Base 77: 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 cycles1,824×(max) 12 nodes1Ξ → Μ3 → Θ7 → zF → jV → DΒ → nR → Lt → Xh → 9Ζ → vJ → bd
912×6 nodes5Κ → ΔB → rN → Tl → Hx → fZ
152×(fixed) 1 node Pp
31 cycle 79,002×(max) 2 nodesbΟd → cΟc
427 cycles69,721×(max) 30 nodesF6ΘΑ → ΒkTE → nGxS → hKtY → Z8Ζg → x6ΘI → ΒeZE → n4ΚS → ΖKtA → vYfK → b6Θe → Β2ΜE → ΚmR6 → ΔKtC → rYfO → T6Θm → ΒIvE → ncbS → L0Ξu → ΞYf2 → Μ6Θ4 → ΘΑD8 → zmRG → jKtW → ZCΒg → p6ΘQ → ΒOpE → nQnS → NKts → ZUjg
69,047×(max) 30 nodesD8ΖΓ → xoPI → fOpa → R4Κo → ΖMrA → vUjK → bEze → l2ΜU → ΚGx6 → ΔgXC → r8ΖO → xSlI → fIva → d4Κc → Ζ0ΞA → ΞuJ2 → Μad4 → Θ2Μ8 → ΚyF6 → ΔiVC → rCΒO → pSlQ → PIvq → dQnc → N0Ξs → ΞUj2 → ΜEz4 → ΘkT8 → zGxG → jgXW
68,552×(max) 30 nodesH8Ζy → xgXI → f8Ζa → x4ΚI → ΖeZA → v4ΚK → ΖadA → v2ΜK → Κad6 → Δ2ΜC → ΚqN6 → ΔSlC → rIvO → dSlc → J0Ξw → Ξcb2 → Μ0Ξ4 → ΞΗ72 → ΜyF4 → ΘiV8 → zCΒG → piVQ → PCΒq → pQnQ → PMrq → VQnk → NEzs → lUjU → HEzy → lgXU
68,492×(max) 30 nodesB0ΞΕ → ΞsL2 → ΜWh4 → ΘAΔ8 → zsLG → jWhW → DAΔΓ → toPM → XOpi → RAΔo → tMrM → XUji → FAΔΑ → tkTM → XGxi → hAΔY → t8ΖM → xWhI → fAΔa → t4ΚM → ΖWhA → vAΔK → tadM → X2Μi → ΚAΔ6 → ΔsLC → rWhO → TAΔm → tIvM → dWhc
68,472×(max) 30 nodes90ΞΗ → ΞwH2 → ΜeZ4 → Θ4Κ8 → ΖyFA → viVK → bCΒe → p2ΜQ → ΚOp6 → ΔQnC → rMrO → VSlk → JEzw → lcbU → H0Ξy → ΞgX2 → Μ8Ζ4 → ΘwH8 → zeZG → j4ΚW → ΖCΒA → voPK → bOpe → R2Μo → ΚMr6 → ΔUjC → rEzO → lSlU → JGxw → hcbY
68,097×(max) 30 nodesD0ΞΓ → ΞoP2 → ΜOp4 → ΘQn8 → zMrG → jUjW → FCΒΑ → pkTQ → PGxq → hQnY → N8Ζs → xUjI → fEza → l4ΚU → ΖGxA → vgXK → b8Ζe → x2ΜI → ΚeZ6 → Δ4ΚC → ΖqNA → vSlK → bIve → d2Μc → Κ0Ξ6 → ΞΓB2 → ΜqN4 → ΘSl8 → zIvG → jcbW
68,055×(max) 30 nodesF0ΞΑ → ΞkT2 → ΜGx4 → ΘgX8 → z8ΖG → xiVI → fCΒa → p4ΚQ → ΖOpA → vQnK → bMre → V2Μk → ΚEz6 → ΔkTC → rGxO → hSlY → J8Ζw → xcbI → f0Ξa → Ξ4Κ2 → ΜΕ94 → ΘuJ8 → zadG → j2ΜW → ΚCΒ6 → ΔoPC → rOpO → TQnm → NIvs → dUjc
67,936×(max) 30 nodes30ΞΝ → ΞΙ52 → ΜΓB4 → ΘqN8 → zSlG → jIvW → dCΒc → p0ΞQ → ΞOp2 → ΜQn4 → ΘMr8 → zUjG → jEzW → lCΒU → pGxQ → hOpY → R8Ζo → xMrI → fUja → F4ΚΑ → ΖkTA → vGxK → hadY → 92ΜΗ → ΚwH6 → ΔeZC → r4ΚO → ΖSlA → vIvK → dadc
