Base 37: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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
212 max steps10 → 0a → Z1 → X3 → T7 → LF → 5V → PB → DN → 9R → HJ → 1Z → X3
321 max steps100 → 0aa → Za1 → Ya2 → Xa3 → Wa4 → Va5 → Ua6 → Ta7 → Sa8 → Ra9 → QaA → PaB → OaC → NaD → MaE → LaF → KaG → JaH → IaI → HaJ → IaI
422 max stepsJ000 → IaaI → IHIJ → 1aaZ → Z0Z2 → ZW32 → XS74 → TKF8 → L4VG → R4VA → RGJA → H2XK → V2X6 → VOB6 → PCNC → DAPO → FAPM → F6TM → N6TE → N8RE → J8RI → J0ZI → Z0Z2
520 max stepsI0000 → HaaaJ → JGaJI → K0aZH → aHaI1 → ZIaH2 → YHaI3 → XGaJ4 → WGaJ5 → VFaK6 → UFaK7 → TEaL8 → SEaL9 → RDaMA → QDaMB → PCaNC → OCaND → OAaPD → QBaOB → PEaLC → OAaPD
689 max steps1000aa → aa0Z01 → aaX201 → aZU511 → ZYOB22 → XWCN44 → TSAP88 → LKELGG → 753WVU → TQMDA8 → LG8RKG → J53WVI → TQ0ZA8 → ZLFKF2 → X64VU4 → TRNC98 → LIAPIG → F4aaVM → WL8RF5 → RJ5UHA → PH1YJC → XD1YN4 → XT9Q74 → TMGJE8 → L82XSG → VK4VG6 → RP3WBA → THDMJ8 → L91YRG → XI4VI4 → TQaa98 → SR2X99 → VJHIH6 → P20ZYC → ZWCN42 → XSAP84 → TKELG8 → L73WTG → TM4VE8 → RL7SFA → LH5UJG → P51YVC → XQCNA4 → TGAPK8 → LF3WLG → T64VU8 → ROKFCA → HC4VOK → RC2XOA → VHBOJ6 → PD1YNC → XD9QN4 → TH9QJ8 → LH1YJG → X51YV4 → XTPA74 → TMELE8 → L86TSG → NK4VGE → R93WRA → TIGJI8 → L2aaXG → YKBOG3 → VD3WN6 → TP9QB8 → LHDMJG → 951YVS → XQIHA4 → TG0ZK8 → ZL3WF2 → XT5U74 → TPLEB8 → LE6TMG → N84VSE → RK8RGA → JH3WJI → T20ZY8 → ZWKF42 → XS4V84 → TRJG98 → LI2XIG → V4aaV6 → WTaa65 → VU2X66 → VPNCB6 → PEAPMC → FD7SNM → LA6TQG → NG4VKE → R93WRA
732 max steps100007a → a70aZT1 → aZRa811 → ZZQa912 → ZXPaA32 → YWMaD43 → XUIaH64 → WRCaN95 → VNEaLD6 → UI8aRI7 → TM8aRE8 → SLCaNF9 → RG7aSKA → TIAaPI8 → SJ6aTH9 → UKAaPG7 → TK8aRG8 → SLAaPF9 → RI9aQIA → RH7aSJA → TI9aQI8 → SK7aSG9 → TJBaOH8 → SI6aTI9 → UK9aQG7 → TL9aQF8 → SKAaPG9 → RI8aRIA → SH8aRJ9 → SJ9aQH9 → RJ8aRHA → SH9aQJ9 → RJ8aRHA
886 max steps30000779 → 9772XTTS → VMMIHEE6 → P880ZSSC → ZKKCNGG2 → XB43WWP4 → USSDM887 → NKK8RGGE → J943WWRI → TSI0ZI88 → ZLJaaGF2 → YLJ1YHF3 → XV61YU54 → XTQNCA74 → TMGAPKE8 → LF83WSLG → TK64VUG8 → ROL3WFCA → THC5UOJ8 → PLC1YOFC → XDC5UON4 → TPC9QOB8 → LHEBOMJG → D851YVSO → XQKAPGA4 → TGF3WLK8 → TL63WUF8 → TOL5UFC8 → PLC5UOFC → PDC5UONC → PDC9QONC → HDC9QONK → HCA2XQOK → VGC2XOK6 → VPC3WOB6 → TPEBOMB8 → LED7SNMG → LA84VSQG → RKG4VKGA → RH43WWJA → TSH1YJ88 → XLK1YGF4 → XT63WU74 → USOLEC87 → NKC6TOGE → NC93WROE → TIC8ROI8 → LJBaaOHG → PK71YTGC → XMD3WNE4 → USA7SQ87 → NLKFKGFE → 9653WVUS → TQOIHCA8 → LGC0ZOKG → ZC53WVO2 → XTQBOA74 → TMGCNKE8 → LB83WSPG → TKE4VMG8 → RL83WSFA → TKH5UJG8 → PL41YWFC → XSD5UN84 → TPK9QGB8 → LHE3WMJG → T851YVS8 → XQLJGFA4 → TG62XUK8 → VOL3WFC6 → TPC5UOB8 → PLEBOMFC → EC85USON → PKC8ROGC → JDC3WONI → TCA0ZQO8 → ZLGBOKF2 → XD63WUN4 → USO9QC87 → NKHBOJGE → D941YWRO → XSIAPI84 → TKEaaLG8 → SMD0ZNE9 → ZJA7SQH2 → XLG1YKF4 → XT63WU74
950 max steps100000000 → 0aaaaaaaa → Zaaaaaaa1 → Z0aaaaaZ2 → aY10aZZ21 → aZYWa3211 → ZZXUa5312 → ZXWRa8432 → YWTNaC743 → XUPGaJB64 → WRJ8aRH95 → VOI9aQIC6 → UME5aUME7 → VNG7aSKD6 → UOF6aTLC7 → UNH8aRJD7 → TME5aUME8 → VMF7aSLE6 → UOE6aTMC7 → UNH9aQJD7 → TLD5aUNF8 → VMG7aSKE6 → UOE5aUMC7 → VNI9aQID6 → UMD4aVNE7 → WOH8aRJC5 → VOF6aTLC6 → UPH8aRJB7 → TMG7aSKE8 → TLE5aUMF8 → VMF6aTLE6 → UPF6aTLB7 → UNI9aQID7 → TLD4aVNF8 → WNG7aSKD5 → VPF6aTLB6 → UPI9aQIB7 → TLF6aTLF8 → ULE5aUMF7 → VNG6aTKD6 → UPG6aTKB7 → UNI8aRID7 → TME4aVME8 → WNF7aSLD5 → VPF7aSLB6 → UOH9aQJC7 → TLE6aTMF8 → ULF6aTLF7 → UNE5aUMD7 → VNH8aRJD6 → UNE5aUMD7
1086 max steps50000055AW → WA554VVVQ5 → SQQQFKAAA9 → JGGG4VKKKI → R4440ZWWWA → ZSSSGJ8882 → XKKK2XGGG4 → VT443WWW76 → TSSPLEB888 → LKKE6TMGGG → N8543WWVSE → TSQK8RGA88 → LKJG3WKHGG → T5441YWWV8 → XSSQKFA884 → TKKG4VKGG8 → RL443WWWFA → TSSH5UJ888 → PLKK1YGGFC → XD643WWUN4 → USSO9QC887 → NKKHBOJGGE → D9441YWWRO → XSSIAPI884 → TKKEaaLGG8 → SMD4aaVNE9 → WRIE0ZMI95 → ZRI7aaSI92 → YTQA8RQA73 → VMJGFKKHE6 → P8541YWVSC → XSQKCNGA84 → TKGB3WPKG8 → TLE43WWMF8 → TSL85USF88 → PLKK5UGGFC → PD643WWUNC → TSOD9QNC88 → LKHC9QOJGG → HC541YWVOK → XSQC2XOA84 → VTKGBOKG76 → PMD43WWNEC → TSDA7SQN88 → MKKG9QKGGF → H7443WWWTK → TSSM2XE888 → VLKK7SGGF6 → PL643WWUFC → TSOD5UNC88 → PLKC9QOGFC → HDC63WUONK → TOCA2XQOC8 → VLGCBOOKF6 → PDC63WUONC → TODC9QONC8 → LHCC9QOOJG → HCC51YVOOK → XQCC2XOOA4 → VTGCBOOK76 → PMDC3WONEC → TDCA7SQON8 → MKGC9QOKGF → HC743WWTOK → TSMC2XOE88 → VLKC7SOGF6 → PLC63WUOFC → TODC5UONC8 → PLCC9QOOFC → HDCC5UOONK → PCCA2XQOOC → VGDCBOONK6 → PDCA3WQONC → TGDC9QONK8 → LHCA3WQOJG → TGC51YVOK8 → XQLC3WOFA4 → USGC5UOK87 → PNKC3WOGDC → TDCA3WQON8 → TLGC9QOKF8 → LHC63WUOJG → TOC51YVOC8 → XQLCBOOFA4 → TGDC5UONK8 → PLCA3WQOFC → TGDC5UONK8