Base 84: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps1 → 0 → 0
210 max steps20 → 1Φ → Τ3 → Ο7 → ΗF → qV → KΒ → gf → 0Χ → Φ1 → Τ3
344 max steps100 → 0ΧΧ → ΦΧ1 → ΥΧ2 → ΤΧ3 → ΣΧ4 → ΡΧ5 → ΠΧ6 → ΟΧ7 → ΞΧ8 → ΝΧ9 → ΜΧA → ΛΧB → ΚΧC → ΙΧD → ΘΧE → ΗΧF → ΖΧG → ΕΧH → ΔΧI → ΓΧJ → ΒΧK → ΑΧL → zΧM → yΧN → xΧO → wΧP → vΧQ → uΧR → tΧS → sΧT → rΧU → qΧV → pΧW → oΧX → nΧY → mΧZ → lΧa → kΧb → jΧc → iΧd → hΧe → gΧf → fΧg → fΧg
416 max steps500L → L4ΡΒ → ΝffA → ΒΧΧK → ΒJΒL → iffe → 3ΧΧΤ → Τ2Τ4 → ΡΞ76 → ΛΖFC → ypVO → aJΒm → iBΚe → y3ΣO → ΟZl8 → ΗBΚG → ypVO
537 max steps10003 → 30ΧΦΥ → ΧΡΧ41 → ΦΡΧ42 → ΥΠΧ53 → ΤΞΧ74 → ΣΛΧA5 → ΡΗΧE6 → ΠΒΧJ7 → ΟvΧP8 → ΞoΧW9 → ΝgΧeA → ΜXΧnB → ΛdΧhC → ΚWΧoD → ΙcΧiE → ΘVΧpF → ΗbΧjG → ΖUΧqH → ΕaΧkI → ΔTΧrJ → ΓZΧlK → ΒSΧsL → ΑYΧmM → zRΧtN → yXΧnO → xQΧuP → wWΧoQ → vPΧvR → wTΧrQ → vSΧsR → uSΧsS → tRΧtT → uPΧvS → wSΧsQ → vTΧrR → uRΧtS → uRΧtS
6348 max stepsH000cp → pcGΕjX → oI6ΟΔY → ΙlFΖaE → uqAΛVS → ΑSKΑtM → geQuhg → U2ΧΧΤs → ΥrPvU3 → ΡWMyp6 → ΛcIΓjC → yk6ΟbO → Ιa8ΝlE → ΕuAΛRI → ΑmSsZM → eQCΙvi → wV3ΣqQ → ΟWKΑp8 → ΗgIΓfG → qk0ΦbW → ΦK8ΝΒ2 → ΤΕgeH4 → Οn1ΥY8 → ΤΗEΗF4 → ΟsqUT8 → ΗPLzwG → qeWohW → KI2ΤΔΓ → Ρlhda6 → ΛB3ΣΛC → ΟzxNM8 → ΗdZliG → qC4ΡΚW → ΝxJΒOA → ΓiYmdK → iE4ΡΘe → Νt3ΣSA → ΟΓQuJ8 → ΗjTrcG → qO6ΟxW → ΙZJΒmE → uiCΙdS → wS4ΡtQ → ΝWQupA → ΓUIΓrK → kiMydc → c84ΡΞk → ΝΖ7ΞGA → ΗΓoWJG → qjHΔcW → mK6ΟΒa → ΙhBΚeE → yu2ΤRO → ΡaSsl6 → ΛQAΛvC → ΑyUqNM → ebLzki → e93ΣΝi → ΟΔ3ΣI8 → ΟΗkaF8 → Ηr9ΜUG → ΓqMyVK → icKΑje → g73ΣΟg → ΟΗΧΧE8 → ΞΘ7ΞE9 → ΗΕsSHG → qnPvYW → WKEΗΒq → shJΒeU → iO2Τxe → ΡZ3Σm6 → ΟΛCΙB8 → ΗzvPMG → qdVpiW → LJ4ΡΓΒ → ΝjffcA → Γ6ΧΧΟK → ΠΒBΚK7 → ΙygeNE → ub1ΥkS → ΤS8Νt4 → ΟΕQuH8 → ΗnTrYG → qOEΗxW → sZJΒmU → iOCΙxe → wZ3ΣmQ → ΟWCΙp8 → ΗwIΓPG → qkWobW → KI8ΝΔΓ → ΕlhdaI → mB3ΣΛa → ΟzBΚM8 → ΗyciNG → qb5ΠkW → ΛK8ΝΒC → ΕygeNI → mb1Υka → ΤC8ΝΚ4 → ΟΕwOH8 → ΗnXnYG → qGEΗΖW → spJΒWU → iOIΓxe → kZ3Σmc → ΟD7ΞΙ8 → ΘΖuQGF → spTrWU → PNIΓyx → kbXnkc → G97ΞΝΗ → ΗΔpVIG → qlJΒaW → iKAΛΒe → Αh3ΣeM → Οe2Τh8 → ΡΗ2ΤF6 → ΡΛqUB6 → ΛzLzMC → yecihO → a62ΤΠm → ΡΚBΚC6 → ΛywONC → ybXnkO → aG8ΝΖm → ΕpBΚWI → ymIΓZO → kaCΙlc → wB7ΞΛQ → ΗzVpMG → qdJΒiW → iK4ΡΒe → Νh3ΣeA → ΟΓ2ΤJ8 → ΡΗicF6 → Λr5ΠUC → ΛyMyNC → ycakjO → aA6ΟΜm → ΙΒBΚKE → yugeRO → aT1Υsm → ΤPBΚw4 → ΟyWoN8 → ΗbHΔkG → qm8ΝZW → ΕKCΙΒI → wmgeZQ → WD1ΥΙq → ΤvJΒQ4 → ΟiUqd8 → ΗM4ΡzG → ΝqciVA → ΓL5ΠΑK → ΛiegdC → y51ΥΡO → ΤΜZlA4 → ΟΒBΚK8 → ΗygeNG → qb1ΥkW → ΤK8ΝΒ4 → ΟΕgeH8 → Ηn1ΥYG → ΤqEΗV4 → ΟsKΑT8 → ΗgOwfG → qY0ΦnW → ΦKEΗΒ2 → ΤsgeT4 → ΟP1Υw8 → ΤΗWoF4 → ΟrHΔU8 → ΗmMyZG → qcCΙjW → wK6ΟΒQ → ΙhVpeE → uK2ΤΒS → ΡhRte6 → ΛS2ΤtC → ΡyQuN6 → ΛbTrkC → yO8ΝxO → ΕaYmlI → mEAΛΘa → ΑtBΚSM → yeQuhO → aU2Τrm → ΡNBΚy6 → ΛyakNC → yb9ΜkO → Γa8ΝlK → ΕiAΛdI → Αm4ΡZM → ΝeCΙhA → Γw2ΤPK → ΡiWod6 → ΛI4ΡΔC → ΝykaNA → Γb9ΜkK → Γi8ΝdK → Εi4ΡdI → Νm4ΡZA → ΝΓCΙJA → ΓwicPK → iX5Πoe → ΛH3ΣΕC → ΟymYN8 → ΗbDΘkG → uq8ΝVS → ΕSKΑtI → mgQufa → UC0ΦΚs → ΦxNxO2 → ΤaYml4 → ΟEAΛΘ8 → ΗΑsSLG → qfPvgW → WK0ΦΒq → ΦhJΒe2 → Τi2Τd4 → ΡΟ4Ρ76 → ΝΛΗEBA → ΓzrTMK → idNxie → a53ΣΡm → ΟΜBΚA8 → ΗΒxNKG → qhZleW → KC2ΤΚΓ → ΡxhdO6 → ΛZ3ΣmC → ΟyCΙN8 → ΗwakPG → qX9ΜoW → ΓKGΕΒK → oigedY → G51ΥΡΗ → ΤΜpVA4 → ΟΒJΒK8 → ΗigedG → q51ΥΡW → ΤΜJΒA4 → ΟΒhdK8 → Ηh3ΣeG → Οq2ΤV8 → ΡΗKΑF6 → ΛrffUC → yMΧΧyO → zwΧΧON → yx2ΤOO → ΡaYml6 → ΛEAΛΘC → ΑysSNM → ebPvki → W93ΣΝq → ΟΔJΒI8 → ΗlhdaG → qB3ΣΛW → ΟzJΒM8 → ΗicidG → q64ΡΠW → ΝΚJΒCA → ΓxhdOK → iZ3Σme → ΟD3ΣΙ8 → ΟΗuQF8 → ΗrTrUG → qOMyxW → cZJΒmk → iD7ΞΙe → Ηv3ΣQG → ΟqUqV8 → ΗMKΑzG → qgcifW → K60ΦΠΓ → ΦΚhdC2 → Τx3ΣO4 → ΠΞYm87 → ΙΖDΘGE → vtoWSR → URHΔus → mTNxsa → aPBΚwm → yXBΚoO → yaGΕlO → oaAΛlY → ΑGAΛΖM → ΑpdhWM → eJ3ΣΓi → Οj3Σc8 → ΟΗ6ΟF8 → ΙΗqUFE → urLzUS → eSMyti → cR3Σuk → ΟT7Ξs8 → ΘΖOwGF → spXnWU → OJFΖΓy → qjZlcW → KC6ΟΚΓ → ΙxhdOE → uZ3ΣmS → ΟSCΙt8 → ΗwQuPG → qXTroW → OKGΕΒy → ohZleY → GC2ΤΚΗ → ΡxpVO6 → ΛZJΒmC → yiCΙdO → wa4ΡlQ → ΝWAΛpA → ΓΑIΓLK → kiegdc → 851ΥΡΟ → ΤΜΖFA4 → ΟΒpVK8 → ΗhJΒeG → qi2ΤdW → ΡK4ΡΒ6 → ΝΛgeBA → Γz1ΥMK → Τicid4 → Ο64ΡΠ8 → ΝΚΖFCA → ΓxpVOK → iZJΒme → iD3ΣΙe → Οv3ΣQ8 → ΟΗUqF8 → ΗrLzUG → qeMyhW → cK2ΤΒk → Ρh7Ξe6 → ΛΗ2ΤFC → ΡyqUN6 → ΛbLzkC → ye8ΝhO → Εa2ΤlI → ΡmAΛZ6 → ΛΑCΙLC → ywegPO → aX1Υom → ΤHBΚΕ4 → ΟymYN8
751 max stepsM000000 → LΧΧΧΧΧΑ → ΑKΧΧΧΑM → ΒzKΧΑML → ΒgdΧhfL → ΑO1ΧΥxM → ΦxbΧjO2 → ΥwLΧzP3 → ΤyZΧlN4 → ΣvOΧwQ5 → ΡtVΧpS6 → ΠoNΧxX7 → ΟsPΧvT8 → ΞpRΧtW9 → ΝmMΧyZA → ΜqOΧwVB → ΛnQΧuYC → ΚkLΧzbD → ΙoNΧxXE → ΘlPΧvaF → ΗiKΧΑdG → ΖmMΧyZH → ΕjOΧwcI → ΔgJΧΒfJ → ΓkLΧzbK → ΒhNΧxeL → ΑeIΧΓhM → ΔgLΧzfJ → ΓiJΧΒdK → ΓiNΧxdK → ΒfJΧΒgL → ΓgLΧzfK → ΒhJΧΒeL → ΓgMΧyfK → ΒgIΧΓfL → ΔhLΧzeJ → ΓiKΧΑdK → ΒiMΧydL → ΑfKΧΑgM → ΒeKΧΑhL → ΒgLΧzfL → ΑgJΧΒfM → ΓfKΧΑgK → ΒiKΧΑdL → ΒgMΧyfL → ΑfIΧΓgM → ΔgKΧΑfJ → ΓjKΧΑcK → ΒiNΧxdL → ΑeJΧΒhM → ΓfLΧzgK → ΒhJΧΒeL