Base 81: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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---
22 cycles1,600×(max) 10 nodes1Σ → Π3 → Μ7 → ΔF → nV → HΒ → jZ → 9Κ → zJ → fd
1,600×(max) 10 nodes5Ξ → ΘB → vN → Xl → DΖ → rR → Pt → Tp → Lx → bh
31 cycle 91,800×(max) 2 nodesdΤf → eΤe
436 cycles74,438×(max) 27 nodesTOtq → VMvo → ZIzk → hAΘc → x4ΞM → ΚahA → z6ΜK → ΖedE → r0ΣS → ΣOt2 → ΠUn4 → ΜIz8 → ΔgbG → n4ΞW → ΚGΒA → zkXK → fCΖe → t0ΣQ → ΣSp2 → ΠMv4 → ΜYj8 → ΔAΘG → xmVM → bGΒi → l6ΜY → ΖCΖE → tqRQ
69,871×(max) 27 nodesR0Σs → ΣQr2 → ΠQr4 → ΜQr8 → ΔQrG → nQrW → RGΒs → lQrY → RCΖs → tQrQ → TQrq → RMvs → ZQrk → RAΘs → xQrM → bQri → R6Μs → ΖQrE → rQrS → ROts → VQro → RIzs → hQrc → R4Ξs → ΚQrA → zQrK → fQre
69,475×(max) 27 nodes96ΜΛ → ΖΑHE → riZS → P8Κu → ΒUnI → jIza → h8Κc → Β4ΞI → ΚiZA → z8ΚK → ΒedI → j0Σa → Σ8Κ2 → ΠΑH4 → ΜiZ8 → Δ8ΚG → ΒmVI → jGΒa → l8ΚY → ΒCΖI → tiZQ → T8Κq → ΒMvI → jYja → B8ΚΙ → ΒwLI → jaha
69,445×(max) 27 nodes52ΠΟ → ΞΙ96 → ΘyJC → vedO → X0Σm → ΣEΔ2 → ΠoT4 → ΜKx8 → ΔcfG → n2ΠW → ΞGΒ6 → ΘkXC → vCΖO → tWlQ → TEΔq → pMvU → ZKxk → dAΘg → x2ΠM → Ξah6 → Θ6ΜC → ΖuNE → rWlS → PEΔu → pUnU → LIzy → hcfc
69,279×(max) 27 nodes72ΠΝ → ΞΕD6 → ΘqRC → vOtO → XUnm → JEΔΑ → pgbU → L4Ξy → ΚcfA → z2ΠK → Ξed6 → Θ0ΣC → ΣuN2 → ΠWl4 → ΜEΔ8 → ΔoTG → nKxW → dGΒg → l2ΠY → ΞCΖ6 → ΘsPC → vSpO → XMvm → ZEΔk → pAΘU → xKxM → dahg
68,995×(max) 27 nodes30ΣΡ → ΣΝ52 → ΠΗB4 → ΜuN8 → ΔWlG → nEΔW → pGΒU → lKxY → dCΖg → t2ΠQ → ΞSp6 → ΘMvC → vYjO → XAΘm → xEΔM → pahU → L6Μy → ΖcfE → r2ΠS → ΞOt6 → ΘUnC → vIzO → hWlc → F4ΞΕ → ΚoTA → zKxK → fcfe
68,683×(max) 27 nodesFCΖΕ → toTQ → TKxq → dMvg → Z2Πk → ΞAΘ6 → ΘwLC → vahO → X6Μm → ΖEΔE → roTS → PKxu → dUng → J2ΠΑ → Ξgb6 → Θ4ΞC → ΚuNA → zWlK → fEΔe → p0ΣU → ΣKx2 → Πcf4 → Μ2Π8 → ΞΓF6 → ΘmVC → vGΒO → lWlY
