Base 87: 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---
21 cycle 3,440×(max) 5 nodes7Σ → ΚF → tV → NΒ → dl
31 cycle 113,477×(max) 2 nodesgαi → hαh
437 cycles88,293×(max) 28 nodesVQxu → XOzs → bKΔo → jCΜg → z2ΧQ → ΥYp6 → ΞGΘC → ΒqXO → dIΖm → n8Πc → ΘAΞI → ΔoZM → hEΚi → v0ΩU → ΩQx2 → ΧWr4 → ΣKΔ8 → ΚifG → t2ΧW → ΥMΒ6 → ΞejC → Β4ΥO → ΠclA → Ζ8ΠK → ΘkdI → p6Σa → ΜEΚE → xuTS
81,830×(max) 28 nodesB8ΠΟ → ΘΓLI → pgha → F0ΩΛ → ΩuT2 → ΧQx4 → ΣWr8 → ΚKΔG → tifW → N2ΧΓ → Υej6 → Ξ4ΥC → ΠΑNA → ΖclK → l8Πe → Θ6ΣI → ΜoZE → xEΚS → vUtU → ROzy → bWro → LCΜΕ → zifQ → Z2Χq → ΥGΘ6 → ΞqXC → ΒIΖO → nclc
81,698×(max) 28 nodesD8ΠΝ → ΘyPI → pYpa → HEΚΙ → vqXU → RIΖy → nWrc → LAΞΕ → ΔifM → h2Χi → Υ0Ω6 → ΩΝB2 → ΧΑN4 → Σcl8 → Κ8ΠG → ΘsVI → pMΒa → fEΚk → v4ΥU → ΠQxA → ΖWrK → lKΔe → j6Σg → Μ2ΧE → ΥwR6 → ΞUtC → ΒOzO → danm
81,666×(max) 28 nodes52ΧΦ → ΥΟ96 → ΞΕJC → ΒkdO → d6Σm → Μ8ΠE → ΘwRI → pUta → PEΚΑ → vanU → RCΜy → zWrQ → ZKΔq → jGΘg → r2ΧY → ΥIΖ6 → ΞmbC → ΒAΞO → ΔclM → h8Πi → Θ0ΩI → ΩoZ2 → ΧEΚ4 → ΣuT8 → ΚQxG → tWrW → NKΔΓ → jejg
81,106×(max) 28 nodes30ΩΨ → ΩΤ52 → ΧΝB4 → ΣΑN8 → ΚclG → t8ΠW → ΘMΒI → peja → F4ΥΛ → ΠuTA → ΖQxK → lWre → L6ΣΕ → ΜifE → x2ΧS → ΥUt6 → ΞOzC → ΒanO → dCΜm → z8ΠQ → ΘYpI → pGΘa → rEΚY → vIΖU → nQxc → XAΞs → ΔKΔM → jghg
80,882×(max) 28 nodes94ΥΡ → ΠΗHA → ΖoZK → lEΚe → v6ΣU → ΜQxE → xWrS → VKΔu → jOzg → b2Χo → ΥCΜ6 → ΞyPC → ΒYpO → dGΘm → r8ΠY → ΘIΖI → pmba → FAΞΛ → ΔuTM → hQxi → X0Ωs → ΩKΔ2 → Χif4 → Σ2Χ8 → ΥΙF6 → ΞsVC → ΒMΒO → fclk
80,770×(max) 28 nodesFCΜΛ → zuTQ → ZQxq → XGΘs → rKΔY → jIΖg → n2Χc → ΥAΞ6 → ΞΓLC → ΒghO → d0Ωm → Ω8Π2 → ΧΗH4 → ΣoZ8 → ΚEΚG → vsVU → RMΒy → fWrk → L4ΥΕ → ΠifA → Ζ2ΧK → Υkd6 → Ξ6ΣC → ΜΑNE → xclS → V8Πu → ΘOzI → pana
