Base 73: 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 2,592×(max) 18 nodes⮎ 1Κ → Θ3 → Δ7 → vF → fV → 9Β → rJ → Xd → 5Ζ → zB → nN → Pl → Lp → Th → Dx → jR → Ht → bZ ⮌
31 cycle 67,452×(max) 2 nodes⮎ ZΛb → aΛa ⮌
470 cycles20,153×(max) 9 nodes⮎ XAze → p6ΔM → xShE → jEvS → hGtU → dCxY → l4ΖQ → ΒKpA → rUfK ⮌
20,097×(max) 9 nodes⮎ bEva → h0ΚU → ΚCx2 → ΘkP4 → ΔKp8 → vUfG → fAzW → p8ΒM → tShI ⮌
20,065×(max) 9 nodes⮎ Z8Βc → t2ΘI → ΖaZ6 → z0ΚC → ΚmN2 → ΘOl4 → ΔMn8 → vQjG → fIrW ⮌
20,057×(max) 9 nodes⮎ b6Δa → x0ΚE → ΚiR2 → ΘGt4 → ΔcX8 → v4ΖG → ΒeVA → r8ΒK → tWdI ⮌
19,844×(max) 9 nodes⮎ JAzs → pYbM → T2Θi → ΖEv6 → zgTC → nCxO → lOlQ → NKpo → VQjg ⮌
19,768×(max) 9 nodes⮎ J2Θs → ΖYb6 → z2ΘC → ΖmN6 → zOlC → nMnO → ROlk → NIro → ZQjc ⮌
19,756×(max) 9 nodes⮎ FAzw → pgTM → TCxi → lEvQ → hKpU → VCxg → lAzQ → pKpM → VShg ⮌
19,355×(max) 9 nodes⮎ B6ΔΑ → xoLE → jShS → HEvu → hcXU → D4Ζy → ΒkPA → rKpK → XUfe ⮌
19,301×(max) 9 nodes⮎ 52ΘΗ → ΖΑ96 → zqJC → nWdO → P6Δm → xMnE → jQjS → JGts → dYbY ⮌
19,240×(max) 9 nodes⮎ D8Βy → tkPI → bKpa → V0Κg → ΚAz2 → ΘoL4 → ΔSh8 → vEvG → heVU ⮌
19,198×(max) 9 nodes⮎ HCxu → lcXQ → L4Ζq → ΒUfA → rAzK → pWdM → T6Δi → xEvE → jgTS ⮌
19,009×(max) 9 nodes⮎ REvk → hIrU → ZCxc → l2ΘQ → ΖKp6 → zUfC → nAzO → pOlM → TMni ⮌
18,977×(max) 9 nodes⮎ PIrm → ZMnc → R2Θk → ΖIr6 → zYbC → n2ΘO → ΖOl6 → zMnC → nQjO ⮌
18,969×(max) 9 nodes⮎ J6Δs → xYbE → j2ΘS → ΖGt6 → zcXC → n4ΖO → ΒOlA → rMnK → XQje ⮌
18,961×(max) 9 nodes⮎ H4Ζu → ΒcXA → r4ΖK → ΒWdA → r6ΔK → xWdE → j6ΔS → xGtE → jcXS ⮌
18,945×(max) 9 nodes⮎ L8Βq → tUfI → bAza → p0ΚM → ΚSh2 → ΘEv4 → ΔgT8 → vCxG → leVQ ⮌
18,913×(max) 9 nodes⮎ N0Κo → ΚQj2 → ΘIr4 → ΔYb8 → v2ΘG → ΖeV6 → z8ΒC → tmNI → bOla ⮌
18,913×(max) 9 nodes⮎ P0Κm → ΚMn2 → ΘQj4 → ΔIr8 → vYbG → f2ΘW → Ζ8Β6 → zsHC → naZO ⮌
