Base 71: 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---
22 cycles1,680×(max) 3 nodes7Β → tF → dV
560×(fixed) 1 node Nl
31 cycle 62,125×(max) 2 nodesYΙa → ZΙZ
417 cycles68,755×(max) 35 nodes74ΔΓ → zuDA → pgRK → VEte → f8zU → rAxI → nYZM → R0Θi → ΘGr2 → ΖaX4 → Β2Ζ8 → ΔsF6 → xcVC → l6ΒO → vMlE → hOjS → LEto → fSfU → DAxw → niPM → RIpi → XGrc → b4ΔY → z2ΖA → ΔoJ6 → xUdC → l8zO → rMlI → ZOja → L0Θo → ΘSf2 → ΖCv4 → ΒiP8 → tIpG → dWbW
68,739×(max) 35 nodes52ΖΕ → Δy96 → xoJC → lUdO → N8zm → rOjI → ZKna → T0Θg → ΘCv2 → ΖiP4 → ΒIp8 → tWbG → d4ΔW → z6ΒA → voJE → hUdS → F8zu → reTI → ZAxa → n0ΘM → ΘQh2 → ΖGr4 → ΒaX8 → t2ΖG → ΔcV6 → x6ΒC → vkNE → hMlS → PEtk → fKnU → TAxg → nCvM → jQhQ → JGrq → bWbY
68,735×(max) 35 nodes94ΔΑ → zqHA → pYZK → V0Θe → Θ8z2 → ΖqH4 → ΒYZ8 → t0ΘG → ΘcV2 → Ζ6Β4 → ΒuD8 → tgRG → dEtW → f6ΒU → vAxE → ngRM → REti → fGrU → bAxY → n2ΖM → ΔQh6 → xGrC → laXO → N2Ζm → ΔOj6 → xKnC → lSfO → NCvm → jOjQ → LIpo → XSfc → D4Δw → ziPA → pIpK → XUdc
68,727×(max) 35 nodesD2Ζw → ΔiP6 → xIpC → lWbO → N4Δm → zOjA → pKnK → VSfe → D8zw → riPI → ZIpa → X0Θc → Θ4Δ2 → Ζy94 → ΒoJ8 → tUdG → d8zW → r6ΒI → vYZE → h0ΘS → ΘEt2 → ΖeT4 → ΒAx8 → tmLG → dQhW → H6Βs → vaXE → h2ΖS → ΔEt6 → xeTC → lAxO → nMlM → ROji → LGro → bSfY
68,447×(max) 35 nodesB2Ζy → ΔmL6 → xQhC → lGrO → bMlY → P2Ζk → ΔKn6 → xSfC → lCvO → jMlQ → PIpk → XKnc → T4Δg → zCvA → piPK → VIpe → X8zc → r4ΔI → zYZA → p0ΘK → ΘUd2 → Ζ8z4 → ΒqH8 → tYZG → d0ΘW → Θ6Β2 → ΖuD4 → ΒgR8 → tEtG → fcVU → B6Βy → vmLE → hQhS → HEts → faXU
68,435×(max) 35 nodes72ΖΓ → ΔuD6 → xgRC → lEtO → fMlU → PAxk → nKnM → TQhg → HCvs → jaXQ → J2Ζq → ΔWb6 → x4ΔC → zkNA → pMlK → VOje → L8zo → rSfI → ZCva → j0ΘQ → ΘIp2 → ΖWb4 → Β4Δ8 → zsFA → pcVK → V6Βe → v8zE → rgRI → ZEta → f0ΘU → ΘAx2 → ΖmL4 → ΒQh8 → tGrG → daXW
68,355×(max) 35 nodes30ΘΗ → ΘΓ52 → ΖwB4 → ΒkN8 → tMlG → dOjW → L6Βo → vSfE → hCvS → jEtQ → fIpU → XAxc → n4ΔM → zQhA → pGrK → bUdY → 92ΖΑ → ΔqH6 → xYZC → l0ΘO → ΘMl2 → ΖOj4 → ΒKn8 → tSfG → dCvW → j6ΒQ → vIpE → hWbS → F4Δu → zeTA → pAxK → nUdM → R8zi → rGrI → bYZY