80,082×(max) 28 nodes90ΩΡ → ΩΗH2 → ΧoZ4 → ΣEΚ8 → ΚuTG → tQxW → XMΒs → fKΔk → j4Υg → Π2ΧA → ΥΕJ6 → ΞkdC → Β6ΣO → ΜclE → x8ΠS → ΘUtI → pOza → bEΚo → vCΜU → zQxQ → ZWrq → LGΘΕ → rifY → J2ΧΗ → Υmb6 → ΞAΞC → ΔΑNM → hcli
79,774×(max) 28 nodesD2ΧΝ → ΥyP6 → ΞYpC → ΒGΘO → rclY → J8ΠΗ → ΘmbI → pAΞa → ΔEΚM → vghU → R0Ωy → ΩWr2 → ΧKΔ4 → Σif8 → Κ2ΧG → ΥsV6 → ΞMΒC → ΒejO → d4Υm → Π8ΠA → ΘΕJI → pkda → F6ΣΛ → ΜuTE → xQxS → XUts → PKΔΑ → jang
79,333×(max) 28 nodesT0Ωw → ΩSv2 → ΧSv4 → ΣSv8 → ΚSvG → tSvW → TMΒw → fSvk → T4Υw → ΠSvA → ΖSvK → lSve → T6Σw → ΜSvE → xSvS → VSvu → TOzw → bSvo → TCΜw → zSvQ → ZSvq → TGΘw → rSvY → TIΖw → nSvc → TAΞw → ΔSvM → hSvi
79,282×(max) 28 nodesB2ΧΟ → ΥΓL6 → ΞghC → Β0ΩO → Ωcl2 → Χ8Π4 → ΣΗH8 → ΚoZG → tEΚW → vMΒU → fQxk → X4Υs → ΠKΔA → ΖifK → l2Χe → Υ6Σ6 → ΞΛDC → ΒwRO → dUtm → P8ΠΑ → ΘanI → pCΜa → zEΚQ → vYpU → RGΘy → rWrY → LIΖΕ → nifc
79,113×(max) 28 nodesD0ΩΝ → ΩyP2 → ΧYp4 → ΣGΘ8 → ΚqXG → tIΖW → nMΒc → fAΞk → Δ4ΥM → ΠghA → Ζ0ΩK → Ωkd2 → Χ6Σ4 → ΣΛD8 → ΚwRG → tUtW → PMΒΑ → fank → D4ΥΝ → ΠyPA → ΖYpK → lGΘe → r6ΣY → ΜIΖE → xmbS → VAΞu → ΔOzM → hani
79,110×(max) 28 nodes72ΧΤ → ΥΛD6 → ΞwRC → ΒUtO → dOzm → b8Πo → ΘCΜI → zoZQ → ZEΚq → vGΘU → rQxY → XIΖs → nKΔc → jAΞg → Δ2ΧM → Υgh6 → Ξ0ΩC → ΩΑN2 → Χcl4 → Σ8Π8 → ΚΗHG → toZW → NEΚΓ → vejU → R4Υy → ΠWrA → ΖKΔK → life
79,101×(max) 28 nodesJAΞΗ → ΔmbM → hAΞi → Δ0ΩM → Ωgh2 → Χ0Ω4 → ΩΡ72 → ΧΙF4 → ΣsV8 → ΚMΒG → tejW → N4ΥΓ → ΠejA → Ζ4ΥK → ΠkdA → Ζ6ΣK → ΜkdE → x6ΣS → ΜUtE → xOzS → bUto → PCΜΑ → zanQ → ZCΜq → zGΘQ → rYpY → JGΘΗ → rmbY
