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 nodes1Κ → Θ3 → Δ7 → vF → fV → 9Β → rJ → Xd → 5Ζ → zB → nN → Pl → Lp → Th → Dx → jR → Ht → bZ
31 cycle 67,452×(max) 2 nodesZΛb → aΛa
470 cycles20,153×(max) 9 nodesXAze → p6ΔM → xShE → jEvS → hGtU → dCxY → l4ΖQ → ΒKpA → rUfK
20,097×(max) 9 nodesbEva → h0ΚU → ΚCx2 → ΘkP4 → ΔKp8 → vUfG → fAzW → p8ΒM → tShI
20,065×(max) 9 nodesZ8Βc → t2ΘI → ΖaZ6 → z0ΚC → ΚmN2 → ΘOl4 → ΔMn8 → vQjG → fIrW
20,057×(max) 9 nodesb6Δa → x0ΚE → ΚiR2 → ΘGt4 → ΔcX8 → v4ΖG → ΒeVA → r8ΒK → tWdI
19,844×(max) 9 nodesJAzs → pYbM → T2Θi → ΖEv6 → zgTC → nCxO → lOlQ → NKpo → VQjg
19,768×(max) 9 nodesJ2Θs → ΖYb6 → z2ΘC → ΖmN6 → zOlC → nMnO → ROlk → NIro → ZQjc
19,756×(max) 9 nodesFAzw → pgTM → TCxi → lEvQ → hKpU → VCxg → lAzQ → pKpM → VShg
19,355×(max) 9 nodesB6ΔΑ → xoLE → jShS → HEvu → hcXU → D4Ζy → ΒkPA → rKpK → XUfe
19,301×(max) 9 nodes52ΘΗ → ΖΑ96 → zqJC → nWdO → P6Δm → xMnE → jQjS → JGts → dYbY
19,240×(max) 9 nodesD8Βy → tkPI → bKpa → V0Κg → ΚAz2 → ΘoL4 → ΔSh8 → vEvG → heVU
19,198×(max) 9 nodesHCxu → lcXQ → L4Ζq → ΒUfA → rAzK → pWdM → T6Δi → xEvE → jgTS
19,009×(max) 9 nodesREvk → hIrU → ZCxc → l2ΘQ → ΖKp6 → zUfC → nAzO → pOlM → TMni
18,977×(max) 9 nodesPIrm → ZMnc → R2Θk → ΖIr6 → zYbC → n2ΘO → ΖOl6 → zMnC → nQjO
18,969×(max) 9 nodesJ6Δs → xYbE → j2ΘS → ΖGt6 → zcXC → n4ΖO → ΒOlA → rMnK → XQje
18,961×(max) 9 nodesH4Ζu → ΒcXA → r4ΖK → ΒWdA → r6ΔK → xWdE → j6ΔS → xGtE → jcXS
18,945×(max) 9 nodesL8Βq → tUfI → bAza → p0ΚM → ΚSh2 → ΘEv4 → ΔgT8 → vCxG → leVQ
18,913×(max) 9 nodesN0Κo → ΚQj2 → ΘIr4 → ΔYb8 → v2ΘG → ΖeV6 → z8ΒC → tmNI → bOla
18,913×(max) 9 nodesP0Κm → ΚMn2 → ΘQj4 → ΔIr8 → vYbG → f2ΘW → Ζ8Β6 → zsHC → naZO
18,905×(max) 9 nodesd8ΒY → t4ΖI → ΒaZA → r0ΚK → ΚWd2 → Θ6Δ4 → ΔwD8 → viRG → fGtW
18,905×(max) 9 nodesX8Βe → t6ΔI → xaZE → j0ΚS → ΚGt2 → ΘcX4 → Δ4Ζ8 → ΒuFA → reVK
18,877×(max) 9 nodes30ΚΙ → ΚΕ52 → ΘyB4 → ΔmN8 → vOlG → fMnW → R8Βk → tIrI → bYba
18,753×(max) 9 nodesTEvi → hEvU → hCxU → lCxQ → lKpQ → VKpg → VAzg → pAzM → pShM
18,726×(max) 9 nodesF6Δw → xgTE → jCxS → lGtQ → dKpY → V4Ζg → ΒAzA → roLK → XShe
18,694×(max) 9 nodesDAzy → pkPM → TKpi → VEvg → hAzU → pCxM → lShQ → LEvq → hUfU