67,734×(max) 30 nodes70ΞΙ → ΞΑD2 → ΜmR4 → ΘKt8 → zYfG → j6ΘW → ΒCΒE → pmRQ → PKtq → ZQng → N6Θs → ΒUjE → nEzS → lKtU → ZGxg → h6ΘY → Β8ΖE → xmRI → fKta → Z4Κg → Ζ6ΘA → ΒuJE → nadS → L2Μu → ΚYf6 → Δ6ΘC → ΒqNE → nSlS → LIvu → dYfc
67,720×(max) 30 nodes96ΘΗ → ΒwHE → neZS → L4Κu → ΖYfA → v6ΘK → ΒadE → n2ΜS → ΚKt6 → ΔYfC → r6ΘO → ΒSlE → nIvS → dKtc → Z0Ξg → Ξ6Θ2 → ΜΑD4 → ΘmR8 → zKtG → jYfW → D6ΘΓ → ΒoPE → nOpS → RKto → ZMrg → V6Θk → ΒEzE → nkTS → LGxu → hYfY
67,621×(max) 30 nodes94ΚΗ → ΖwHA → veZK → b4Κe → Ζ2ΜA → ΚuJ6 → ΔadC → r2ΜO → ΚSl6 → ΔIvC → rcbO → T0Ξm → ΞIv2 → Μcb4 → Θ0Ξ8 → ΞyF2 → ΜiV4 → ΘCΒ8 → zoPG → jOpW → RCΒo → pMrQ → VOpk → REzo → lMrU → VGxk → hEzY → l8ΖU → xGxI → heZY
67,485×(max) 30 nodesH4Κy → ΖgXA → v8ΖK → xadI → f2Μa → Κ4Κ6 → ΖΓBA → vqNK → bSle → J2Μw → Κcb6 → Δ0ΞC → ΞqN2 → ΜSl4 → ΘIv8 → zcbG → j0ΞW → ΞCΒ2 → ΜoP4 → ΘOp8 → zQnG → jMrW → VCΒk → pEzQ → lOpU → RGxo → hMrY → V8Ζk → xEzI → leZU
67,424×(max) 30 nodesB4ΚΕ → ΖsLA → vWhK → bAΔe → t2ΜM → ΚWh6 → ΔAΔC → tqNM → XSli → JAΔw → tcbM → X0Ξi → ΞAΔ2 → ΜsL4 → ΘWh8 → zAΔG → tiVM → XCΒi → pAΔQ → tOpM → XQni → NAΔs → tUjM → XEzi → lAΔU → tGxM → hWhY → B8ΖΕ → xsLI → fWha
67,397×(max) 30 nodesRMro → VMrk → VEzk → lEzU → lGxU → hGxY → h8ΖY → x8ΖI → xeZI → f4Κa → Ζ4ΚA → ΖuJA → vadK → b2Μe → Κ2Μ6 → ΚΓB6 → ΔqNC → rSlO → TIvm → dIvc → d0Ξc → Ξ0Ξ2 → ΞΛ32 → ΜΗ74 → ΘyF8 → ziVG → jCΒW → pCΒQ → pOpQ → ROpo
67,108×(max) 30 nodes50ΞΛ → ΞΕ92 → ΜuJ4 → Θad8 → z2ΜG → ΚiV6 → ΔCΒC → roPO → TOpm → RIvo → dMrc → V0Ξk → ΞEz2 → ΜkT4 → ΘGx8 → zgXG → j8ΖW → xCΒI → peZQ → P4Κq → ΖQnA → vMrK → bUje → F2ΜΑ → ΚkT6 → ΔGxC → rgXO → T8Ζm → xIvI → fcba
66,915×(max) 30 nodesB2ΜΕ → ΚsL6 → ΔWhC → rAΔO → tSlM → XIvi → dAΔc → t0ΞM → ΞWh2 → ΜAΔ4 → ΘsL8 → zWhG → jAΔW → tCΒM → pWhQ → PAΔq → tQnM → XMri → VAΔk → tEzM → lWhU → HAΔy → tgXM → X8Ζi → xAΔI → teZM → X4Κi → ΖAΔA → vsLK → bWhe
66,862×(max) 30 nodes52ΜΛ → ΚΕ96 → ΔuJC → radO → T2Μm → ΚIv6 → ΔcbC → r0ΞO → ΞSl2 → ΜIv4 → Θcb8 → z0ΞG → ΞiV2 → ΜCΒ4 → ΘoP8 → zOpG → jQnW → NCΒs → pUjQ → PEzq → lQnU → NGxs → hUjY → F8ΖΑ → xkTI → fGxa → h4ΚY → Ζ8ΖA → xuJI → fada
