Base 101: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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 Max Steps Max Step Example
Cycle Start
11 max steps10
23 max steps10 → 0ο → ξ1 → μ3
351 max steps100 → 0οο → ξο1 → νο2 → μο3 → λο4 → κο5 → ιο6 → θο7 → ηο8 → ζο9 → εοA → δοB → γοC → βοD → αοE → ΩοF → ΨοG → ΧοH → ΦοI → ΥοJ → ΤοK → ΣοL → ΡοM → ΠοN → ΟοO → ΞοP → ΝοQ → ΜοR → ΛοS → ΚοT → ΙοU → ΘοV → ΗοW → ΖοX → ΕοY → ΔοZ → Γοa → Βοb → Αοc → zοd → yοe → xοf → wοg → vοh → uοi → tοj → sοk → rοl → qοm → pοn → oοo
44 max stepsp000 → oοοo → onop → 1οοξ → ξ0ξ2
539 max stepsn0000 → mοοοq → qlοqn → r2ομm → νmοp3 → μnοo4 → λlοq5 → κmοp6 → ιkοr7 → θlοq8 → ηjοs9 → ζkοrA → εiοtB → δjοsC → γhοuD → βiοtE → αgοvF → ΩhοuG → ΨfοwH → ΧgοvI → ΦeοxJ → ΥfοwK → ΤdοyL → ΣeοxM → ΡcοzN → ΠdοyO → ΟbοΑP → ΞcοzQ → ΝaοΒR → ΜbοΑS → ΛZοΓT → ΚaοΒU → ΙYοΔV → ΘZοΓW → ΗXοΕX → ΖYοΔY → ΕWοΖZ → ΗVοΗX → ΘYοΔW → ΗYοΔX
6454 max steps9000BE → EB8ζδβ → ΧΡΛRMI → Δuitia → TCAδγΛ → ΣΟgvOM → vqEΩmi → ΚD3λβU → θΝexQ8 → ΩmIΥqG → ΘΒ3λbW → θbPΝΒ8 → ΩnPΝpG → Θn1νpW → μb1νΒ4 → μθPΝ74 → θαmpE8 → ΩΛ2μSG → κΘhuV6 → δcCβΑC → ΠΞNΟPO → sqnoml → 740ξλι → ξηαD82 → μΨΛRG4 → θΗitW8 → ΩaAδΓG → ΣΘRΛVM → vjbΑti → PD9εβΟ → ΥΝonQK → zm0ξqe → ξL3λΣ2 → μθvg74 → θαEΩE8 → ΩΛΙTSG → ΘiexuW → bJBγΥΓ → ΠΑQΜcO → rlNΟrm → r64κιm → ζγ4κCA → ζΥΞOJA → ΥΑoncK → zO0ξΟe → ξqKΣm2 → μx3λf4 → ιηHΦ87 → βΨΓZGE → ΜΗSΚWS → jhZΓvu → TEAδαΛ → ΣΛgvSM → viEΩui → ΚDBγβU → ΠΝexQO → rmIΥqm → Β53λκc → θεOΞA8 → ΩΤonKG → Θy0ξeW → ξbJΤΒ2 → μzPΝd4 → θnLΡp8 → Ωv1νhG → μΘDαV4 → θΜbΑR8 → ΩkOΞsG → Θp7ηnW → Ωb1νΒG → μΘPΝV4 → θnbΑp8 → ΩP1νΞG → μΘnoV4 → θc0ξΑ8 → ξΩNΟF2 → μΙqlU4 → θe4κy8 → ζΩJΤFA → ΥΙydUK → zeKΣye → xLJΤΣg → zwGΧge → ΖLFΨΣY → ΘwWΖgW → bZFΨΔΓ → ΘUQΜΙW → leaΒys → RK6θΤΝ → βykreE → ΜK6θΤS → βyiteE → ΜKAδΤS → ΣyiteM → vKAδΤi → ΣyCβeM → ΞvJΤhQ → znDαpe → ΜL1νΣS → μwitg4 → θGAδΨ8 → ΩΣΖWLG → ΘwYΔgW → bVFΨΘΓ → ΘcQΜΑW → lbNΟΒs → rQ6θΝm → βm4κqE → ζΜ3λRA → θΥjsJ8 → ΩΑ8ζcG → ΧΘNΟVI → ΔrbΑla → TP5ιΞΛ → δogvoC → ΠEοοΩO → αΟ7ηOF → ΩΚpmTG → Θg2μwW → κbFΨΒ6 → δΘPΝVC → ΠnbΑpO → rP1νΞm → μo4κo4 → θεοο98 → ηζ2μ99 → κΧΥIH6 → δΕΑbYC → ΠWOΞΗO → rpZΓnm → T51νκΛ → μεgvA4 → θΤEΩK8 → ΩΚxeTG → ΘgIΥwW → ΒbFΨΒc → ΘQOΞΝW → pmaΒqo → R40ξλΝ → ξηkr82 → μΨ6θG4 → θβΖWD8 → ΩΝYΔQG → ΘmUΘqW → db3λΒΑ → θQMΠΝ8 → ΩtlqjG → ΘA4κεW → ζΤaΒKA → ΥyQΜeK → zlJΤre → zL5ιΣe → δwKΣgC → ΠxFΨfO → ΘrHΦlW → Δb5ιΒa → δTPΝΚC → ΠnfwpO → rH1νΧm → μΕ4κY4 → θζVΗ98 → ΩΦaΒIG → ΘΓQΜaW → lbRΛΒs → jQ6θΝu → βmAδqE → ΣΜ3λRM → θvjsh8 → ΩE8ζαG → ΧΛΗVSI → ΔiaΒua → TRBγΜΛ → ΠkgvsO → rF7ηΩm → ΩΙ4κUG → ζΘdyVA → ΥcKΣΑK → zxNΟfe → rLHΦΣm → Δw4κga → ζTFΨΚA → ΥΘfwVK → zcGΧΑe → ΖOKΣΟY → xqWΖmg → ZH3λΧΕ → θΕUΘY8 → ΩdVΗzG → ΘbLΡΒW → vbPΝΒi → nQCβΝq → Ξm2μqQ → κn3λp6 → θδ1νB8 → μΩΠMF4 → θΙsjU8 → Ωe8ζyG → ΧΘJΤVI → ΔzbΑda → TPLΡΞΛ → vogvoi → FCοοβα → γΩ0ξFD → ξΞΘUP2 → μoczo4 → θMοοΠ8 → ηΡFΨM9 → ΧΘtiVI → ΔcAδΑa → ΣTNΟΚM → vrfwli → HD5ιβΨ → δΝΕXQC → ΠmWΖqO → rZ3λΔm → θU4κΙ8 → ζΩdyFA → ΥΙKΣUK → zxdyfe → MKHΦΤΣ → Δyuhea → TKCβΤΛ → ΞygveQ → nKEΩΤq → Κy2μeU → κfJΤx6 → δzHΦdC → ΠΔLΡZO → vrTΙli → fD5ιβy → δΝIΥQC → ΠΒlqbO → rQ4κΝm → ζm4κqA → ζΥ3λJA → θΥzcJ8 → ΩΑMΠcG → ΘtNΟjW → rb9εΒm → ΥQ4κΝK → ζzlqdA → ΥM4κΡK → ζztidA → ΥMAδΡK → ΣztidM → vMAδΡi → ΣuCβiM → ΞvBγhQ → ΠnDαpO → Μr1νlS → μj5ιt4 → θδ9εB8 → ΩΥΠMJG → ΘΑsjcW → bO8ζΟΓ → ΧqQΜmI → Δl3λra → θT5ιΚ8 → δΩfwFC → ΠΙGΧUO → ΖrdylY → XL5ιΣΗ → δwYΔgC → ΠVFΨΘO → ΘrbΑlW → bP5ιΞΓ → δoQΜoC → ΠkοοrO → ΟsNΟkP → rp7ηnm → Ω51νκG → μεΗVA4 → θΤaΒK8 → ΩyQΜeG → ΘlJΤrW → zb5ιΒe → δQKΣΝC → ΠxlqfO → rI4κΦm → ζΓ4κaA → ζΥRΛJA → ΥΑitcK → zOAδΟe → ΣqKΣmM → xv3λhg → θHDαΧ8 → ΩΜΔYRG → ΘkUΘsW → db7ηΒΑ → ΩQMΠΝG → ΘtlqjW → bA4κεΓ → ζΤQΜKA → ΥykreK → zK6θΤe → βyKΣeE → ΜxJΤfS → zjHΦte → ΔL9εΣa → ΥwSΚgK → zhFΨve → ΘLDαΣW → ΜwaΒgS → jRFΨΜu → ΘkAδsW → Σb7ηΒM → ΩvPΝhG → ΘnDαpW → Μb1νΒS → μjPΝt4 → θn9εp8 → ΩΥ1νJG → μΘzcV4 → θcMΠΑ8 → ΩtNΟjG → Θr9εlW → Υb5ιΒK → δzPΝdC → ΠnLΡpO → vr1νli → μD5ιβ4 → θδΜQB8 → ΩΡkrMG → Θu6θiW → βbBγΒE → ΠΜPΝRO → rnjspm → 951νκη → μεΦHA4 → θΤΓZK8 → ΩySΚeG → ΘhJΤvW → zbDαΒe → ΜQKΣΝS → xmitqg → HB3λδΨ → θΡΕXM8 → ΩuWΖiG → ΘZBγΔW → ΠbTΙΒO → rfPΝxm → nI4κΦq → ζΓ2μaA → κΥRΛJ6 → δΑitcC → ΠOAδΟO → ΣrpmlM → v62μιi → κγCβC6 → δΟΝPOC → ΠqmpmO → r42μλm → κη4κ86 → ζδΧGBA → ΥΡΕXMK → zuWΖie → ZLBγΣΕ → ΠwUΘgO → rdFΨzm → ΘM4κΡW → ζuaΒiA → ΥRBγΜK → ΠzjsdO → rM8ζΡm → Χu4κiI → ζΔBγZA → ΥΠTΙNK → zsexke → LJ7ηΥΤ → ΩΑwfcG → ΘOGΧΟW → ΖqaΒmY → XR3λΜΗ → θkYΔs8 → ΩV7ηΘG → ΩΘbΑVG → ΘcOΞΑW → pbNΟΒo → rQ0ξΝm → ξm4κq2 → μζ3λ94 → ιηΥI87 → βΨΑbGE → ΜΗOΞWS → pjZΓto → TA0ξεΛ → ξΤgvK2 → μyEΩe4 → θΚJΤT8 → ΩzfwdG → ΘMGΧΡW → ΖuaΒiY → XRBγΜΗ → ΠkYΔsO → rV7ηΘm → Ωc4κΑG → ζΘNΟVA → ΥrbΑlK → zP5ιΞe → δoKΣoC → ΠwοοfO → ΟxIΥfP → ΒpHΦnc → ΔP1νΞa → μoSΚo4 → θgοοv8 → ηwZΓg9 → ΧTFΨΚI → ΘΔfwZW → bUGΧΙΓ → ΖeQΜyY → lXJΤΖs → zY6θΕe → βWKΣΗE → ΜxZΓfS → jTHΦΚu → ΔgAδwa → ΣTFΨΚM → ΘvfwhW → bHDαΧΓ → ΜΕQΜYS → ljVΗts → bA6θεΓ → βΤQΜKE → ΜykreS → jK6θΤu → βyAδeE → ΣΜJΤRM → zvjshe → LE8ζαΤ → ΧΛwfSI → ΔiGΧua → ΖTBγΚY → ΠgWΖwO → rZFΨΔm → ΘU4κΙW → ζeaΒyA → ΥRJΤΜK → Αyjsed → NK8ζΤΡ → ΧysjeI → ΔK8ζΤa → ΧySΚeI → ΔhJΤva → zTDαΚe → ΜgKΣwS → xjFΨtg → ΘH9εΧW → ΥΕaΒYK → zWQΜΗe → laKΣΓs → xS6θΛg → βiGΧuE → ΜΖBγXS → ΠjXΕtO