Base 59: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps100
28 max steps10 → 0w → v1 → t3 → p7hFRV3tp7
332 max steps100 → 0ww → vw1 → uw2 → tw3 → sw4 → rw5 → qw6 → pw7 → ow8 → nw9 → mwA → lwB → kwC → jwD → iwE → hwF → gwG → fwH → ewI → dwJ → cwK → bwL → awM → ZwN → YwO → XwP → WwQ → VwR → UwS → TwTSwUTwT
433 max stepsU000 → TwwT → TSTU → 1wwv → v0v2vs32to74pgF8hQVGR4rWn4rAncJAdIdKLIdcLGfcPGfYP8nYf8nIfMZINCjaXCjQX6pQj6pEjUREV2tSr2t6rkB6lYNCZAlObAlMbEhMTEhUT0vUv0v2
529 max steps30000 → 2wwwu → u1wu3 → vqw52 → upw63 → tnw84 → skwB5 → rgwF6 → qbwK7 → pVwQ8 → oOwX9 → nPwWA → mNwYB → lOwXC → kMwZD → jNwYE → iLwaF → hMwZG → gKwbH → fLwaI → eJwcJ → dKwbK → cIwdL → eHweJ → fKwbI → eKwbJdJwcKdIwdKeIwdJeKwbJ
6244 max stepsK000dd → ddJcJK → KKHecd → NJHeda → NKCjca → XICjeQ → XM6paQ → jE6piE → jVTSRE → V40vsS → vo2t82 → trfG54 → pmOXA8 → hc8nKG → fRHeVI → OM3saZ → pEAli8 → hbTSLG → RG0vgW → vQ4rW2 → tn5q94 → pldIB8 → haKbMG → RHDifW → VO4rYS → nA2tmA → rdbKJ6 → lKGfcC → ZPHeXO → NB7ola → haCjMG → XRDiVQ → V73spS → pi2tE8 → rhTSF6 → lS0vUC → vZ1uN2 → usBk43 → roYN86 → lgAlGC → bZPWNM → FC6pki → jYSTOE → VA0vmS → vc2tK2 → trHe54 → pmMZA8 → hcCjKG → XRHeVQ → N73spa → piCjE8 → hXTSPG → R80voW → vg4rG2 → tnPW94 → pe6pI8 → jhLaFE → VSEhUS → T31utU → tq0v64 → vpjC72 → tiWPE4 → pU6pS8 → jh1uFE → tVRUR4 → p42ts8 → rogF86 → lgQVGC → ZQ4rWO → nB5qlA → ldZMJC → ZKCjcO → XIAleQ → bM6paM → jFDihE → WURUSR → 531uts → tqm964 → pkcJC8 → hYIdOG → RL9mbW → dG4rgK → nQIdWA → dL5qbK → lJFgdC → ZRJcVO → JB3sle → paKbM8 → hHDifG → VRNYVS → B42tsm → roaL86 → lgEhGC → ZTPWTO → B6wwpm → ql2tB7 → rjZMD6 → lWCjQC → ZX5qPO → lB7olC → haYNMG → REAliW → bU4rSM → nF1uhA → tdRUJ4 → pK2tc8 → rhHeF6 → lSMZUC → ZD1ujO → tWAlQ4 → pb5qL8 → lhFgFC → ZSQVUO → B51urm → tmaLA4 → pcEhK8 → hTHeTG → RMwwZW → aV2tRN → rD3sj6 → plVQB8 → ha4rMG → nRDiVA → dV3sRK → pJ3sd8 → 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
748 max stepsB00000T → TAwwwlU → mTRwUTB → lL0wvbC → wjPwWD1 → vjJwcD2 → uiPwWE3 → tgIwdG4 → sdNwYJ5 → rZFwgN6 → qcIwdK7 → pYIwdO8 → oXEwhP9 → naHweMA → mWHweQB → lVDwiRC → kYGwfOD → jUGwfSE → iTCwjTF → kUEwhSD → jWEwhQE → iVGwfRF → hSDwiUG → jSEwhUE → iVEwhRF → iTFwgTF → hTCwjTG → kTDwiTD → jXEwhPE → iVHweRF → hRCwjVG → kTFwgTD → jVCwjRE → kVHweRD → jTCwjTE → kVFwgRD → jVEwhRE → iVFwgRF → hTEwhTG → iRDwiVF → jTGwfTEiTBwkTFlVEwhRCkXFwgPDjVGwfREiTDwiTFjTEwhTEiVDwiRFjTGwfTE
