Base 73: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps100
221 max steps10 → 0Λ → Κ1 → Θ3Δ7vFfVrJXdzBnNPlLpThDxjRHtbZΘ3
339 max steps100 → 0ΛΛ → ΚΛ1 → ΙΛ2 → ΘΛ3 → ΗΛ4 → ΖΛ5 → ΕΛ6 → ΔΛ7 → ΓΛ8 → ΒΛ9 → ΑΛA → zΛB → yΛC → xΛD → wΛE → vΛF → uΛG → tΛH → sΛI → rΛJ → qΛK → pΛL → oΛM → nΛN → mΛO → lΛP → kΛQ → jΛR → iΛS → hΛT → gΛU → fΛV → eΛW → dΛX → cΛY → bΛZ → aΛaZΛbaΛa
413 max stepsb000 → aΛΛa → aZab → 1ΛΛΚ → Κ0Κ2ΚΗ32ΘΓ74ΔuF8veVGf8ΒWt8ΒItaZIb0ΚaΚ0Κ2
533 max steps10006 → 60ΛΚΖ → ΛΓΛ71 → ΚΓΛ72 → ΙΒΛ83 → ΘzΛA4 → ΗwΛD5 → ΖsΛH6 → ΕnΛM7 → ΔhΛS8 → ΓaΛZ9 → ΒSΛhA → ΑYΛbB → zRΛiC → yXΛcD → xQΛjE → wWΛdF → vPΛkG → uVΛeH → tOΛlI → sUΛfJ → rNΛmK → qTΛgL → pMΛnM → oSΛhN → nLΛoO → pPΛkM → oPΛkN → nOΛlO → mOΛlP → mMΛnPoNΛmNnQΛjOmMΛnP
6264 max stepsL000ΖΖ → ΖΖKp56 → ΑzUfBB → poAzMM → pTRihM → THDwti → jcEvYS → hH3ΗtU → ΔcCxY8 → vl3ΗPG → ΔfLoV8 → vT9ΑhG → rfDwVK → jX9ΑdS → rH5ΕtK → zcWdYC → n73ΗΔO → ΔwOlE8 → viMnSG → fRFujW → fI8ΒsW → ta8ΒaI → taΛΛZI → sbIrZJ → aY1Ιcb → Θ40ΚΗ4 → ΚΔΒ872 → ΘwsHE4 → ΔiaZS8 → vG0ΚuG → ΚfdWV2 → ΘA6ΔΑ4 → ΔxpKD8 → vkUfQG → fKAzqW → pW8ΒeM → tT7ΓhI → vbDwZG → jf1ΙVS → ΘH9Αt4 → ΔrbYJ8 → vY2ΘcG → Ζf3ΗV6 → Δz9ΑB8 → vrnMJG → fYQjcW → J93ΗΒs → ΔsYbI8 → va2ΘaG → ΖeΛΛV6 → ΕfQjV7 → xJ9ΑrE → rjXcRK → XI4Ζse → Βa6ΔaA → xqΛΛJE → wr6ΔJF → xhXcTE → jE4ΖwS → ΒiGtSA → rdFuXK → fX5ΕdW → z95ΕΒC → zsmNIC → naOlaO → PMΛΛnm → ol0ΚPN → ΚRLoj2 → ΘTHsh4 → ΔbDwZ8 → vj1ΙRG → ΘfHsV4 → Δb9ΑZ8 → vr1ΙJG → ΘfXcV4 → ΔA4ΖΑ8 → ΒvpKFA → rgUfUK → XCAzye → pm6ΔOM → xTNmhE → jPDwlS → jMGtoS → dSGtiY → dG4ΖuY → Βe4ΖWA → Βr7ΓJA → vrXcJG → fY4ΖcW → Β93ΗΒA → ΔsqJI8 → vaWdaG → f6ΛΛΔW → ΕeNmW7 → xP7ΓlE → vjLoRG → fTHshW → bE8Βwa → ti0ΚSI → ΚbFuZ2 → Θf1ΙV4 → ΘΔ9Α74 → ΔwqJE8 → viWdSG → fG6ΔuW → xe8ΒWE → tj7ΓRI → vbHsZG → fb1ΙZW → Θ91ΙΒ4 → ΘΔrI74 → ΔwYbE8 → vi2ΘSG → ΖfFuV6 → zf9ΑVC → rn9ΑNK → rXPkdK → XL5Εpe → zU6ΔgC → xnByNE → njPkRO → PLHspm → bUMnga → RC0Κyk → ΚmIrO2 → ΘZNmb4 → ΔP1Ιl8 → ΘvLoF4 → ΔgShU8 → vFByvG → ngeVUO → PC8Βym → tmMnOI → bRNmja → PI0Κsm → ΚaMna2 → ΘQΛΛj4 → ΗkNmQ5 → ΒPJqlA → rXLodK → XT5Εhe → zE6ΔwC → xnhSNE → jQEvkS → hKGtqU → dWCxeY → l84ΖΓQ → ΒuKpGA → reUfWK → XB7Γze → vo6ΔMG → xfRiVE → jH9ΑtS → rcGtYK → dX3ΗdY → Δ64ΖΕ8 → ΒyuFCA → rmeVOK → XO8Βme → tO6ΔmI → xbNmZE → jP1ΙlS → ΘMGto4 → ΔdRiX8 → vH5ΕtG → zfbYVC → nA2ΘΑO → ΖqOlK6 → zWMneC → nR7ΓjO → vPHslG → fbLoZW → T91ΙΒi → ΘsEvI4 → ΔhZaT8 → vE0ΚwG → ΚieVS2 → ΘG8Βu4 → ΔtdWH8 → vc6ΔYG → xf3ΗVE → Δj9ΑR8 → vrHsJG → fbXcZW → 951ΙΖΓ → ΘΑsHA4 → ΔqaZK8 → vW0ΚeG → Κf7ΓV2 → Θv9ΑF4 → ΔrfUJ8 → vYAzcG → pf3ΗVM → ΔT9Αh8 → vrDwJG → jfXcVS → HA4ΖΑu → ΒqcXKA → rW4ΖeK → ΒX7ΓdA → vr5ΕJG → zfXcVC → nA4ΖΑO → ΒqOlKA → rWMneK → XR7Γje → vI6ΔsG → xfZaVE → jA0ΚΑS → ΚqGtK2 → ΘdVeX4 → Δ95ΕΒ8 → zvrIFC → ngYbUO → PC2Θym → ΖmMnO6 → zRNmjC → nPHslO → bPLola → TM0Κoi → ΚSEvi2 → ΘhFuT4 → ΔfDwV8 → vj9ΑRG → rfHsVK → bX9Αda → r60ΚΕK → ΚyWdC2 → Θm6ΔO4 → ΔxNmD8 → vkOlQG → fNJqnW → XQ8Βke → tK6ΔqI → xbVeZE → j91ΙΒSΘsGtI4ΔdZaX8v60ΚΕGΚyeVC2Θm8ΒO4ΔtNmH8vcOlYGfN3ΗnWΔQ8Βk8vtJqHGfcWdYW973ΗΔΓΔwsHE8viaZSGfG0ΚuWΚe8ΒW2Θt7ΓH4ΔvbYF8vg2ΘUGΖfByV6zn9ΑNCrnPkNKXQKpkeVK6ΔqgxWAzeEpj7ΓRMvTHshGfbDwZWj91ΙΒS
743 max stepsJ000000 → IΛΛΛΛΛs → sHΛΛΛsJ → trHΛsJI → tbYΛbZI → sL1ΛΙpJ → ΚpWΛdL2 → ΙoIΛrM3 → ΘqUΛfK4 → ΗnLΛoN5 → ΖlQΛjP6 → ΕgKΛpU7 → ΔkKΛpQ8 → ΓjOΛlR9 → ΒeJΛqWA → ΑiJΛqSB → zhNΛmTC → ycIΛrYD → xgIΛrUE → wfMΛnVF → vaHΛsaG → ueHΛsWH → tdLΛoXI → sYGΛtcJ → uaJΛqaH → tbFΛuZI → vcJΛqYG → ucHΛsYH → tdJΛqXI → saIΛraJ → sZGΛtbJ → uaIΛraH → tcGΛtYI → ubKΛpZH → taFΛuaI → vcIΛrYG → udIΛrXH → tcJΛqYI → saHΛsaJ → tZHΛsbI → tbIΛrZI → sbHΛsZJtZIΛrbIsbHΛsZJ