Base 83: 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---
23 cycles1,968×(max) 6 nodes3Σ → Ξ7 → ΖF → pV → JΒ → hd
984×3 nodesBΚ → xN → Zl
328×(fixed) 1 node Rt
31 cycle 98,687×(max) 2 nodeseΦg → fΦf
420 cycles107,885×(max) 41 nodesHEΖΕ → rmXU → NEΖy → rajU → N8Μy → ΔajI → l8Μa → ΔAΚI → zkZM → dAΚi → z4ΠM → ΜchA → Β4ΠK → ΜgdA → Β2ΣK → Πgd6 → Κ2ΣC → ΠwN6 → ΚYlC → xCΘO → vYlQ → VCΘq → vKzQ → fUpg → L0ΥΑ → Υef2 → Σ0Υ4 → ΥΝ72 → ΣΕF4 → ΞoV8 → ΖIΒG → pibW → J6ΞΓ → ΘibE → t6ΞS → ΘQtE → tSrS → ROvu → XSro → PGΔw → nWnY
107,765×(max) 41 nodes90ΥΝ → ΥΓH2 → ΣkZ4 → ΞAΚ8 → ΖyLG → pchW → J4ΠΓ → ΜibA → Β6ΞK → ΘgdE → t2ΣS → ΠQt6 → ΚSrC → xOvO → ZWnm → HCΘΕ → vmXQ → VEΖq → rKzU → fMxg → b0Υk → Υ8Μ2 → ΣΓH4 → ΞkZ8 → ΖAΚG → zoVM → dIΒi → j4Πc → Μ6ΞA → ΘΑJE → tgdS → R2Σu → ΠSr6 → ΚOvC → xWnO → ZGΔm → nCΘY → vEΖQ → rUpU → NKzy → fajg
107,661×(max) 41 nodes74ΠΟ → ΜΗDA → ΒsRK → hQte → T2Σs → ΠOv6 → ΚWnC → xGΔO → nYlY → FCΘΗ → vqTQ → VMxq → bKzk → f8Μg → Δ0ΥI → ΥkZ2 → ΣAΚ4 → ΞyL8 → ΖchG → p4ΠW → ΜIΒA → ΒibK → h6Ξe → Θ2ΣE → ΠsR6 → ΚQtC → xSrO → ZOvm → XCΘo → vGΔQ → nUpY → LEΖΑ → refU → N0Υy → Υaj2 → Σ8Μ4 → ΞΓH8 → ΖkZG → pAΚW → zIΒM → jchc
107,637×(max) 41 nodes94ΠΝ → ΜΓHA → ΒkZK → hAΚe → z2ΣM → Πch6 → Κ4ΠC → ΜwNA → ΒYlK → hCΘe → v2ΣQ → ΠUp6 → ΚKzC → xefO → Z0Υm → ΥCΘ2 → ΣuP4 → ΞUp8 → ΖKzG → pefW → J0ΥΓ → Υib2 → Σ6Ξ4 → ΞΗD8 → ΖsRG → pQtW → TIΒs → jOvc → X6Ξo → ΘGΔE → tmXS → REΖu → rSrU → PMxw → bWnk → H8ΜΕ → ΔmXI → lEΖa → rAΚU → zMxM → daji
107,629×(max) 41 nodesD8ΜΙ → ΔuPI → lUpa → LAΚΑ → zefM → d0Υi → Υ4Π2 → ΣΛ94 → ΞΑJ8 → ΖgdG → p2ΣW → ΠIΒ6 → ΚibC → x6ΞO → ΘYlE → tCΘS → vQtQ → VSrq → PKzw → fWng → H0ΥΕ → ΥmX2 → ΣEΖ4 → ΞqT8 → ΖMxG → pajW → J8ΜΓ → ΔibI → l6Ξa → ΘAΚE → zsRM → dQti → T4Πs → ΜOvA → ΒWnK → hGΔe → n2ΣY → ΠEΖ6 → ΚqTC → xMxO → bYlk