68,665×(max) 27 nodesD2ΠΗ → ΞsP6 → ΘSpC → vMvO → ZWlk → FAΘΕ → xoTM → bKxi → d6Μg → Ζ2ΠE → ΞqR6 → ΘOtC → vUnO → XIzm → hEΔc → p4ΞU → ΚKxA → zcfK → f2Πe → Ξ0Σ6 → ΣΗB2 → ΠuN4 → ΜWl8 → ΔEΔG → pmVU → LGΒy → lcfY
68,539×(max) 27 nodes94ΞΛ → ΚΑHA → ziZK → f8Κe → Β0ΣI → ΣiZ2 → Π8Κ4 → ΜΑH8 → ΔiZG → n8ΚW → ΒGΒI → liZY → D8ΚΗ → ΒsPI → jSpa → N8Κw → ΒYjI → jAΘa → x8ΚM → ΒahI → j6Μa → Ζ8ΚE → ΒqRI → jOta → V8Κo → ΒIzI → jgba
67,265×(max) 27 nodesB2ΠΙ → ΞwL6 → ΘahC → v6ΜO → ΖWlE → rEΔS → pOtU → VKxo → dIzg → h2Πc → Ξ4Ξ6 → ΚΗBA → zuNK → fWle → F0ΣΕ → ΣoT2 → ΠKx4 → Μcf8 → Δ2ΠG → ΞmV6 → ΘGΒC → vkXO → XCΖm → tEΔQ → pSpU → NKxw → dYjg
66,914×(max) 27 nodesD4ΞΗ → ΚsPA → zSpK → fMve → Z0Σk → ΣAΘ2 → ΠwL4 → Μah8 → Δ6ΜG → ΖmVE → rGΒS → lOtY → VCΖo → tIzQ → hSpc → N4Ξw → ΚYjA → zAΘK → xedM → b0Σi → Σ6Μ2 → ΠΕD4 → ΜqR8 → ΔOtG → nUnW → JGΒΑ → lgbY
66,680×(max) 27 nodesB6ΜΙ → ΖwLE → rahS → P6Μu → ΖUnE → rIzS → hOtc → V4Ξo → ΚIzA → zgbK → f4Ξe → Κ0ΣA → ΣyJ2 → Πed4 → Μ0Σ8 → ΣΓF2 → ΠmV4 → ΜGΒ8 → ΔkXG → nCΖW → tGΒQ → lSpY → NCΖw → tYjQ → TAΘq → xMvM → bYji
66,617×(max) 27 nodesHEΔΓ → pkXU → LCΖy → tcfQ → T2Πq → ΞMv6 → ΘYjC → vAΘO → xWlM → bEΔi → p6ΜU → ΖKxE → rcfS → P2Πu → ΞUn6 → ΘIzC → vgbO → X4Ξm → ΚEΔA → zoTK → fKxe → d0Σg → Σ2Π2 → ΠΝ54 → ΜΗB8 → ΔuNG → nWlW
66,201×(max) 27 nodesH2ΠΓ → ΞkX6 → ΘCΖC → vsPO → XSpm → NEΔw → pYjU → LAΘy → xcfM → b2Πi → Ξ6Μ6 → ΘΕDC → vqRO → XOtm → VEΔo → pIzU → hKxc → d4Ξg → Κ2ΠA → ΞyJ6 → ΘedC → v0ΣO → ΣWl2 → ΠEΔ4 → ΜoT8 → ΔKxG → ncfW
66,127×(max) 27 nodes90ΣΛ → ΣΑH2 → ΠiZ4 → Μ8Κ8 → ΔΑHG → niZW → H8ΚΓ → ΒkXI → jCΖa → t8ΚQ → ΒSpI → jMva → Z8Κk → ΒAΘI → xiZM → b8Κi → Β6ΜI → ΖiZE → r8ΚS → ΒOtI → jUna → J8ΚΑ → ΒgbI → j4Ξa → Κ8ΚA → ΒyJI → jeda
65,948×(max) 27 nodesD0ΣΗ → ΣsP2 → ΠSp4 → ΜMv8 → ΔYjG → nAΘW → xGΒM → lahY → D6ΜΗ → ΖsPE → rSpS → PMvu → ZUnk → JAΘΑ → xgbM → b4Ξi → Κ6ΜA → ΖyJE → redS → P0Σu → ΣUn2 → ΠIz4 → Μgb8 → Δ4ΞG → ΚmVA → zGΒK → ledY