18,905×(max) 9 nodes⮎ d8ΒY → t4ΖI → ΒaZA → r0ΚK → ΚWd2 → Θ6Δ4 → ΔwD8 → viRG → fGtW ⮌
18,905×(max) 9 nodes⮎ X8Βe → t6ΔI → xaZE → j0ΚS → ΚGt2 → ΘcX4 → Δ4Ζ8 → ΒuFA → reVK ⮌
18,877×(max) 9 nodes⮎ 30ΚΙ → ΚΕ52 → ΘyB4 → ΔmN8 → vOlG → fMnW → R8Βk → tIrI → bYba ⮌
18,753×(max) 9 nodes⮎ TEvi → hEvU → hCxU → lCxQ → lKpQ → VKpg → VAzg → pAzM → pShM ⮌
18,726×(max) 9 nodes⮎ F6Δw → xgTE → jCxS → lGtQ → dKpY → V4Ζg → ΒAzA → roLK → XShe ⮌
18,694×(max) 9 nodes⮎ DAzy → pkPM → TKpi → VEvg → hAzU → pCxM → lShQ → LEvq → hUfU ⮌
18,689×(max) 9 nodes⮎ N2Θo → ΖQj6 → zIrC → nYbO → P2Θm → ΖMn6 → zQjC → nIrO → ZOlc ⮌
18,681×(max) 9 nodes⮎ RGtk → dIrY → Z4Ζc → Β2ΘA → ΖqJ6 → zWdC → n6ΔO → xOlE → jMnS ⮌
18,681×(max) 9 nodes⮎ P4Ζm → ΒMnA → rQjK → XIre → Z6Δc → x2ΘE → ΖiR6 → zGtC → ncXO ⮌
18,673×(max) 9 nodes⮎ X6Δe → x6ΔE → xiRE → jGtS → dGtY → d4ΖY → Β4ΖA → ΒqJA → rWdK ⮌
18,657×(max) 9 nodes⮎ L0Κq → ΚUf2 → ΘAz4 → ΔoL8 → vShG → fEvW → h8ΒU → tCxI → laZQ ⮌
18,657×(max) 9 nodes⮎ T0Κi → ΚEv2 → ΘgT4 → ΔCx8 → vkPG → fKpW → V8Βg → tAzI → paZM ⮌
18,642×(max) 9 nodes⮎ PMnm → RMnk → RIrk → ZIrc → Z2Θc → Ζ2Θ6 → ΖyB6 → zmNC → nOlO ⮌
18,625×(max) 9 nodes⮎ R0Κk → ΚIr2 → ΘYb4 → Δ2Θ8 → ΖuF6 → zeVC → n8ΒO → tOlI → bMna ⮌
18,561×(max) 9 nodes⮎ f0ΚW → Κ8Β2 → ΘsH4 → ΔaZ8 → v0ΚG → ΚeV2 → Θ8Β4 → ΔsH8 → vaZG ⮌
18,500×(max) 9 nodes⮎ 74ΖΕ → ΒwDA → riRK → XGte → d6ΔY → x4ΖE → ΒiRA → rGtK → dWdY ⮌
18,428×(max) 9 nodes⮎ FCxw → lgTQ → LCxq → lUfQ → LAzq → pUfM → TAzi → pEvM → hShU ⮌
18,414×(max) 9 nodes⮎ B2ΘΑ → ΖoL6 → zShC → nEvO → hOlU → NCxo → lQjQ → LIrq → ZUfc ⮌
18,326×(max) 9 nodes⮎ D2Θy → ΖkP6 → zKpC → nUfO → PAzm → pMnM → TQji → JEvs → hYbU ⮌
18,280×(max) 9 nodes⮎ B8ΒΑ → toLI → bSha → F0Κw → ΚgT2 → ΘCx4 → ΔkP8 → vKpG → fUfW ⮌
18,220×(max) 9 nodes⮎ 50ΚΗ → ΚΑ92 → ΘqJ4 → ΔWd8 → v6ΔG → xeVE → j8ΒS → tGtI → daZY ⮌