66,586×(max) 30 nodes72ΜΙ → ΚΑD6 → ΔmRC → rKtO → ZSlg → J6Θw → ΒcbE → n0ΞS → ΞKt2 → ΜYf4 → Θ6Θ8 → ΒyFE → niVS → LCΒu → pYfQ → P6Θq → ΒQnE → nMrS → VKtk → ZEzg → l6ΘU → ΒGxE → ngXS → L8Ζu → xYfI → f6Θa → Β4ΚE → ΖmRA → vKtK → bYfe
66,502×(max) 30 nodes74ΚΙ → ΖΑDA → vmRK → bKte → Z2Μg → Κ6Θ6 → ΔΑDC → rmRO → TKtm → ZIvg → d6Θc → Β0ΞE → ΞmR2 → ΜKt4 → ΘYf8 → z6ΘG → ΒiVE → nCΒS → pKtQ → ZOpg → R6Θo → ΒMrE → nUjS → LEzu → lYfU → H6Θy → ΒgXE → n8ΖS → xKtI → fYfa
65,577×(max) 30 nodesH2Μy → ΚgX6 → Δ8ΖC → xqNI → fSla → J4Κw → ΖcbA → v0ΞK → Ξad2 → Μ2Μ4 → ΚΗ76 → ΔyFC → riVO → TCΒm → pIvQ → dOpc → R0Ξo → ΞMr2 → ΜUj4 → ΘEz8 → zkTG → jGxW → hCΒY → p8ΖQ → xOpI → fQna → N4Κs → ΖUjA → vEzK → ladU
65,126×(max) 30 nodesHCΒy → pgXQ → P8Ζq → xQnI → fMra → V4Κk → ΖEzA → vkTK → bGxe → h2ΜY → Κ8Ζ6 → ΔwHC → reZO → T4Κm → ΖIvA → vcbK → b0Ξe → Ξ2Μ2 → ΜΙ54 → ΘΓB8 → zqNG → jSlW → JCΒw → pcbQ → P0Ξq → ΞQn2 → ΜMr4 → ΘUj8 → zEzG → liVU
64,592×(max) 30 nodesD2ΜΓ → ΚoP6 → ΔOpC → rQnO → TMrm → VIvk → dEzc → l0ΞU → ΞGx2 → ΜgX4 → Θ8Ζ8 → zwHG → jeZW → D4ΚΓ → ΖoPA → vOpK → bQne → N2Μs → ΚUj6 → ΔEzC → rkTO → TGxm → hIvY → d8Ζc → x0ΞI → ΞeZ2 → Μ4Κ4 → ΘΕ98 → zuJG → jadW
34,595×15 nodesP2Μq → ΚQn6 → ΔMrC → rUjO → TEzm → lIvU → dGxc → h0ΞY → Ξ8Ζ2 → ΜwH4 → ΘeZ8 → z4ΚG → ΖiVA → vCΒK → padQ
34,182×15 nodesB6ΘΕ → ΒsLE → nWhS → LAΔu → tYfM → X6Θi → ΒAΔE → tmRM → XKti → ZAΔg → t6ΘM → ΒWhE → nAΔS → tKtM → ZWhg
11,305×5 nodesZ6Θg → Β6ΘE → ΒmRE → nKtS → ZKtg
11,305×5 nodesL6Θu → ΒYfE → n6ΘS → ΒKtE → nYfS
7,095×3 nodesXAΔi → tAΔM → tWhM
51 cycle 25,621,519×(max) 4 nodespOΟpQ → qOΟpP → qQΟnP → pPΟoQ
64 cycles236,806,668×68 nodesHE2ΜΑy → ΚmgXS6 → ΔK8ΖuC → xrZeNI → fU4Κka → ΖG4ΚyA → ΖvhWJA → vcAΔcK → taΟΟdM → seFyaN → jV3ΛjW → ΘECΒΑ8 → zplSPG → jQIvoW → dOCΒqc → pS0ΞmQ → ΞPJup2 → ΜbPod4 → ΘP1Νp8 → ΜzPoF4 → ΘkOpU8 → zRFynG → kiLsWV → XFBΓzi → rkAΔUO → tTFylM → jXHwhW → fD9ΕΒa → vo4ΚQK → ΖbNqdA → vT1ΝlK → ΜbHwd4 → Θf1ΝZ8 → Μz5ΙF4 → ΘΔjUB8 → zsEzMG → ljViVU → HECΒΑy → pmgXSQ → PK8Ζuq → xaQneI → fN3Λra → ΘU4Κk8 → ΖzFyFA → vkiVUK → bGCΒye → pi2ΜWQ → ΚPBΓp6 → ΔrPoNC → rUOpkO → TRFynm → jMIvsW → dWCΒic → pC0ΞΓQ → ΞqOpO2 → ΜSQnm4 → ΘNJur8 → zbTkdG → jH1ΝxW → ΜgCΒY4 → Θp7ΗP8 → ΑyPoGF → liOpWU → RHBΓxo → rgMrYO → VT7Ηlk → zIEzwG → ljdaVU