65,888×(max) 27 nodesDAΘΗ → xsPM → bSpi → N6Μw → ΖYjE → rAΘS → xOtM → bUni → J6ΜΑ → ΖgbE → r4ΞS → ΚOtA → zUnK → fIze → h0Σc → Σ4Ξ2 → ΠΙ94 → ΜyJ8 → ΔedG → n0ΣW → ΣGΒ2 → ΠkX4 → ΜCΖ8 → ΔsPG → nSpW → NGΒw → lYjY
65,870×(max) 27 nodesB4ΞΙ → ΚwLA → zahK → f6Μe → Ζ0ΣE → ΣqR2 → ΠOt4 → ΜUn8 → ΔIzG → ngbW → H4ΞΓ → ΚkXA → zCΖK → tedQ → T0Σq → ΣMv2 → ΠYj4 → ΜAΘ8 → ΔwLG → nahW → H6ΜΓ → ΖkXE → rCΖS → tOtQ → VSpo → NIzw → hYjc
65,750×(max) 27 nodes74ΞΝ → ΚΕDA → zqRK → fOte → V0Σo → ΣIz2 → Πgb4 → Μ4Ξ8 → ΚΓFA → zmVK → fGΒe → l0ΣY → ΣCΖ2 → ΠsP4 → ΜSp8 → ΔMvG → nYjW → HAΘΓ → xkXM → bCΖi → t6ΜQ → ΖSpE → rMvS → ZOtk → VAΘo → xIzM → hahc
65,498×(max) 27 nodes50ΣΟ → ΣΙ92 → ΠyJ4 → Μed8 → Δ0ΣG → ΣmV2 → ΠGΒ4 → ΜkX8 → ΔCΖG → tmVQ → TGΒq → lMvY → ZCΖk → tAΘQ → xSpM → bMvi → Z6Μk → ΖAΘE → xqRM → bOti → V6Μo → ΖIzE → rgbS → P4Ξu → ΚUnA → zIzK → hedc
65,449×(max) 27 nodesF6ΜΕ → ΖoTE → rKxS → dOtg → V2Πo → ΞIz6 → ΘgbC → v4ΞO → ΚWlA → zEΔK → pedU → L0Σy → Σcf2 → Π2Π4 → ΞΛ76 → ΘΓFC → vmVO → XGΒm → lEΔY → pCΖU → tKxQ → dSpg → N2Πw → ΞYj6 → ΘAΘC → xuNM → bWli
65,204×(max) 27 nodesHCΖΓ → tkXQ → TCΖq → tMvQ → ZSpk → NAΘw → xYjM → bAΘi → x6ΜM → ΖahE → r6ΜS → ΖOtE → rUnS → PIzu → hUnc → J4ΞΑ → ΚgbA → z4ΞK → ΚedA → z0ΣK → Σed2 → Π0Σ4 → ΣΛ72 → ΠΓF4 → ΜmV8 → ΔGΒG → nkXW
64,655×(max) 27 nodesTMvq → ZMvk → ZAΘk → xAΘM → xahM → b6Μi → Ζ6ΜE → ΖqRE → rOtS → VOto → VIzo → hIzc → h4Ξc → Κ4ΞA → ΚyJA → zedK → f0Σe → Σ0Σ2 → ΣΟ32 → ΠΛ74 → ΜΓF8 → ΔmVG → nGΒW → lGΒY → lCΖY → tCΖQ → tSpQ
64,400×(max) 27 nodes70ΣΝ → ΣΕD2 → ΠqR4 → ΜOt8 → ΔUnG → nIzW → hGΒc → l4ΞY → ΚCΖA → zsPK → fSpe → N0Σw → ΣYj2 → ΠAΘ4 → ΜwL8 → ΔahG → n6ΜW → ΖGΒE → rkXS → PCΖu → tUnQ → TIzq → hMvc → Z4Ξk → ΚAΘA → zwLK → fahe