68,343×(max) 35 nodesFAxu → neTM → RAxi → nGrM → bQhY → H2Ζs → ΔaX6 → x2ΖC → ΔkN6 → xMlC → lOjO → NKnm → TOjg → LCvo → jSfQ → JCvq → jWbQ → J4Δq → zWbA → p4ΔK → zUdA → p8zK → rUdI → Z8za → r0ΘI → ΘYZ2 → Ζ0Θ4 → ΘΑ72 → ΖsF4 → ΒcV8 → t6ΒG → vcVE → h6ΒS → vEtE → heTS
67,975×(max) 35 nodesPKnk → TKng → TCvg → jCvQ → jIpQ → XIpc → X4Δc → z4ΔA → zoJA → pUdK → V8ze → r8zI → rYZI → Z0Θa → Θ0Θ2 → ΘΕ32 → ΖΑ74 → ΒsF8 → tcVG → d6ΒW → v6ΒE → vgRE → hEtS → fEtU → fAxU → nAxM → nQhM → RGri → bGrY → b2ΖY → Δ2Ζ6 → ΔwB6 → xkNC → lMlO → PMlk
67,779×(max) 35 nodes50ΘΕ → Θy92 → ΖoJ4 → ΒUd8 → t8zG → rcVI → Z6Βa → v0ΘE → ΘgR2 → ΖEt4 → ΒeT8 → tAxG → ncVM → R6Βi → vGrE → haXS → F2Ζu → ΔeT6 → xAxC → nkNM → RMli → PGrk → bKnY → T2Ζg → ΔCv6 → xiPC → lIpO → XMlc → P4Δk → zKnA → pSfK → VCve → j8zQ → rIpI → ZWba
67,235×(max) 35 nodesB4Δy → zmLA → pQhK → VGre → b8zY → r2ΖI → ΔYZ6 → x0ΘC → ΘkN2 → ΖMl4 → ΒOj8 → tKnG → dSfW → D6Βw → viPE → hIpS → XEtc → f4ΔU → zAxA → pmLK → VQhe → H8zs → raXI → Z2Ζa → Δ0Θ6 → ΘwB2 → ΖkN4 → ΒMl8 → tOjG → dKnW → T6Βg → vCvE → jgRQ → JEtq → fWbU
66,899×(max) 35 nodes96ΒΑ → vqHE → hYZS → F0Θu → ΘeT2 → ΖAx4 → ΒmL8 → tQhG → dGrW → b6ΒY → v2ΖE → ΔgR6 → xEtC → leTO → NAxm → nOjM → RKni → TGrg → bCvY → j2ΖQ → ΔIp6 → xWbC → l4ΔO → zMlA → pOjK → VKne → T8zg → rCvI → jYZQ → J0Θq → ΘWb2 → Ζ4Δ4 → Βy98 → toJG → dUdW
66,855×(max) 35 nodes70ΘΓ → ΘuD2 → ΖgR4 → ΒEt8 → teTG → dAxW → n6ΒM → vQhE → hGrS → bEtY → f2ΖU → ΔAx6 → xmLC → lQhO → NGrm → bOjY → L2Ζo → ΔSf6 → xCvC → liPO → NIpm → XOjc → L4Δo → zSfA → pCvK → jUdQ → J8zq → rWbI → Z4Δa → z0ΘA → ΘoJ2 → ΖUd4 → Β8z8 → tqHG → dYZW
66,755×(max) 35 nodesB8zy → rmLI → ZQha → H0Θs → ΘaX2 → Ζ2Ζ4 → ΔΑ76 → xsFC → lcVO → N6Βm → vOjE → hKnS → TEtg → fCvU → jAxQ → nIpM → XQhc → H4Δs → zaXA → p2ΖK → ΔUd6 → x8zC → rkNI → ZMla → P0Θk → ΘKn2 → ΖSf4 → ΒCv8 → tiPG → dIpW → X6Βc → v4ΔE → zgRA → pEtK → fUdU