18,192×(max) 9 nodes⮎ H8Βu → tcXI → b4Ζa → Β0ΚA → ΚqJ2 → ΘWd4 → Δ6Δ8 → xuFE → jeVS ⮌
18,136×(max) 9 nodes⮎ 72ΘΕ → ΖwD6 → ziRC → nGtO → dOlY → N4Ζo → ΒQjA → rIrK → ZWdc ⮌
18,094×(max) 9 nodes⮎ PGtm → dMnY → R4Ζk → ΒIrA → rYbK → X2Θe → Ζ6Δ6 → zwDC → niRO ⮌
17,940×(max) 9 nodes⮎ B4ΖΑ → ΒoLA → rShK → XEve → h6ΔU → xCxE → liRQ → LGtq → dUfY ⮌
17,924×(max) 9 nodes⮎ N6Δo → xQjE → jIrS → ZGtc → d2ΘY → Ζ4Ζ6 → ΒyBA → rmNK → XOle ⮌
17,857×(max) 9 nodes⮎ PCxm → lMnQ → RKpk → VIrg → ZAzc → p2ΘM → ΖSh6 → zEvC → ngTO ⮌
17,850×(max) 9 nodes⮎ 94ΖΓ → ΒsHA → raZK → X0Κe → Κ6Δ2 → ΘwD4 → ΔiR8 → vGtG → fcXW ⮌
17,849×(max) 9 nodes⮎ TGti → dEvY → h4ΖU → ΒCxA → rkPK → XKpe → V6Δg → xAzE → piRM ⮌
17,834×(max) 9 nodes⮎ F2Θw → ΖgT6 → zCxC → nkPO → PKpm → VMng → RAzk → pIrM → ZShc ⮌
17,793×(max) 9 nodes⮎ F8Βw → tgTI → bCxa → l0ΚQ → ΚKp2 → ΘUf4 → ΔAz8 → voLG → fShW ⮌
17,761×(max) 9 nodes⮎ 92ΘΓ → ΖsH6 → zaZC → n0ΚO → ΚOl2 → ΘMn4 → ΔQj8 → vIrG → fYbW ⮌
17,712×(max) 9 nodes⮎ JCxs → lYbQ → L2Θq → ΖUf6 → zAzC → pmNM → TOli → NEvo → hQjU ⮌
17,569×(max) 9 nodes⮎ NAzo → pQjM → TIri → ZEvc → h2ΘU → ΖCx6 → zkPC → nKpO → VOlg ⮌
17,561×(max) 9 nodes⮎ D6Δy → xkPE → jKpS → VGtg → dAzY → p4ΖM → ΒShA → rEvK → hWdU ⮌
17,561×(max) 9 nodes⮎ HAzu → pcXM → T4Ζi → ΒEvA → rgTK → XCxe → l6ΔQ → xKpE → jUfS ⮌
17,549×(max) 9 nodes⮎ b0Κa → Κ0Κ2 → ΚΗ32 → ΘΓ74 → ΔuF8 → veVG → f8ΒW → t8ΒI → taZI ⮌
17,529×(max) 9 nodes⮎ J4Ζs → ΒYbA → r2ΘK → ΖWd6 → z6ΔC → xmNE → jOlS → NGto → dQjY ⮌
17,521×(max) 9 nodes⮎ H6Δu → xcXE → j4ΖS → ΒGtA → rcXK → X4Ζe → Β6ΔA → xqJE → jWdS ⮌
17,505×(max) 9 nodes⮎ B0ΚΑ → ΚoL2 → ΘSh4 → ΔEv8 → vgTG → fCxW → l8ΒQ → tKpI → bUfa ⮌
17,505×(max) 9 nodes⮎ D0Κy → ΚkP2 → ΘKp4 → ΔUf8 → vAzG → peVM → T8Βi → tEvI → haZU ⮌
