Base 77: 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
215 max steps10 → 0Ο → Ξ1 → Μ3Θ7zFjVnRLtXhvJbdΜ3
341 max steps100 → 0ΟΟ → ΞΟ1 → ΝΟ2 → ΜΟ3 → ΛΟ4 → ΚΟ5 → ΙΟ6 → ΘΟ7 → ΗΟ8 → ΖΟ9 → ΕΟA → ΔΟB → ΓΟC → ΒΟD → ΑΟE → zΟF → yΟG → xΟH → wΟI → vΟJ → uΟK → tΟL → sΟM → rΟN → qΟO → pΟP → oΟQ → nΟR → mΟS → lΟT → kΟU → jΟV → iΟW → hΟX → gΟY → fΟZ → eΟa → dΟb → cΟcbΟdcΟc
434 max stepsd000 → cΟΟc → cbcd → 1ΟΟΞ → Ξ0Ξ2ΞΛ32ΜΗ74ΘyF8ziVGjCΒWpCΒQpOpQROpoRMroVMrkVEzklEzUlGxUhGxYh8ΖYx8ΖIxeZIf4ΚaΖ4ΚAΖuJAvadKb2ΜeΚ2Μ6ΚΓB6ΔqNCrSlOTIvmdIvcd0ΞcΞ0Ξ2
535 max steps30000 → 2ΟΟΟΝ → Ν1ΟΝ3 → ΞΙΟ52 → ΝΘΟ63 → ΜΖΟ84 → ΛΓΟB5 → ΚyΟF6 → ΙtΟK7 → ΘnΟQ8 → ΗgΟX9 → ΖYΟfA → ΕWΟhB → ΔXΟgC → ΓVΟiD → ΒWΟhE → ΑUΟjF → zVΟiG → yTΟkH → xUΟjI → wSΟlJ → vTΟkK → uRΟmL → tSΟlM → sQΟnN → rRΟmO → qPΟoP → pQΟnQ → oOΟpR → qNΟqP → rQΟnO → qQΟnPpPΟoQpOΟpQqOΟpPqQΟnP
6304 max stepsN000cg → gcMrcZ → V6ΟΟΘk → ΙjMrV7 → ΒVDΑjE → omDΑSR → nNJurS → bUKtke → ZG2Μyg → Κi6ΘW6 → ΔΒBΓDC → sqnQON → VSMrmk → VKEzuk → laEzeU → lH3ΛxU → ΘgGxY8 → zh7ΗXG → zj9ΕVG → vjDΑVK → nbDΑdS → nL1ΝtS → ΜYKtg4 → ΘZ7Ηf8 → Αy5ΙGF → ΔlhWTC → rIAΔwO → teSlaM → XJ3Λvi → ΘcAΔc8 → zsΟΟLG → yt6ΘLH → ΒhXgXE → nA8ΖΕS → xuKtKI → faYfea → 753ΛΚΙ → ΘΕΑDA8 → zumRKG → jaKteW → ZD3ΛΒg → Θo6ΘQ8 → ΒzNqFE → nkSlUS → LJFyvu → jcYfcW → D6ΟΟΘΓ → ΙΒ4ΚD7 → ΖΒnQDA → voMrQK → bVNqje → TE2ΜΑm → ΚmIvS6 → ΔdJubC → rb1ΝdO → ΜT1Νl4 → ΜΘHw74 → ΘΑeZE8 → zm4ΚSG → ΖjJuVA → vbDΑdK → nb1ΝdS → ΜL1Νt4 → ΜΘXg74 → ΘΑ8ΖE8 → zxlSHG → jgIvYW → dD7ΗΒc → zo0ΞQG → ΞjNqV2 → ΜTDΑl4 → ΘnHwR8 → zfLsZG → jX5ΙhW → ΔD9ΕΒC → vrnQNK → bUMrke → VG2Μyk → ΚiEzW6 → ΔlBΓTC → sqHwON → fVRmja → LE4ΚΑu → ΖmYfSA → vK6ΘuK → ΒbZedE → n51ΝΚS → ΜΕKtA4 → ΘuYfK8 → za6ΘeG → Βj3ΛVE → ΘnDΑR8 → znLsRG → jXLshW → XD9ΕΒi → voAΔQK → tbNqdM → XT1Νli → ΜIAΔw4 → ΘtdaL8 → zY2ΜgG → Κj7ΗV6 → ΔzDΑFC → rnjURO → TMEzsm → lWIviU → dHBΓxc → rg0ΞYO → ΞT7Ηl2 → ΜzHwF4 → ΘkeZU8 → zG4ΚyG → ΖjhWVA → vEAΔΑK → tmadSM → XK2Μui → ΚaAΔe6 → Δt3ΛLC → ΘrXgN8 → zU8ΖkG → xjFyVI → jfDΑZW → nD5ΙΒS → ΔoKtQC → rZNqfO → US5Ιml → ΔKGxuC → rhZeXO → TA4ΚΕm → ΖuIvKA → vdZebK → b51ΝΚe → ΜΕ2ΜA4 → ΚΘtK76 → ΔΑYfEC → rm6ΘSO → ΒTJulE → nbHwdS → fL1Νta → ΜY4Κg4 → ΘΖ7Η98 → ΑyvIGF → licbWU → HC0ΞΓy → ΞqgXO2 → ΜS8Ζm4 → ΘxJuH8 → zgadYG → j82ΜΗW → ΚyCΒG6 → ΔphWPC → rQAΔoO → tTNqlM → XTHwli → fIAΔwa → te4ΚaM → ΖX3ΛhA → Θv9ΕJ8 → zvbcJG → jc0ΞcW → ΞCΟΟΒ2 → ΝΓBΓC3 → ΚrpON6 → ΔUQnkC → rNFyrO → jUSlkW → JGCΒyw → picbWQ → PC0ΞΓq → ΞqQnO2 → ΜSMrm4 → ΘVJuj8 → zbDΑdG → nj1ΝVS → ΜLDΑt4 → ΘnXgR8 → zM8ΖsG → xjViVI → fECΒΑa → pm4ΚSQ → ΖPJupA → vbPodK → bP1Νpe → ΜQ2Μo4 → ΚΘNq76 → ΔΑSlEC → rmIvSO → dTJulc → bI0Ξwe → Ξe2Μa2 → ΜΚ3Λ54 → ΙΗΔA87 → ΒysLGE → niWhWS → LCAΔΓu → tqYfOM → XS6Θmi → ΒKAΔuE → tnZeRM → XM4Κsi → ΖWAΔiA → vtBΓLK → rbXgdO → T91ΝΖm → ΜwIvI4 → Θecba8 → z40ΞΛG → ΞΗiV82 → ΜyCΒG4 → ΘphWP8 → zQAΔoG → tjNqVM → XTDΑli → nIAΔwS → teKtaM → ZX3Λhg → ΘA6ΘΕ8 → ΒztKFE → nkYfUS → LG6Θyu → ΒiYfWE → nC6ΘΓS → ΒqKtOE → nZRmfS → MK5Ιut → ΔaWheC → rB3ΛΔO → ΘsSlM8 → zWIviG → jdBΓbW → rD1ΝΒO → ΜoSlQ4 → ΘOIvq8 → zdRmbG → jL1ΝtW → ΜYCΒg4 → Θp7ΗP8ΑyPoGFliOpWURHBΓxorgMrYOVT7ΗlkzIEzwGljdaVUHE2ΜΑyΚmgXS6ΔK8ΖuCxrZeNIfU4ΚkaΖG4ΚyAΖvhWJAvcAΔcKtaΟΟdMseFyaNjV3ΛjWΘECΒΑ8zplSPGjQIvoWdOCΒqcpS0ΞmQΞPJup2ΜbPod4ΘP1Νp8ΜzPoF4ΘkOpU8zRFynGkiLsWVXFBΓzirkAΔUOtTFylMjXHwhWfD9ΕΒavo4ΚQKΖbNqdAvT1ΝlKΜbHwd4Θf1ΝZ8Μz5ΙF4ΘΔjUB8zsEzMGljViVUHECΒΑypmgXSQPK8ΖuqxaQneIfN3ΛraΘU4Κk8ΖzFyFAvkiVUKbGCΒyepi2ΜWQΚPBΓp6ΔrPoNCrUOpkOTRFynmjMIvsWdWCΒicpC0ΞΓQΞqOpO2ΜSQnm4ΘNJur8zbTkdGjH1ΝxWΜgCΒY4Θp7ΗP8
743 max steps900000c → c8ΟΟΟΖd → ΗcaΟdc9 → ΖW0ΟΞiA → ΟΔYΟfB1 → ΞΔUΟjB2 → ΝΓYΟfC3 → ΜΑTΟkE4 → ΛxWΟhH5 → ΚtQΟnL6 → ΙoSΟlQ7 → ΘiLΟsW8 → ΗmLΟsS9 → ΖlPΟoTA → ΕgKΟtYB → ΔkKΟtUC → ΓjOΟpVD → ΒeJΟuaE → ΑiJΟuWF → zhNΟqXG → ycIΟvcH → xgIΟvYI → wfMΟrZJ → vaHΟweK → xcKΟtcI → wdGΟxbJ → yeKΟtaH → xeIΟvaI → wfKΟtZJ → vcJΟucK → vbHΟwdK → xcJΟucI → weHΟwaJ → xdLΟsbI → wcGΟxcJ → yeJΟuaH → xfJΟuZI → weKΟtaJ → vcIΟvcK → wbIΟvdJ → wdJΟubJ → vdIΟvbKwbJΟudJvdIΟvbK