107,133×(max) 41 nodes30ΥΤ → ΥΟ52 → ΣΙB4 → ΞwN8 → ΖYlG → pCΘW → vIΒQ → jUpc → L6ΞΑ → ΘefE → t0ΥS → ΥQt2 → ΣSr4 → ΞOv8 → ΖWnG → pGΔW → nIΒY → jEΖc → r6ΞU → ΘMxE → tajS → R8Μu → ΔSrI → lOva → XAΚo → zGΔM → nchY → F4ΠΗ → ΜqTA → ΒMxK → haje → 92ΣΝ → ΠΓH6 → ΚkZC → xAΚO → zYlM → dCΘi → v4ΠQ → ΜUpA → ΒKzK → hefe
106,845×(max) 41 nodes70ΥΟ → ΥΗD2 → ΣsR4 → ΞQt8 → ΖSrG → pOvW → XIΒo → jGΔc → n6ΞY → ΘEΖE → tqTS → RMxu → bSrk → P8Μw → ΔWnI → lGΔa → nAΚY → zEΖM → rchU → N4Πy → ΜajA → Β8ΜK → ΔgdI → l2Σa → ΠAΚ6 → ΚyLC → xchO → Z4Πm → ΜCΘA → ΒuPK → hUpe → L2ΣΑ → Πef6 → Κ0ΥC → ΥwN2 → ΣYl4 → ΞCΘ8 → ΖuPG → pUpW → LIΒΑ → jefc
106,805×(max) 41 nodes96ΞΝ → ΘΓHE → tkZS → RAΚu → zSrM → dOvi → X4Πo → ΜGΔA → ΒmXK → hEΖe → r2ΣU → ΠMx6 → ΚajC → x8ΜO → ΔYlI → lCΘa → vAΚQ → zUpM → dKzi → f4Πg → Μ0ΥA → ΥΑJ2 → Σgd4 → Ξ2Σ8 → ΠΕF6 → ΚoVC → xIΒO → jYlc → D6ΞΙ → ΘuPE → tUpS → RKzu → fSrg → P0Υw → ΥWn2 → ΣGΔ4 → ΞmX8 → ΖEΖG → roVU → NIΒy → jajc
106,497×(max) 41 nodesTOvs → XOvo → XGΔo → nGΔY → nEΖY → rEΖU → rMxU → bMxk → b8Μk → Δ8ΜI → ΔkZI → lAΚa → zAΚM → zchM → d4Πi → Μ4ΠA → ΜΑJA → ΒgdK → h2Σe → Π2Σ6 → ΠΙB6 → ΚwNC → xYlO → ZCΘm → vCΘQ → vUpQ → VKzq → fKzg → f0Υg → Υ0Υ2 → ΥΡ32 → ΣΝ74 → ΞΕF8 → ΖoVG → pIΒW → jIΒc → j6Ξc → Θ6ΞE → ΘsRE → tQtS → TQts
106,445×(max) 41 nodesB4ΠΛ → ΜyLA → ΒchK → h4Πe → Μ2ΣA → ΠΑJ6 → ΚgdC → x2ΣO → ΠYl6 → ΚCΘC → xuPO → ZUpm → LCΘΑ → vefQ → V0Υq → ΥKz2 → Σef4 → Ξ0Υ8 → ΥΕF2 → ΣoV4 → ΞIΒ8 → ΖibG → p6ΞW → ΘIΒE → tibS → R6Ξu → ΘSrE → tOvS → XQto → TGΔs → nOvY → XEΖo → rGΔU → nMxY → bEΖk → r8ΜU → ΔMxI → laja → B8ΜΛ → ΔyLI → lcha
106,405×(max) 41 nodesD4ΠΙ → ΜuPA → ΒUpK → hKze → f2Σg → Π0Υ6 → ΥΙB2 → ΣwN4 → ΞYl8 → ΖCΘG → voVQ → VIΒq → jKzc → f6Ξg → Θ0ΥE → ΥsR2 → ΣQt4 → ΞSr8 → ΖOvG → pWnW → JGΔΓ → nibY → F6ΞΗ → ΘqTE → tMxS → bQtk → T8Μs → ΔOvI → lWna → HAΚΕ → zmXM → dEΖi → r4ΠU → ΜMxA → ΒajK → h8Μe → Δ2ΣI → ΠkZ6 → ΚAΚC → zwNM → dYli