79,017×(max) 28 nodesDAΞΝ → ΔyPM → hYpi → H0ΩΙ → ΩqX2 → ΧIΖ4 → Σmb8 → ΚAΞG → ΔsVM → hMΒi → f0Ωk → Ω4Υ2 → ΧΟ94 → ΣΕJ8 → ΚkdG → t6ΣW → ΜMΒE → xejS → V4Υu → ΠOzA → ΖanK → lCΜe → z6ΣQ → ΜYpE → xGΘS → rUtY → PIΖΑ → nanc
78,921×(max) 28 nodesB0ΩΟ → ΩΓL2 → Χgh4 → Σ0Ω8 → ΩΙF2 → ΧsV4 → ΣMΒ8 → ΚejG → t4ΥW → ΠMΒA → ΖejK → l4Υe → Π6ΣA → ΜΕJE → xkdS → V6Σu → ΜOzE → xanS → VCΜu → zOzQ → bYpo → HCΜΙ → zqXQ → ZIΖq → nGΘc → rAΞY → ΔIΖM → nghc
78,878×(max) 28 nodes96ΣΡ → ΜΗHE → xoZS → VEΚu → vOzU → bQxo → XCΜs → zKΔQ → jYpg → H2ΧΙ → ΥqX6 → ΞIΖC → ΒmbO → dAΞm → Δ8ΠM → ΘghI → p0Ωa → ΩEΚ2 → ΧuT4 → ΣQx8 → ΚWrG → tKΔW → jMΒg → f2Χk → Υ4Υ6 → ΠΝBA → ΖΑNK → lcle
78,861×(max) 28 nodes74ΥΤ → ΠΛDA → ΖwRK → lUte → P6ΣΑ → ΜanE → xCΜS → zUtQ → ZOzq → bGΘo → rCΜY → zIΖQ → nYpc → HAΞΙ → ΔqXM → hIΖi → n0Ωc → ΩAΞ2 → ΧΓL4 → Σgh8 → Κ0ΩG → ΩsV2 → ΧMΒ4 → Σej8 → Κ4ΥG → ΠsVA → ΖMΒK → leje
78,717×(max) 28 nodes50ΩΦ → ΩΟ92 → ΧΕJ4 → Σkd8 → Κ6ΣG → ΜsVE → xMΒS → fUtk → P4ΥΑ → ΠanA → ΖCΜK → zkdQ → Z6Σq → ΜGΘE → xqXS → VIΖu → nOzc → bAΞo → ΔCΜM → zghQ → Z0Ωq → ΩGΘ2 → ΧqX4 → ΣIΖ8 → ΚmbG → tAΞW → ΔMΒM → heji
78,441×(max) 28 nodesB6ΣΟ → ΜΓLE → xghS → V0Ωu → ΩOz2 → Χan4 → ΣCΜ8 → ΚyPG → tYpW → NGΘΓ → rejY → J4ΥΗ → ΠmbA → ΖAΞK → ΔkdM → h6Σi → Μ0ΩE → ΩwR2 → ΧUt4 → ΣOz8 → ΚanG → tCΜW → zMΒQ → fYpk → H4ΥΙ → ΠqXA → ΖIΖK → nkdc
78,093×(max) 28 nodesB4ΥΟ → ΠΓLA → ΖghK → l0Ωe → Ω6Σ2 → ΧΛD4 → ΣwR8 → ΚUtG → tOzW → bMΒo → fCΜk → z4ΥQ → ΠYpA → ΖGΘK → rkdY → J6ΣΗ → ΜmbE → xAΞS → ΔUtM → hOzi → b0Ωo → ΩCΜ2 → ΧyP4 → ΣYp8 → ΚGΘG → tqXW → NIΖΓ → nejc
77,673×(max) 28 nodesJ0ΩΗ → Ωmb2 → ΧAΞ4 → ΣΓL8 → ΚghG → t0ΩW → ΩMΒ2 → Χej4 → Σ4Υ8 → ΠΙFA → ΖsVK → lMΒe → f6Σk → Μ4ΥE → ΠwRA → ΖUtK → lOze → b6Σo → ΜCΜE → zwRQ → ZUtq → PGΘΑ → ranY → JCΜΗ → zmbQ → ZAΞq → ΔGΘM → rghY
