Base 70: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
21 cycle 35 nodes0Θ → Η1 → Ε3 → Α7 → sF → cV → 6Β → uD → gR → Et → eT → Ax → mL → Qh → Gr → aX → 2Ζ → Γ5 → wB → kN → Ml → Oj → Kn → Sf → Cv → iP → Ip → Wb → 4Δ → y9 → oJ → Ud → 8z → qH → YZ
31 cycle (fixed) 1 node YΘZ
414 cycles12 nodesE5Βu → wfRC → kDtO → gLlS → QDti → gHpS → YDta → g1ΖS → ΕDt4 → ΑfR8 → sDtG → gbVS
53 cycles4 nodeskMΘkO → lLΘlN → mNΘjM → lOΘiN
66 cycles114 nodesA40ΗΔy → ΗznJ82 → ΕrTdG4 → Αb9xW8 → so4ΓJG → ycUcVA → o86ΑzK → urTdGE → gb9xWS → oE4ΓtK → yfTdSA → oD9xuK → ohTdQK → UH9xqe → oZ9xYK → oU0ΗdK → ΗU8yd2 → Εq8yH4 → ΑqYYH8 → sYΘΘYG → rZJnYH → aU0ΗdY → Η91Ζy2 → ΖΔoI43 → ΓzVb86 → wr5ΒGC → wkaWNC → kN3ΔkO → ΑNLlk8 → sQMkhG → cOGqjW → aL5ΒmY → wR1ΖgC → ΕkEsN4 → ΑeMkT8 → sOAwjG → mcKmVM → SQ6Αhg → uHDtqE → hfYYSR → GCΘΘus → vr1ΖGD → ΕiaWP4 → ΑJ3Δo8 → ΑsUcF8 → sd7zUG → sc8yVG → qc6ΑVI → uY6ΑZE → ug0ΗRE → ΗgEsR2 → ΕeEsT4 → ΑeAwT8 → smAwLG → mcQgVM → QG6Αri → ubHpWE → gY4ΓZS → yE0ΗtA → ΗoeSJ2 → ΕVBvc4 → Αk6ΑN8 → usMkFE → gdNjUS → ME8ytm → qfPhSI → YICupa → iX1ΖaQ → ΕI2Εp4 → ΓΑWa76 → wt3ΔEC → ΑkeSN8 → sNBvkG → kcMkVO → OM6Αlk → uPLliE → gQIohS → WHDtqc → gZ5ΒYS → wE0ΗtC → ΗkeSN2 → ΕNBvk4 → ΑkMkN8 → sOMkjG → cOKmjW → SL5Βmg → wRDtgC → kgEsRO → eMEslU → eP9xiU → oJ9xoK → oVTdcK → UA6Αxe → un9xKE → ogSeRK → UFBvse → kd9xUO → oM8ylK → qUOidI → YK8yna → qT1ΖeI → ΕYAwZ4 → Αm0ΗL8 → ΗsQgF2 → ΕdFrU4 → Αc8yV8 → sq6ΑHG → ucYYVE → g6ΘΘΑS → ΒfJnS7 → uUCudE → ig8yRQ → qIEspI → eYWaZU
71 cycle 4 nodesqYFΘrZI → sZHΘpYG → rbGΘqWH → raJΘnXH
84 cycles540 nodesA870ΗΑzy → ΗtrnJGE2 → ΕfbTdWS4 → ΑDA4Γxu8 → ysngQKFA → odTFreUK → cUB8ywdW → ql95ΒyMI → wpYOiZIC → kXK0ΗnaO → ΗTM2Εle2 → ΕΓPAwi54 → ΑxmIoLA8 → snWQgbKG → cTG4ΓreW → ybB5ΒwWA → wol4ΓMJC → ykVOicNA → oNK6ΑnkK → uUTMkedE → gOB8ywjS → qlLDtmMI → gYROigZS → KFE0Ηtso → ΗfdTdUS2 → ΕDA8yxu4 → ΑqngQKH8 → sZTFreYG → dbB0ΗwWV → Ηl84ΓzM2 → ΕyrOiG94 → ΑpbJnWI8 → sXU4ΓdaG → yc92ΕyVA → Γpo6ΑJI6 → wuXUcaDC → kh82ΕzQO → ΓrMGqlG6 → wbaOiXWC → kK52ΕΓnO → ΓxTLleA6 → wnQAwhKC → mkTGqeNM → aQNAwkhY → mNH1ΖqkM → ΕZQMkhY4 → ΑOH0Ηqj8 → ΗsZKmYF2 → ΕdS0ΗfU4 → ΗΑD8yu72 → ΕtqgQHE4 → ΑfZFrYS8 → scD0ΗuVG → Ηhc6ΑVQ2 → ΕuH6ΑqD4 → ΑuhYYQD8 → shGΘΘqQG → rrS8yfGH → qbaCuXWI → iY52ΕΓZQ → ΓxI0ΗpA6 → ΗwnWaKB2 → ΕlT3ΔeM4 → ΒzPAwi87 → urmIoLGE → gbWQgbWS → GE54ΓΓts → yxfbVSAA → onD5ΒuKK → whUSedQC → kHC8yvqO → qjZLlYOI → YQL0Ηmha → ΗRH1Ζqg2 → ΖΔZEsY43 → Γze0ΗT86 → ΗwrAwGB2 → ΕmlaWML4 → ΑRP3Δig8 → ΑsJEsoF8 → sedUcUTG → cB97zywW → spl5ΒMIG → wcXOiaVC → kK72ΕΑnO → ΓtTLleE6 → wfQAwhSC → mkHCuqNM → iZQMkhYQ → OIH0Ηqpk → ΗZXLlaY2 → ΕQ30ΗΕh4 → ΗΒΑGq762 → ΕvtZXEC4 → Αjf1ΖSO8 → ΕsLCumF4 → ΑidQgUP8 → sJG8yroG → qcbUcWVI → Y874ΓΑza → ytr1ΖGEA → ΕofaWSJ4 → ΑVD3Δuc8 → Αsh6ΑQF8 → usdGqUFE → gda8yXUS → qE92ΕytI → ΓpfXZSI6 → wXD1ΖuaC → Εkh2ΕQN4 → ΓΑNGqk76 → wtaMkXEC → kfO2ΕjSO → ΓMLCuml6 → wiROigPC → kKJEsonO → eVTLlecU → QBA6Αxwi → unlHpMKE → gYTOieZS → KEB0Ηwto → ΗlfTdSM2 → ΕPD9xui4 → ΑohIoQJ8 → sWVGqcbG → ca74ΓΑXW → yt62ΕΒEA → ΓvoeSJC6 → wjVBvcOC → ljL6ΑmON → uROKmjgE → gSLEsmfS → eRECutgU → ifF9xsSQ → odICupUK → iXU8ydaQ → qI92ΕypI → ΓpYWaZI6 → wX40ΗΔaC → Ηzk2ΕN82 → ΕΓrMkG54 → ΑxbNjWA8 → snM4ΓlKG → ycTOieVA → oKB6ΑwnK → ulUSedME → gPC8yviS → qjJDtoOI → gYVKmcZS → SE70ΗΑtg → ΗtfDtSE2 → ΕgfCuSR4 → ΑiFCusP8 → sidIoUPG → cWJ8yobW → qV64ΓΒcI → yvY6ΑZCA → uoj0ΗOJE → ΗgVKmcR2 → ΕSF6Αsf4 → ΑudCuUD8 → sih8yQPG → qcJGqoVI → aYV6ΑcZY → u720ΗΖΑE → ΗΔtfRE42 → ΕzfDtS84 → ΑrgCuRG8 → sibEsWPG → ecJ4ΓoVU → yVA6ΑxcA → uon6ΑKJE → ugVSecRE → gFC6ΑvsS → ujdDtUOE → hfL8ymSR → qRGCurgI → ibYEsZWQ → eI50ΗΓpU → ΗxX9xaA2 → Εon2ΕKJ4 → ΓΑVSec76 → wtC6ΑvEC → ukjeSONE → gNLBvmkS → kRNDtkgO → gNMEslkS → ePNDtkiU → gNJ9xokS → oVNDtkcK → gUN6ΑkdS → uNE8ytkE → qgfMkSRI → YOFCusja → idL1ΖmUQ → ΕRI8ypg4 → ΑqXEsaH8 → seZ2ΕYTG → ΓcB0ΗwV6 → Ηwl6ΑMB2 → ΕulOiMD4 → ΑhPJniQ8 → sUJGqodG → caV8ycXW → q762ΕΒΑI → ΓvtXZEC6 → wjf1ΖSOC → ΕkLCumN4 → ΑiRMkgP8 → sOJEsojG → ecVKmcVU → SA76ΑΑxg → utnDtKEE → hffSeSSR → GDDBvuus → khhbVQQO → MHH5Βqqm → wZZPhYYC → kI10ΗΗpO → ΗΖXLla22 → ΕΔQ2Εh44 → ΓΑzGq876 → wtrZXGEC → kfb1ΖWSO → ΕMD4Γul4 → ΑyhOiQ98 → spKGqnIG → caXSeaXW → C632ΕΕΒw → ΓΒvjNC66 → wvjLlOCC → kjQKmhOO → SMLGqmlg → aRPDtigY → gJF1ΖsoS → ΕdVDtcU4 → Αg96ΑyR8 → uspEsIFE → gedWaUTS → EB93Δywu → ΑplfRMI8 → sXPDtiaG → gcJ2ΕoVS → ΓVE6Αtc6 → wuf6ΑSDC → ukhCuQNE → igNGqkRQ → aNIEspkY → eXN1ΖkaU → ΕNA2Εxk4 → ΓΑnMkK76 → wtTNjeEC → kfMAwlSO → mPMCuliM → iQPIoihQ → WJIGqpoc → aXV5ΒcaY → w731ΖΕΑC → ΕΒtjNE64 → ΑvfLlSC8 → sjQCuhOG → icLGqmVQ → aRI6ΑpgY → uXF1ΖsaE → Εgd2ΕUR4 → ΓΑF8ys76 → wtqcUHEC → kfZ7zYSO → sMD0ΗulG → ΗhcOiVQ2 → ΕKH6Αqn4 → ΑuZSeYD8 → shC0ΗvQG → ΗjcGqVO2 → ΕaL6ΑmX4 → ΑuR2ΕgD8 → ΓshEsQF6 → wedGqUTC → kaB8ywXO → qlM2ΕlMI → ΓYPOiiZ6 → wKJ0ΗonC → ΗkVSecN2 → ΕNC6Αvk4 → ΑujMkOD8 → shOKmjQG → cSLGqmfW → aRD5ΒugY → whF1ΖsQC → ΕkdGqUN4 → ΑaN8ykX8 → sqN2ΕkHG → ΓcZMkYV6 → wO70ΗΑjC → ΗtkKmNE2 → ΕfSMkfS4 → ΑODCuuj8 → sihKmQPG → cSJGqofW → aVD5ΒucY → wh71ΖΑQC → ΕtkGqNE4 → ΑfaMkXS8 → sOD2ΕujG → ΓhcKmVQ6 → wSH6ΑqfC → ukZCuYNE → igN0ΗkRQ → ΗNIEspk2 → ΕeXMkaT4 → ΑOB2Εwj8 → ΓslKmMF6 → wdSOifUC → kKD8yunO → qhTLleQI → YQHAwqha → mZH1ΖqYM → ΕZQ0ΗhY4 → ΗΑH0Ηq72 → ΗΕtYYE32 → ΕΒeΘΘS64 → ΔΒcMkV65 → yvO6ΑjCA → uojKmOJE → gVSKmfcS → SED6Αutg → uhfDtSQE → hfHCuqSR → iZGCurYQ → ibI0ΗpWQ → ΗXI4Γpa2 → ΕyX2Εa94 → ΓΑp2ΕI76 → ΓwtWaEB6 → wlf3ΔSMC → ΑkPCuiN8 → siNIokPG → cWNIokbW → WN64ΓΒkc → yvN5ΒkCA → wojMkOJC → kVOKmjcO → SML6Αmlg → uRPDtigE → hfJEsoSR → eVGCurcU → ibA6ΑxWQ → unI4ΓpKE → ygXSeaRA → oFC2ΕvsK → ΓjdTdUO6 → wLA8yxmC → qnkQgNKI → YTNFrkea → cNB1ΖwkW → ΕlN5ΒkM4 → ΑwPMkiB8 → slOIojMG → cWPKmibW → SJ64ΓΒog → yvVDtcCA → ojg6ΑROK → uULEsmdE → geR8ygTS → qFEAwtsI → mfdXZUSM → QD91Ζyui → ΕphHpQI4 → ΑYXGqaZ8 → sa30ΗΕXG → ΗΒc2ΕV62 → ΕΓv6ΑC54 → ΑxuiODA8 → snhJnQKG → cUTGqedW → aB95ΒywY → wpl1ΖMIC → ΕkXOiaN4 → ΑNK2Εnk8 → ΓsTMkeF6 → wdOAwjUC → mkL8ymNM → qRQMkhgI → YOHEsqja → eZL1ΖmYU → ΕRA0Ηxg4 → ΗΑnEsK72 → ΕteSeTE4 → ΑfCAwvS8 → smjCuOLG → icRKmgVQ → SIF6Αspg → udXDtaUE → hf92ΕySR → ΓpGCurI6 → wibWaWPC → kJ53ΔΓoO → ΑxVLlcA8 → snQ6ΑhKG → ucTGqeVE → gaB6ΑwXS → ulE2ΕtME → ΓgfOiSR6 → wKFCusnC → kidSeUPO → MJC8yvom → qjVPhcOI → YLI6Αpma → uXR1ΖgaE → ΕgF2ΕsR4 → ΓΑdEsU76 → wte8yTEC → qkfAwSNI → mYNCukZM → iQN0ΗkhQ → ΗNIGqpk2 → ΕaXMkaX4 → ΑO32ΕΕj8 → ΓΒsKmF66 → wvdRfUCC → kjE8ytOO → qfMKmlSI → YSPCuifa → iJD1ΖuoQ → ΕhVHpcQ4 → ΑYH6ΑqZ8 → usZ0ΗYFE → Ηgd0ΗUR2 → ΗΕF8ys32 → ΕΒqcUH64 → ΑvZ7zYC8 → trj0ΗOGF → ΗebKmWT2 → ΕSB4Γwf4 → ΑylCuM98 → spiOiPIG → cXKIonaW → WT62ΕΒec → ΓvB5ΒwC6 → xvliOMCB → mjPJniOM → UQLIomhe → WRH9xqgc → oZF5ΒsYK → wdU0ΗdUC → Ηk98yyN2 → ΕqpMkIH4 → ΑZXNjaY8 → sM30ΗΕlG → ΗΒcOiV62 → ΕvK6ΑnC4 → ΑujSeOD8 → shLBvmQG → kcRGqgVO → aMF6ΑslY → udP1ΖiUE → ΕgJ8yoR4 → ΑqVEscH8 → seZ6ΑYTG → ucB0ΗwVE → Ηlg6ΑRM2 → ΕuPEsiD4 → ΑheIoTQ8 → sWHAwqbG → mcZ4ΓYVM → yQ70ΗΑhA → ΗtoGqJE2 → ΕfaUcXS4 → ΑD82Εzu8 → ΓsrgQGF6 → wdbFrWUC → kc94ΓyVO → ypM6ΑlIA → uoXOiaJE → gVK2ΕncS → ΓTE6Αte6 → wufAwSDC → mkhCuQNM → iQNGqkhQ → aNIGqpkY → aXN1ΖkaY → ΕN31ΖΕk4 → ΕΒΑMk764 → ΑvtNjEC8 → sjfLlSOG → cQLCumhW → iRH5ΒqgQ → wZIEspYC → keX0ΗaTO → ΗMB2Εwl2 → ΕΓlOiM54 → ΑxPJniA8 → snUIodKG → cWT8yebW → qB64ΓΒwI → yvlXZMCA → ojP1ΖiOK → ΕULIomd4 → ΑWR8ygb8 → sqF4ΓsHG → ydcYYVUA → o96ΘΘΑyK → Βyg9xR97 → upoEsJIE → geXUcaTS → EB82Εzwu → ΓrlfRMG6 → wbPDtiWC → kgJ4ΓoRO → yVMEslcA → oeP6ΑiTK → uUJAwodE → mgV8ycRM → qQF6ΑshI → udYGqZUE → ga90ΗyXS → ΗpE2ΕtI2 → ΕΓfWaS54 → ΑxD3ΔuA8 → ΑsngQKF8 → sdTFreUG → dbB8ywWV → ql84ΓzMI → yrYOiZGA → obK0ΗnWK → ΗUT4Γed2 → ΕyB8yw94 → ΑqpkMIH8 → sZXNjaYG → cM30ΗΕlW → ΗΒP5Βi62 → ΕwvIoCB4 → ΑljVbOM8 → sPL5ΒmiG → wcRIogVC → kWF6ΑsbO → udM4ΓlUE → ygP8yiRA → qoJEsoJI → eYVUccZU