106,349×(max) 41 nodes50ΥΡ → ΥΛ92 → ΣΑJ4 → Ξgd8 → Ζ2ΣG → ΠoV6 → ΚIΒC → xibO → Z6Ξm → ΘCΘE → vsRQ → VQtq → TKzs → fOvg → X0Υo → ΥGΔ2 → ΣmX4 → ΞEΖ8 → ΖqTG → pMxW → bIΒk → j8Μc → Δ6ΞI → ΘkZE → tAΚS → zQtM → dSri → P4Πw → ΜWnA → ΒGΔK → ngdY → F2ΣΗ → ΠqT6 → ΚMxC → xajO → Z8Μm → ΔCΘI → vkZQ → VAΚq → zKzM → fchg
105,965×(max) 41 nodes52ΣΡ → ΠΛ96 → ΚΑJC → xgdO → Z2Σm → ΠCΘ6 → ΚuPC → xUpO → ZKzm → fCΘg → v0ΥQ → ΥUp2 → ΣKz4 → Ξef8 → Ζ0ΥG → ΥoV2 → ΣIΒ4 → Ξib8 → Ζ6ΞG → ΘoVE → tIΒS → jQtc → T6Ξs → ΘOvE → tWnS → RGΔu → nSrY → PEΖw → rWnU → NGΔy → najY → F8ΜΗ → ΔqTI → lMxa → bAΚk → z8ΜM → ΔchI → l4Πa → ΜAΚA → ΒyLK → hche
105,413×(max) 41 nodesB0ΥΛ → ΥyL2 → Σch4 → Ξ4Π8 → ΜΕFA → ΒoVK → hIΒe → j2Σc → Π6Ξ6 → ΚΗDC → xsRO → ZQtm → TCΘs → vOvQ → XUpo → LGΔΑ → nefY → F0ΥΗ → ΥqT2 → ΣMx4 → Ξaj8 → Ζ8ΜG → ΔoVI → lIΒa → jAΚc → z6ΞM → ΘchE → t4ΠS → ΜQtA → ΒSrK → hOve → X2Σo → ΠGΔ6 → ΚmXC → xEΖO → rYlU → NCΘy → vajQ → V8Μq → ΔKzI → lefa
105,381×(max) 41 nodes72ΣΟ → ΠΗD6 → ΚsRC → xQtO → ZSrm → PCΘw → vWnQ → VGΔq → nKzY → fEΖg → r0ΥU → ΥMx2 → Σaj4 → Ξ8Μ8 → ΖΓHG → pkZW → JAΚΓ → zibM → d6Ξi → Θ4ΠE → ΜsRA → ΒQtK → hSre → P2Σw → ΠWn6 → ΚGΔC → xmXO → ZEΖm → rCΘU → vMxQ → bUpk → L8ΜΑ → ΔefI → l0Υa → ΥAΚ2 → ΣyL4 → Ξch8 → Ζ4ΠG → ΜoVA → ΒIΒK → jgdc
105,357×(max) 41 nodesB2ΣΛ → ΠyL6 → ΚchC → x4ΠO → ΜYlA → ΒCΘK → vgdQ → V2Σq → ΠKz6 → ΚefC → x0ΥO → ΥYl2 → ΣCΘ4 → ΞuP8 → ΖUpG → pKzW → fIΒg → j0Υc → Υ6Ξ2 → ΣΗD4 → ΞsR8 → ΖQtG → pSrW → PIΒw → jWnc → H6ΞΕ → ΘmXE → tEΖS → rQtU → TMxs → bOvk → X8Μo → ΔGΔI → nkZY → FAΚΗ → zqTM → dMxi → b4Πk → Μ8ΜA → ΔΑJI → lgda