77,553×(max) 28 nodesVOzu → bOzo → bCΜo → zCΜQ → zYpQ → ZGΘq → rGΘY → rIΖY → nIΖc → nAΞc → ΔAΞM → ΔghM → h0Ωi → Ω0Ω2 → ΩΦ32 → ΧΡ74 → ΣΙF8 → ΚsVG → tMΒW → fMΒk → f4Υk → Π4ΥA → ΠΕJA → ΖkdK → l6Σe → Μ6ΣE → ΜwRE → xUtS
77,490×(max) 28 nodesJEΚΗ → vmbU → RAΞy → ΔWrM → hKΔi → j0Ωg → Ω2Χ2 → ΧΤ54 → ΣΝB8 → ΚΑNG → tclW → N8ΠΓ → ΘejI → p4Υa → ΠEΚA → ΖuTK → lQxe → X6Σs → ΜKΔE → xifS → V2Χu → ΥOz6 → ΞanC → ΒCΜO → zclQ → Z8Πq → ΘGΘI → roZY
77,181×(max) 28 nodes70ΩΤ → ΩΛD2 → ΧwR4 → ΣUt8 → ΚOzG → tanW → NCΜΓ → zejQ → Z4Υq → ΠGΘA → ΖqXK → lIΖe → n6Σc → ΜAΞE → ΔwRM → hUti → P0ΩΑ → Ωan2 → ΧCΜ4 → ΣyP8 → ΚYpG → tGΘW → rMΒY → fIΖk → n4Υc → ΠAΞA → ΖΓLK → lghe
77,026×(max) 28 nodesH8ΠΙ → ΘqXI → pIΖa → nEΚc → vAΞU → ΔQxM → hWri → L0ΩΕ → Ωif2 → Χ2Χ4 → ΥΡ76 → ΞΙFC → ΒsVO → dMΒm → f8Πk → Θ4ΥI → ΠoZA → ΖEΚK → vkdU → R6Σy → ΜWrE → xKΔS → jUtg → P2ΧΑ → Υan6 → ΞCΜC → ΒyPO → dYpm
76,617×(max) 28 nodesH6ΣΙ → ΜqXE → xIΖS → nUtc → PAΞΑ → ΔanM → hCΜi → z0ΩQ → ΩYp2 → ΧGΘ4 → ΣqX8 → ΚIΖG → tmbW → NAΞΓ → ΔejM → h4Υi → Π0ΩA → ΩΕJ2 → Χkd4 → Σ6Σ8 → ΜΙFE → xsVS → VMΒu → fOzk → b4Υo → ΠCΜA → ΖyPK → lYpe
75,981×(max) 28 nodesD6ΣΝ → ΜyPE → xYpS → VGΘu → rOzY → bIΖo → nCΜc → zAΞQ → ΔYpM → hGΘi → r0ΩY → ΩIΖ2 → Χmb4 → ΣAΞ8 → ΚΓLG → tghW → N0ΩΓ → Ωej2 → Χ4Υ4 → ΣΟ98 → ΚΕJG → tkdW → N6ΣΓ → ΜejE → x4ΥS → ΠUtA → ΖOzK → lane
43,358×14 nodesZMΒq → fGΘk → r4ΥY → ΠIΖA → ΖmbK → lAΞe → Δ6ΣM → ΜghE → x0ΩS → ΩUt2 → ΧOz4 → Σan8 → ΚCΜG → zsVQ
41,099×14 nodesT2Χw → ΥSv6 → ΞSvC → ΒSvO → dSvm → T8Πw → ΘSvI → pSva → TEΚw → vSvU → TQxw → XSvs → TKΔw → jSvg