18,689×(max) 9 nodesN2Θo → ΖQj6 → zIrC → nYbO → P2Θm → ΖMn6 → zQjC → nIrO → ZOlc
18,681×(max) 9 nodesRGtk → dIrY → Z4Ζc → Β2ΘA → ΖqJ6 → zWdC → n6ΔO → xOlE → jMnS
18,681×(max) 9 nodesP4Ζm → ΒMnA → rQjK → XIre → Z6Δc → x2ΘE → ΖiR6 → zGtC → ncXO
18,673×(max) 9 nodesX6Δe → x6ΔE → xiRE → jGtS → dGtY → d4ΖY → Β4ΖA → ΒqJA → rWdK
18,657×(max) 9 nodesL0Κq → ΚUf2 → ΘAz4 → ΔoL8 → vShG → fEvW → h8ΒU → tCxI → laZQ
18,657×(max) 9 nodesT0Κi → ΚEv2 → ΘgT4 → ΔCx8 → vkPG → fKpW → V8Βg → tAzI → paZM
18,642×(max) 9 nodesPMnm → RMnk → RIrk → ZIrc → Z2Θc → Ζ2Θ6 → ΖyB6 → zmNC → nOlO
18,625×(max) 9 nodesR0Κk → ΚIr2 → ΘYb4 → Δ2Θ8 → ΖuF6 → zeVC → n8ΒO → tOlI → bMna
18,561×(max) 9 nodesf0ΚW → Κ8Β2 → ΘsH4 → ΔaZ8 → v0ΚG → ΚeV2 → Θ8Β4 → ΔsH8 → vaZG
18,500×(max) 9 nodes74ΖΕ → ΒwDA → riRK → XGte → d6ΔY → x4ΖE → ΒiRA → rGtK → dWdY
18,428×(max) 9 nodesFCxw → lgTQ → LCxq → lUfQ → LAzq → pUfM → TAzi → pEvM → hShU
18,414×(max) 9 nodesB2ΘΑ → ΖoL6 → zShC → nEvO → hOlU → NCxo → lQjQ → LIrq → ZUfc
18,326×(max) 9 nodesD2Θy → ΖkP6 → zKpC → nUfO → PAzm → pMnM → TQji → JEvs → hYbU
18,280×(max) 9 nodesB8ΒΑ → toLI → bSha → F0Κw → ΚgT2 → ΘCx4 → ΔkP8 → vKpG → fUfW
18,220×(max) 9 nodes50ΚΗ → ΚΑ92 → ΘqJ4 → ΔWd8 → v6ΔG → xeVE → j8ΒS → tGtI → daZY
18,192×(max) 9 nodesH8Βu → tcXI → b4Ζa → Β0ΚA → ΚqJ2 → ΘWd4 → Δ6Δ8 → xuFE → jeVS
18,136×(max) 9 nodes72ΘΕ → ΖwD6 → ziRC → nGtO → dOlY → N4Ζo → ΒQjA → rIrK → ZWdc
18,094×(max) 9 nodesPGtm → dMnY → R4Ζk → ΒIrA → rYbK → X2Θe → Ζ6Δ6 → zwDC → niRO
17,940×(max) 9 nodesB4ΖΑ → ΒoLA → rShK → XEve → h6ΔU → xCxE → liRQ → LGtq → dUfY
17,924×(max) 9 nodesN6Δo → xQjE → jIrS → ZGtc → d2ΘY → Ζ4Ζ6 → ΒyBA → rmNK → XOle
17,857×(max) 9 nodesPCxm → lMnQ → RKpk → VIrg → ZAzc → p2ΘM → ΖSh6 → zEvC → ngTO
17,850×(max) 9 nodes94ΖΓ → ΒsHA → raZK → X0Κe → Κ6Δ2 → ΘwD4 → ΔiR8 → vGtG → fcXW
17,849×(max) 9 nodesTGti → dEvY → h4ΖU → ΒCxA → rkPK → XKpe → V6Δg → xAzE → piRM
17,834×(max) 9 nodesF2Θw → ΖgT6 → zCxC → nkPO → PKpm → VMng → RAzk → pIrM → ZShc
17,793×(max) 9 nodesF8Βw → tgTI → bCxa → l0ΚQ → ΚKp2 → ΘUf4 → ΔAz8 → voLG → fShW