104,829×(max) 41 nodesDAΚΙ → zuPM → dUpi → L4ΠΑ → ΜefA → Β0ΥK → Υgd2 → Σ2Σ4 → ΠΝ76 → ΚΕFC → xoVO → ZIΒm → jCΘc → v6ΞQ → ΘUpE → tKzS → fQtg → T0Υs → ΥOv2 → ΣWn4 → ΞGΔ8 → ΖmXG → pEΖW → rIΒU → jMxc → b6Ξk → Θ8ΜE → ΔsRI → lQta → TAΚs → zOvM → dWni → H4ΠΕ → ΜmXA → ΒEΖK → rgdU → N2Σy → Πaj6 → Κ8ΜC → ΔwNI → lYla
104,501×(max) 41 nodesB6ΞΛ → ΘyLE → tchS → R4Πu → ΜSrA → ΒOvK → hWne → H2ΣΕ → ΠmX6 → ΚEΖC → xqTO → ZMxm → bCΘk → v8ΜQ → ΔUpI → lKza → fAΚg → z0ΥM → Υch2 → Σ4Π4 → ΞΛ98 → ΖΑJG → pgdW → J2ΣΓ → Πib6 → Κ6ΞC → ΘwNE → tYlS → RCΘu → vSrQ → VOvq → XKzo → fGΔg → n0ΥY → ΥEΖ2 → ΣqT4 → ΞMx8 → ΖajG → p8ΜW → ΔIΒI → liba
103,845×(max) 41 nodesJCΘΓ → vibQ → V6Ξq → ΘKzE → tefS → R0Υu → ΥSr2 → ΣOv4 → ΞWn8 → ΖGΔG → pmXW → JEΖΓ → ribU → N6Ξy → ΘajE → t8ΜS → ΔQtI → lSra → PAΚw → zWnM → dGΔi → n4ΠY → ΜEΖA → ΒqTK → hMxe → b2Σk → Π8Μ6 → ΚΓHC → xkZO → ZAΚm → zCΘM → vchQ → V4Πq → ΜKzA → ΒefK → h0Υe → Υ2Σ2 → ΣΟ54 → ΞΙB8 → ΖwNG → pYlW
103,125×(max) 41 nodesD0ΥΙ → ΥuP2 → ΣUp4 → ΞKz8 → ΖefG → p0ΥW → ΥIΒ2 → Σib4 → Ξ6Ξ8 → ΘΕFE → toVS → RIΒu → jSrc → P6Ξw → ΘWnE → tGΔS → nQtY → TEΖs → rOvU → XMxo → bGΔk → n8ΜY → ΔEΖI → rkZU → NAΚy → zajM → d8Μi → Δ4ΠI → ΜkZA → ΒAΚK → zgdM → d2Σi → Π4Π6 → ΜΙBA → ΒwNK → hYle → D2ΣΙ → ΠuP6 → ΚUpC → xKzO → fYlg
51 cycle 36,949,774×(max) 4 nodestQΦtS → uQΦtR → uSΦrR → tRΦsS
66 cycles529,179,309×(max) 11 nodesig3Ρed → Ξ51ΤΠ8 → ΣΛΕFA4 → ΞΑoVK8 → ΖgIΒeG → pj1ΤbW → ΣJ7ΝΒ4 → ΞΖhcF8 → Ζq4ΠUG → ΜpLyVA → ΒdJΑhK
4,907,885×8 nodesl40ΥΡa → ΥΝAΚ82 → ΣΕyLG4 → ΞochW8 → ΖI4ΠΓG → ΜpjaVA → ΒK8ΜΑK → ΔhfedI
3,598,471×(fixed) 1 node xZBΙlO
3,475,076×3 nodesxp3ΡVO → ΞZJΑl8 → ΖhBΙdG
506,645×4 nodesΖO0ΥwG → ΥpXmV2 → ΣKEΖΑ4 → ΞrfeT8
263,767×4 nodesΖG0ΥΕG → ΥpnWV2 → ΣKGΔΑ4 → ΞnfeX8
71 cycle 6,890,268,489×(max) 8 nodesΑfHΦΓfL → ΔhKΦzdI → ΓjLΦybJ → ΒhMΦxdK → ΑfJΦΑfL → ΒfKΦzfK → ΑhJΦΑdL → ΒfMΦxfK
8+---Not showing digit sets 8+ due to verbosity.