Base 61: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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--
23 cycles5 nodes9p → fJ → Ld → Hh → PZ
31 cycle 2 nodesTyV → UyU
415 cycles30 nodes94tq → pgHA → fOZK → LAne → dIfM → NGhc → REjY → V6rU → l0xE → xWR2 → v4t4 → ro98 → jeJG → TKdW → J2vg → tMb6 → nEjC → bUTO → D0xm → xYP2 → v8p4 → rgH8 → jOZG → TAnW → d2vM → tGh6 → nQXC → b6rO → lClE → ZWRQ
52 cycles4 nodeseJyeL → fIyfK → gKydJ → fLycK
69 cycles59 nodesFD3ulk → rYUTQ8 → j80xqG → xiSVG2 → vS2vW4 → tr3u76 → rnjEB8 → jcUTMG → TG0xiW → xS2vW2 → vt3u54 → sqnA87 → licLGE → XSGhWS → R53utY → ro6rA8 → ljdKFE → XUIfUS → N4yytc → ubGhN5 → pRDkXA → fX5sRK → nL5sdC → nbHgNC → bPDkZO → XD9olS → fY4tQK → pL7qdA → jfHgJG → TPLcZW → HA2voi → teQXK6 → nK6reC → lbJeNE → XLDkdS → XI4tgS → pO4taA → pfBmJA → fbLcNK → LHDkhe → XQIfYS → N84tqc → piEjGA → fVRWTK → L51wte → voIfA4 → reMbK8 → jKEjeG → VTJeVU → L20xwe → xuIf42 → vqMb84 → riEjG8 → jVRWTG → T51wtW → vo2vA4 → trdK76 → nkIfEC → bWMbSO
73 cycles4 nodesiTDykVH → lTEyjVE → kXFyiRF → jVGyhTG
810 cycles111 nodesLC62vsme → tmaIfOC6 → naNBmbOC → caEBmkON → bWFBmjSO → bUD3ulUO → rYCyylQ8 → qmRClXC9 → haZ5sPOI → nPC9omZC → fba9oONK → fLEBmkdK → bWLHgdSO → PID3ulga → rYOAnaQ8 → jdC7qmLG → jaTHgVOG → TPC1wmZW → vaA2voO4 → treBmK76 → nkbJeNEC → bWLDkdSO → XID3ulgS → rYO4taQ8 → pjC7qmFA → jfaTUOJG → TMC0xmcW → xaG2viO2 → vtSBmW54 → rob3uNA8 → rjeDkKF8 → jXUJeURG → TL5yysdW → tdP6rZL6 → nlI9ogDC → fbYNaQNK → LED7qlke → jYWIfSQG → TN83uqbW → riE2vkG8 → tjWRWSF6 → nU53utUC → roayyNA8 → qoUDkUA9 → heWyyRKI → geG7qiKJ → jSNJebWG → TLE3ukdW → rWI2vgS8 → tjO3uaF6 → rnUBmUB8 → jcayyNMG → icM1wcMH → vRGFiiX4 → rTS5sWV8 → nj41wuFC → vqbTUN84 → riE0xkG8 → xjWRWSF2 → vU53utU4 → sqnyyA87 → rqi2vG88 → tjiRWGF6 → nUS4tWUC → pb3yyuNA → voXDkRA4 → reX5sRK8 → njK5seFC → nbUJeUNC → bLDyykdO → ldM1wcLE → vXIFigR4 → rTO5saV8 → njC1wmFC → vbaTUON4 → rEC0xmk8 → xjaVSOF2 → vUC2vmU4 → trZyyO76 → srVHgT77 → lkP1wZEE → vXW9oSR4 → rf63usJ8 → rmjLcFC8 → jaUGhUOG → TRByymXW → nXJ0xfRC → xbM5scN2 → vnGDkiB4 → rcXRWRM8 → jG64tsiG → pmTRWVCA → fa51wtOK → voLBmdA4 → rebHgNK8 → jPKDkeZG → XTK9oeVS → fK51wteK → voLJedA4 → reLHgdK8 → jPKHgeZG → TPK9oeZW → fKA2voeK → teLJedK6 → nLKHgedC → bPKHgeZO → PKD9olea → fYKAneQK → dLK7qedM → jKIGhgeG → TROJeaXW