17,761×(max) 9 nodes92ΘΓ → ΖsH6 → zaZC → n0ΚO → ΚOl2 → ΘMn4 → ΔQj8 → vIrG → fYbW
17,712×(max) 9 nodesJCxs → lYbQ → L2Θq → ΖUf6 → zAzC → pmNM → TOli → NEvo → hQjU
17,569×(max) 9 nodesNAzo → pQjM → TIri → ZEvc → h2ΘU → ΖCx6 → zkPC → nKpO → VOlg
17,561×(max) 9 nodesD6Δy → xkPE → jKpS → VGtg → dAzY → p4ΖM → ΒShA → rEvK → hWdU
17,561×(max) 9 nodesHAzu → pcXM → T4Ζi → ΒEvA → rgTK → XCxe → l6ΔQ → xKpE → jUfS
17,549×(max) 9 nodesb0Κa → Κ0Κ2 → ΚΗ32 → ΘΓ74 → ΔuF8 → veVG → f8ΒW → t8ΒI → taZI
17,529×(max) 9 nodesJ4Ζs → ΒYbA → r2ΘK → ΖWd6 → z6ΔC → xmNE → jOlS → NGto → dQjY
17,521×(max) 9 nodesH6Δu → xcXE → j4ΖS → ΒGtA → rcXK → X4Ζe → Β6ΔA → xqJE → jWdS
17,505×(max) 9 nodesB0ΚΑ → ΚoL2 → ΘSh4 → ΔEv8 → vgTG → fCxW → l8ΒQ → tKpI → bUfa
17,505×(max) 9 nodesD0Κy → ΚkP2 → ΘKp4 → ΔUf8 → vAzG → peVM → T8Βi → tEvI → haZU
17,465×(max) 9 nodesbGta → d0ΚY → Κ4Ζ2 → ΘΑ94 → ΔqJ8 → vWdG → f6ΔW → x8ΒE → tiRI
17,409×(max) 9 nodesb8Βa → t0ΚI → ΚaZ2 → Θ0Κ4 → ΚΓ72 → ΘuF4 → ΔeV8 → v8ΒG → teVI
17,340×(max) 9 nodes70ΚΕ → ΚwD2 → ΘiR4 → ΔGt8 → vcXG → f4ΖW → Β8ΒA → tqJI → bWda
17,281×(max) 9 nodesPEvm → hMnU → RCxk → lIrQ → ZKpc → V2Θg → ΖAz6 → zoLC → nShO
17,273×(max) 9 nodesF4Ζw → ΒgTA → rCxK → lWdQ → L6Δq → xUfE → jAzS → pGtM → dShY
17,267×(max) 9 nodes96ΔΓ → xsHE → jaZS → H0Κu → ΚcX2 → Θ4Ζ4 → ΔΑ98 → vqJG → fWdW
17,241×(max) 9 nodesH2Θu → ΖcX6 → z4ΖC → ΒmNA → rOlK → XMne → R6Δk → xIrE → jYbS
17,185×(max) 9 nodesJ8Βs → tYbI → b2Θa → Ζ0Κ6 → ΚyB2 → ΘmN4 → ΔOl8 → vMnG → fQjW
16,850×(max) 9 nodes90ΚΓ → ΚsH2 → ΘaZ4 → Δ0Κ8 → ΚuF2 → ΘeV4 → Δ8Β8 → vsHG → faZW
16,064×(max) 9 nodesJ0Κs → ΚYb2 → Θ2Θ4 → ΖΓ76 → zuFC → neVO → P8Βm → tMnI → bQja
15,870×(max) 9 nodesN8Βo → tQjI → bIra → Z0Κc → Κ2Θ2 → ΘΕ54 → ΔyB8 → vmNG → fOlW
52 cycles13,133,727×3 nodesmMΛnP → oNΛmN → nQΛjO
6,624,015×(max) 4 nodesmNΛmP → nMΛnO → oOΛlN → nPΛkO
62 cycles237,715,292×(max) 29 nodes973ΗΔΓ → 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 nodesLE6Δwq → 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 nodessbHΛsZJ → tZIΛrbI
265,250,712×2 nodestbGΛtZI → ubJΛqZH
248,142,942×(max) 4 nodesrZGΛtbK → uZHΛsbH → tdIΛrXI → sbJΛqZJ
8+---Not showing digit sets 8+ due to verbosity.