dbBuVU → j95ΑxO → voKlIC → jWQfaO → LF3Γrm → zcQfU8 → rF7yrG → rcaVUG → b84ΒyW → xq4ΒGA → xnZWJA → nU2ΔcK → ΒT7yd6 → vr9wFC → njbUNK → TM6zke → tOAviE → lfJmRM → TPDshe → fIAvoS → lWCtaM → hP3ΓhQ → zIGpo8 → rZVaXG → b51ΕΒW → Δw4ΒA4 → zxlK98 → roQfIG → bWEraW → d53ΓΒU → zw8xA8 → rplKHG → bYQfYW ⮌
277,189×(fixed) 1 node ⮎ nT9wdK ⮌
49,501×3 nodes⮎ z80Ζy8 → ΖrpGF2 → ΔcYXU4 ⮌
73 cycles1,644,484,860×2 nodes⮎ pZGΗpXI → qXHΗoZH ⮌
173,775,959×2 nodes⮎ qZFΗqXH → rZIΗnXG ⮌
166,568,962×(max) 4 nodes⮎ oXFΗqZJ → rXGΗpZG → qbHΗoVH → pZIΗnXI ⮌
85 cycles18,617,348,987×(max) 7 nodes⮎ bU93ΓxcW → zo84ΒyI8 → xrqVaGFA → nca4ΒWUK → xT83ΓydA → zqn9wJG8 → rnaTcWJG ⮌
176,930,758×4 nodes⮎ nTC9wudK → niT9wdOK → nTK9wmdK → nTS9wedK ⮌
60,783,179×(max) 7 nodes⮎ bUT7ydcW → rA84ΒywG → xqmaVKGA → naS4ΒeWK → xTC3ΓudA → zni9wOJ8 → rnUJmcJG ⮌
717,982×2 nodes⮎ wlY4ΒYLB → xlPΗΗgLA ⮌
102,600×(fixed) 1 node ⮎ kjMΗΗjNN ⮌
9+---Not showing digit sets 9+ due to verbosity.