64,268×(max) 27 nodesH0ΣΓ → ΣkX2 → ΠCΖ4 → ΜsP8 → ΔSpG → nMvW → ZGΒk → lAΘY → xCΖM → tahQ → T6Μq → ΖMvE → rYjS → PAΘu → xUnM → bIzi → h6Μc → Ζ4ΞE → ΚqRA → zOtK → fUne → J0ΣΑ → Σgb2 → Π4Ξ4 → ΜΙ98 → ΔyJG → nedW
63,890×(max) 27 nodesB0ΣΙ → ΣwL2 → Πah4 → Μ6Μ8 → ΖΓFE → rmVS → PGΒu → lUnY → JCΖΑ → tgbQ → T4Ξq → ΚMvA → zYjK → fAΘe → x0ΣM → Σah2 → Π6Μ4 → ΜΕD8 → ΔqRG → nOtW → VGΒo → lIzY → hCΖc → t4ΞQ → ΚSpA → zMvK → fYje
23,937×9 nodesXKxm → dEΔg → p2ΠU → ΞKx6 → ΘcfC → v2ΠO → ΞWl6 → ΘEΔC → voTO
21,057×9 nodesXEΔm → pEΔU → pKxU → dKxg → d2Πg → Ξ2Π6 → ΞΗB6 → ΘuNC → vWlO
21,057×9 nodesL2Πy → Ξcf6 → Θ2ΠC → ΞuN6 → ΘWlC → vEΔO → pWlU → LEΔy → pcfU
21,057×9 nodesF2ΠΕ → ΞoT6 → ΘKxC → vcfO → X2Πm → ΞEΔ6 → ΘoTC → vKxO → dWlg
20,817×9 nodesR2Πs → ΞQr6 → ΘQrC → vQrO → XQrm → REΔs → pQrU → RKxs → dQrg
20,745×9 nodes92ΠΛ → ΞΑH6 → ΘiZC → v8ΚO → ΒWlI → jEΔa → p8ΚU → ΒKxI → jcfa
20,745×9 nodesF8ΚΕ → ΒoTI → jKxa → d8Κg → Β2ΠI → ΞiZ6 → Θ8ΚC → ΒuNI → jWla
20,745×9 nodesL8Κy → ΒcfI → j2Πa → Ξ8Κ6 → ΘΑHC → viZO → X8Κm → ΒEΔI → piZU
8,091×3 nodesj8Κa → Β8ΚI → ΒiZI
7,155×3 nodesR8Κs → ΒQrI → jQra
51 cycle 32,801,436×(fixed) (max) 1 node sQΤrR
62 cycles331,311,981×(max) 28 nodesHD5ΝΖΓ → ΘskXQC → vSCΖqO → tXNulQ → XTDΕpm → rMEΔwS → paOtiU → VL7Λxo → ΔcIzgG → nh3ΟbW → ΜH5ΝΒ8 → ΘΔjYFC → voAΘUO → xXJylM → fbDΕhe → r60ΣΝS → ΣΗOtC2 → ΠuUnO4 → ΜWIzm8 → ΔhFΓbG → om5ΝWV → ΘJFΓzC → vnfcVO → XI2ΠΑm → ΞiEΔa6 → Θp7ΛTC → ΔvLwNG → nbXkhW
138,843,015×27 nodesF4ΤΤΞΕ → ΟΔ8ΚF5 → ΚΒnUHA → zkIzYK → hfBΗdc → v51ΡΞO → ΠΙWlA4 → ΜyEΔK8 → ΔpdeTG → nM0ΣwW → ΣaGΒi2 → Πl7ΛX4 → ΜΔDΕF8 → ΔrnURG → nQIzsW → hSGΒqc → lO4ΞuY → ΚWCΖmA → ztFΓPK → nfTodW → LH1ΡΒy → ΠkcfY4 → ΜC2ΠΗ8 → ΞΔtOF6 → ΘoUnUC → vKIzyO → heWlec
73 cycles4,821,719,226×2 nodesyfJΤydL → zdKΤxfK
522,394,347×2 nodeszfIΤzdK → ΑfLΤwdJ
499,242,303×(max) 4 nodesxdIΤzfM → ΑdJΤyfJ → zhKΤxbK → yfLΤwdL
8+---Not showing digit sets 8+ due to verbosity.