89,914,512×(max) 172 nodes951ΝΚΗ → ΜΕwHA4 → ΘueZK8 → za4ΚeG → Ζj3ΛVA → ΘvDΑJ8 → znbcRG → jM0ΞsW → ΞWCΒi2 → ΜpBΓP4 → ΘrPoN8 → zUOpkG → jRFynW → jMCΒsW → pWCΒiQ → pPBΓpQ → rQOpoO → TRNqnm → TMIvsm → dWIvic → dC0ΞΓc → Ξq0ΞO2 → ΞΜRm32 → ΜΙKt64 → ΘΓYfC8 → zq6ΘOG → ΒjRmVE → nLDΑtS → nYKtgS → ZL7Ηtg → zY6ΘgG → Βj7ΗVE → znDΑRG → njLsVS → XLDΑti → nYAΔgS → tL7ΗtM → zYWhgG → jB7ΗΔW → zsCΒMG → pjViVQ → PECΒΑq → pmQnSQ → PNJurq → bUQnke → NG2Μys → ΚiUjW6 → ΔFBΓzC → sqjUON → VSEzmk → lKEzuU → laGxeU → hH3ΛxY → Θg8ΖY8 → zx7ΗHG → zjfYVG → jE6ΘΑW → ΒmCΒSE → pnJuRQ → bPLspe → XQ2Μoi → ΚOAΔq6 → ΔtRmLC → rYKtgO → ZT7Ηlg → zI6ΘwG → ΒjdaVE → nE2ΜΑS → ΚmKtS6 → ΔZJufC → rb5ΙdO → ΔT1ΝlC → ΜrHwN4 → ΘfTkZ8 → zH5ΙxG → ΔjfYVC → rE6ΘΑO → ΒmSlSE → nKIvuS → daKtec → Z40ΞΛg → ΞΗ6Θ82 → ΜΒxGD4 → ΘogXQ8 → zO8ΖqG → xjRmVI → fLDΑta → nY4ΚgS → ΖL7ΗtA → zvXgJG → jc8ΖcW → xCΟΟΒI → Γw3ΛID → ΘpdaP8 → zQ2ΜoG → ΚjNqV6 → ΔTDΑlC → rnHwRO → fTLsla → XI4Κwi → ΖeAΔaA → vt3ΛLK → ΘbXgd8 → z91ΝΖG → ΜwiVI4 → ΘeCΒa8 → zp3ΛPG → ΘjPoV8 → zPDΑpG → njPoVS → PLDΑtq → nYQngS → NL7Ηts → zYUjgG → jF7ΗzW → zkCΒUG → pjFyVQ → jPDΑpW → nQCΒoS → pOKtqQ → ZSOpmg → RK6Θuo → ΒaMreE → nV3ΛjS → ΘLDΑt8 → znXgRG → jM8ΖsW → xWCΒiI → pfBΓZQ → rP5ΙpO → ΔTPolC → rPHwpO → fTPola → PI4Κwq → ΖeQnaA → vN3ΛrK → ΘbTkd8 → zH1ΝxG → ΜjfYV4 → ΘE6ΘΑ8 → ΒzlSFE → nkIvUS → dLFytc → jY0ΞgW → ΞD7ΗΒ2 → ΜznQF4 → ΘkMrU8 → zVFyjG → kiDΑWV → nFBΓzS → rkKtUO → ZTFylg → jI6ΘwW → ΒeCΒaE → pn3ΛRQ → ΘPLsp8 → zXPohG → jP9ΕpW → vQCΒoK → pbNqdQ → TP1Νpm → ΜQIvo4 → ΘdNqb8 → zT1ΝlG → ΜjHwV4 → ΘfDΑZ8 → zn5ΙRG → ΔjLsVC → rXDΑhO → nT9ΕlS → vLHwtK → fbXgda
23,296,533×6 nodesrn1ΝRO → ΜTLsl4 → ΘXHwh8 → zf9ΕZG → vj5ΙVK → ΔbDΑdC
144,022×5 nodesZC6ΘΓg → Βq6ΘOE → ΒnRmRE → nMKtsS → ZWKtig
73 cycles3,392,317,703×2 nodesvdIΟvbK → wbJΟudJ
400,449,030×2 nodeswdHΟwbJ → xdKΟtbI
359,151,818×(max) 4 nodesubHΟwdL → xbIΟvdI → wfJΟuZJ → vdKΟtbK
8+---Not showing digit sets 8+ due to verbosity.