66,615×(max) 35 nodesFCvu → jeTQ → JAxq → nWbM → R4Δi → zGrA → paXK → V2Ζe → Δ8z6 → xqHC → lYZO → N0Θm → ΘOj2 → ΖKn4 → ΒSf8 → tCvG → jcVQ → J6Βq → vWbE → h4ΔS → zEtA → peTK → VAxe → n8zM → rQhI → ZGra → b0ΘY → Θ2Ζ2 → ΖΓ54 → ΒwB8 → tkNG → dMlW → P6Βk → vKnE → hSfS
66,335×(max) 35 nodes90ΘΑ → ΘqH2 → ΖYZ4 → Β0Θ8 → ΘsF2 → ΖcV4 → Β6Β8 → vsFE → hcVS → F6Βu → veTE → hAxS → nEtM → fQhU → HAxs → naXM → R2Ζi → ΔGr6 → xaXC → l2ΖO → ΔMl6 → xOjC → lKnO → TMlg → PCvk → jKnQ → TIpg → XCvc → j4ΔQ → zIpA → pWbK → V4Δe → z8zA → roJI → ZUda
65,571×(max) 35 nodesB0Θy → ΘmL2 → ΖQh4 → ΒGr8 → taXG → d2ΖW → Δ6Β6 → xuDC → lgRO → NEtm → fOjU → LAxo → nSfM → RCvi → jGrQ → bIpY → X2Ζc → Δ4Δ6 → zwBA → pkNK → VMle → P8zk → rKnI → ZSfa → D0Θw → ΘiP2 → ΖIp4 → ΒWb8 → t4ΔG → zcVA → p6ΒK → vUdE → h8zS → rEtI → fYZU
51 cycle 17,259,319×(max) 4 nodeslMΙlO → mMΙlN → mOΙjN → lNΙkO
66 cycles128,049,781×(max) 50 nodesB82ΖΑy → ΔsmLG6 → xcQhWC → lH5ΓrO → xaMlYC → lP1ΗjO → ΖNJol4 → ΒVNkd8 → tN7ΑlG → tdNkVG → dN7ΑlW → tO6ΒkG → vdLmVE → hR7ΑhS → tGEtsG → fdbWVU → B84ΔΑy → zsmLGA → pcQhWK → VH5Γre → xa8zYC → rl1ΗNI → ΖZNkZ4 → ΒMΙΙl8 → ΑmFsM9 → rdPiVI → ZJ7Αpa → tW0ΘcG → Θd5ΓV2 → Ζx7ΑB4 → ΒtlMF8 → teOjUG → dL9ynW → pS6ΒgK → vVDudE → ig7ΑSR → tHDurG → hdZYVS → F80ΘΑu → ΘseTG2 → ΖcAxW4 → Βn5ΓL8 → xtRgFC → leEtUO → fN9ylU → pOAxkK → nVLmdM → SQ7Αih → tIEtqG → fdXaVU
47,354,897×(fixed) 1 node td7ΑVG
36,640,419×12 nodesZR7Αha → tG0ΘsG → ΘdbWV2 → Ζ84ΔΑ4 → ΒzrG98 → tqaXIG → dY2ΖaW → Δ71ΗΒ6 → ΖxtEB4 → ΒmeTM8 → tQAxiG → ndHqVM
4,809,379×9 nodesXF9ytc → pe4ΔUK → zV9ydA → qo7ΑKJ → tXTebG → dB3ΕxW → Βm6ΒM8 → vtPiFE → heIpUS
965,223×17 nodesRKGroi → bUGreY → bA2ΖyY → Δo2ΖK6 → ΔxTeB6 → xmAxMC → nlPiNM → ROIpki → XMGrmc → bQ4ΔiY → zI2ΖqA → ΔpXaJ6 → xW2ΖcC → Δl5ΓN6 → ywNkCB → nkMlOM → RPLmji
799,170×6 nodesF6ΙΙΒu → Γt6ΒF7 → wudUED → jg8zSQ → rJDupI → hZVcZS
71 cycle 2,404,808,269×(max) 8 nodesrZEΙtZI → ubHΙqXF → tdIΙpVG → sbJΙoXH → rZGΙrZI → sZHΙqZH → rbGΙrXI → sZJΙoZH
8+---Not showing digit sets 8+ due to verbosity.