17,465×(max) 9 nodes⮎ bGta → d0ΚY → Κ4Ζ2 → ΘΑ94 → ΔqJ8 → vWdG → f6ΔW → x8ΒE → tiRI ⮌
17,409×(max) 9 nodes⮎ b8Βa → t0ΚI → ΚaZ2 → Θ0Κ4 → ΚΓ72 → ΘuF4 → ΔeV8 → v8ΒG → teVI ⮌
17,340×(max) 9 nodes⮎ 70ΚΕ → ΚwD2 → ΘiR4 → ΔGt8 → vcXG → f4ΖW → Β8ΒA → tqJI → bWda ⮌
17,281×(max) 9 nodes⮎ PEvm → hMnU → RCxk → lIrQ → ZKpc → V2Θg → ΖAz6 → zoLC → nShO ⮌
17,273×(max) 9 nodes⮎ F4Ζw → ΒgTA → rCxK → lWdQ → L6Δq → xUfE → jAzS → pGtM → dShY ⮌
17,267×(max) 9 nodes⮎ 96ΔΓ → xsHE → jaZS → H0Κu → ΚcX2 → Θ4Ζ4 → ΔΑ98 → vqJG → fWdW ⮌
17,241×(max) 9 nodes⮎ H2Θu → ΖcX6 → z4ΖC → ΒmNA → rOlK → XMne → R6Δk → xIrE → jYbS ⮌
17,185×(max) 9 nodes⮎ J8Βs → tYbI → b2Θa → Ζ0Κ6 → ΚyB2 → ΘmN4 → ΔOl8 → vMnG → fQjW ⮌
16,850×(max) 9 nodes⮎ 90ΚΓ → ΚsH2 → ΘaZ4 → Δ0Κ8 → ΚuF2 → ΘeV4 → Δ8Β8 → vsHG → faZW ⮌
16,064×(max) 9 nodes⮎ J0Κs → ΚYb2 → Θ2Θ4 → ΖΓ76 → zuFC → neVO → P8Βm → tMnI → bQja ⮌
15,870×(max) 9 nodes⮎ N8Βo → tQjI → bIra → Z0Κc → Κ2Θ2 → ΘΕ54 → ΔyB8 → vmNG → fOlW ⮌
52 cycles13,133,727×3 nodes⮎ mMΛnP → oNΛmN → nQΛjO ⮌
6,624,015×(max) 4 nodes⮎ mNΛmP → nMΛnO → oOΛlN → nPΛkO ⮌
62 cycles237,715,292×(max) 29 nodes⮎ 973ΗΔΓ → ΔwsHE8 → viaZSG → fG0ΚuW → Κe8ΒW2 → Θt7ΓH4 → ΔvbYF8 → vg2ΘUG → ΖfByV6 → zn9ΑNC → rnPkNK → XQKpke → VK6Δqg → xWAzeE → pj7ΓRM → vTHshG → fbDwZW → j91ΙΒS → ΘsGtI4 → ΔdZaX8 → v60ΚΕG → ΚyeVC2 → Θm8ΒO4 → ΔtNmH8 → vcOlYG → fN3ΗnW → ΔQ8Βk8 → vtJqHG → fcWdYW ⮌
19,136,230×23 nodes⮎ LE6Δwq → xiUfSE → jGAzuS → peGtWM → dT7ΓhY → vE4ΖwG → ΒieVSA → rG8ΒuK → teWdWI → b86ΔΓa → xu0ΚGE → ΚjdWR2 → ΘI6Δs4 → ΔxZaD8 → vk0ΚQG → ΚfJqV2 → ΘX9Αd4 → Δr5ΕJ8 → zvXcFC → ng4ΖUO → ΒPBylA → rnLoNK → XTPkhe ⮌
73 cycles2,385,359,988×2 nodes⮎ sbHΛsZJ → tZIΛrbI ⮌
265,250,712×2 nodes⮎ tbGΛtZI → ubJΛqZH ⮌
248,142,942×(max) 4 nodes⮎ rZGΛtbK → uZHΛsbH → tdIΛrXI → sbJΛqZJ ⮌
8+---Not showing digit sets 8+ due to verbosity.