38,178×14 nodesXKΔs → jKΔg → j2Χg → Υ2Χ6 → ΥΝB6 → ΞΑNC → ΒclO → d8Πm → Θ8ΠI → ΘoZI → pEΚa → vEΚU → vQxU → XQxs
38,178×14 nodes92ΧΡ → ΥΗH6 → ΞoZC → ΒEΚO → vclU → R8Πy → ΘWrI → pKΔa → jEΚg → v2ΧU → ΥQx6 → ΞWrC → ΒKΔO → jclg
38,178×14 nodesL2ΧΕ → Υif6 → Ξ2ΧC → ΥΑN6 → ΞclC → Β8ΠO → ΘclI → p8Πa → ΘEΚI → voZU → REΚy → vWrU → RKΔy → jWrg
38,178×14 nodesF2ΧΛ → ΥuT6 → ΞQxC → ΒWrO → dKΔm → j8Πg → Θ2ΧI → ΥoZ6 → ΞEΚC → ΒuTO → dQxm → X8Πs → ΘKΔI → pifa
38,178×14 nodesF8ΠΛ → ΘuTI → pQxa → XEΚs → vKΔU → jQxg → X2Χs → ΥKΔ6 → ΞifC → Β2ΧO → Υcl6 → Ξ8ΠC → ΘΑNI → pcla
38,178×14 nodesLEΚΕ → vifU → R2Χy → ΥWr6 → ΞKΔC → ΒifO → d2Χm → Υ8Π6 → ΞΗHC → ΒoZO → dEΚm → v8ΠU → ΘQxI → pWra
19,089×7 nodesL8ΠΕ → ΘifI → p2Χa → ΥEΚ6 → ΞuTC → ΒQxO → dWrm
51 cycle 46,504,371×(fixed) (max) 1 node wSαvT
65 cycles654,330,252×17 nodesdN7ΡΒm → Κe8ΠkG → Θt5ΤVI → ΞpNΑZC → ΒdFΙlO → td7ΡlW → ΚN7ΡΒG → ΚtdkVG → tO6ΣΑW → ΜcMΒmE → xf9ΟjS → ΖV3ΦtK → ΣlNΑd8 → Κd7ΡlG → Κt7ΡVG → ΚtNΑVG → tdNΑlW
26,299,948×(max) 19 nodesJF3ΦΚΗ → ΣumbU8 → ΚQAΞyG → ΔtXqVM → hOIΖΑi → nc0Ωmc → ΩB9ΟΞ2 → ΧΖΒMJ4 → Σmejc8 → ΚA4ΥΟG → ΠΕsVKA → ΖkMΒeK → lf5Τje → Ξ73ΦΣC → ΣΛΑNE8 → ΚwclSG → tU8ΠuW → ΘQMΒyI → pfXqja
24,091,803×15 nodesVNFΙΒu → teOzkW → bN5ΤΒo → ΞeCΜkC → Βz5ΤPO → ΞdZolC → ΒF7ΡΚO → ΚuclUG → tQ8ΠyW → ΘYMΒqI → pfHΗja → pF3ΦΚa → ΣuEΚU8 → ΚvPyTG → tZRwpW
7,575,957×12 nodesJB7ΡΞΗ → ΚΓmbMG → tgAΞiW → ΔN1ΨΒM → Χhdkh4 → Σ6ααΣ8 → ΤΠαα87 → ΣΡ2Χ88 → ΥΚΘGF6 → ΞuqXUC → ΒQIΖyO → ndXqlc
770,309×4 nodesdHDΛΘm → xq8ΠYS → ΘVHΗtI → qoNΑaZ
71 cycle 9,473,622,357×(max) 8 nodesΔhIαΖhM → ΗjLαΓfJ → ΖlMαΒdK → ΕjNαΑfL → ΔhKαΔhM → ΕhLαΓhL → ΔjKαΔfM → ΕhNαΑhL
8+---Not showing digit sets 8+ due to verbosity.