8381 max steps800008Gp → pG87oog8 → iggPWGGF → TQQ6pWWU → j660vqqE → vkkURCC2 → tYY2tOO4 → rpA9mm76 → lidbKJEC → ZUKGfcSO → PIB1uleY → taM8naM4 → pfEDiiH8 → hVUNYSRG → RB41uslW → toa4rM84 → pngDiG98 → heVPWRIG → RM73spaW → piE4riE8 → nhUTSSFA → dS20vuUK → vsJ1ud42 → usoJc843 → rogIdG86 → lgQKbWGC → ZQH5qfWO → lOB5qlYC → laZ9mNMC → dZEBkiNK → ZUJBkdSO → ZKB1ulcO → taIAleM4 → pbMDiaL8 → hVGDigRG → VRQ3sWVS → p642tsq8 → rokgFC86 → lgYQVOGC → ZQA4rmWO → ncB5qlKA → ldaHeMJC → ZNKDicZO → VICAlkeS → bYM2taOM → rFE9mih6 → ldURUSJC → ZK31utcO → tqIAle64 → pkbLaLC8 → hYGEhgOG → TRQ9mWVU → d640vsqK → vokIdC82 → tgYKbOG4 → pQH9mfW8 → hdO5qYJG → lRK9mcVC → dZI3seNK → pMJBkda8 → hZKDicNG → VRIBkeVS → ZM42tsaO → roEAli86 → lgbTSLGC → ZQG0vgWO → vQB5qlW2 → tla5qMB4 → plaDiMB8 → haVDiRMG → VRE3siVS → pU42tsS8 → roh1uF86 → tlgRUGB4 → paQ2tWM8 → rhE5qiF6 → mkURUSCB → bY31utOM → tqF9mh64 → pkdRUJC8 → hYK2tcOG → rRI9meV6 → ldM3saJC → pZKDicN8 → hVIBkeRG → ZRM3saVO → pEB3sli8 → phaTSMF8 → hSE0viUG → vUR1uVS2 → us41us43 → tron8854 → pmgeHGA8 → hcQMZWKG → RID5qjeW → lWM4raQC → nZE5qiNA → ldUBkSJC → aYK1ucON → tID9mje4 → pdWLaQJ8 → hKF5qhcG → lSRHeVUC → ZN41usZO → toCAlk84 → pgbXOLG8 → hQG8ngWG → fRQ5qWVI → lN63sqZC → pkZBkNC8 → hZYBkONG → ZRC9mkVO → dYB3slOK → paJ9mdM8 → hdKDicJG → VRKHecVS → NI42tsea → roMCja86 → lgXDiPGC → ZVQ7oWRO → hB63sqlG → pkaQVMC8 → hYE4riOG → nUR9mVSA → ec41usKJ → toLHeb84 → pgNFgZG8 → hRQBkWVG → ZR63sqVO → pkB3slC8 → phaXOMF8 → hSE8niUG → fUR1uVSI → tN41usZ4 → tpoBk874 → pigYNGE8 → hUQAlWSG → bR61uqVM → tkF3shC4 → qoYRUO87 → jgA2tmGE → rcVPWRK6 → lI73speC → piZLaNE8 → hUFBkhSG → ZSR1uVUO → tB41usl4 → tpoZM874 → pigCjGE8 → hXUPWSPG → R871upoW → tig4rGE4 → pnUPWS98 → he71upIG → tiRLaVE4 → pUF3shS8 → phS1uUF8 → thS1uUF4 → tpS1uU74 → tpi1uE74 → tpiTSE74 → piU0vSE8 → vhU1uSF2 → usS1uU43 → tro1u854 → tpmfGA74 → picOXKE8 → hUI8neSG → fRM1uaVI → tNE3siZ4 → qoUBkS87 → jgZ1uNGE → tVQBkWR4 → pZ63sqN8 → pkhBkFC8 → hZYRUONG → RCA2tmkW → rcY4rOK6 → nlI9meBA → ecaLaMKJ → LIFDihec → VSMGfaUS → PE31utiY → tqU8nS64 → pkf1uHC8 → thYNYOF4 → pSB9mlU8 → hda1uMJG → tRKDicV4 → pVI3seR8 → phM3saF8 → phSDiUF8 → hVS1uURG → tR41usV4 → tpo3s874 → qoifGE87 → jgUOXSGE → VQ91unWS → te62tqI4 → rpkLaC76 → liYEhOEC → ZUT9mTSO → dB1wwulK → vla7oMB2 → 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