Base 39: 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 steps100
27 max steps10 → 0c → b1 → Z3 → V7 → NF7VNF
322 max steps100 → 0cc → bc1 → ac2 → Zc3 → Yc4 → Xc5 → Wc6 → Vc7 → Uc8 → Tc9 → ScA → RcB → QcC → PcD → OcE → NcF → McG → LcH → KcI → JcJIcKJcJ
416 max stepsK000 → JccJ → JIJK → 1ccb → b0b2bY32ZU74VMF8N6VGP6VEPAREHARMH4XMT4XATIJAJ0bKb0b2
522 max stepsJ0000 → IcccK → KHcKJ → L0cbI → cIcJ1 → bJcI2 → aIcJ3 → ZHcK4 → YHcK5 → XGcL6 → WGcL7 → VFcM8 → UFcM9 → TEcNA → SEcNB → RDcOC → QDcOD → PCcPE → QAcRD → SDcOB → REcNC → QCcPDQCcPD
684 max steps10007b → b70bV2 → bZNE32 → ZW8T64 → VQKHC8 → NE2ZOG → XA6VS6 → RPHKDC → FC2ZQO → XE8TO6 → RL9SHC → JF3YNK → V80bU8 → bNLGF2 → Z84XU4 → VTLG98 → NK4XIG → T71aVA → ZOIJE4 → VA0bS8 → bNHKF2 → Z82ZU4 → XVLG76 → RO4XEC → TF9SNA → KI7UKJ → N20baG → bY6V42 → ZUOD84 → VMARG8 → NH5WLG → R73YVC → VOENE8 → NA8TSG → LI6VKI → P31aZE → ZWAR64 → VQGLC8 → NE4XOG → TA6VSA → PJHKJE → B2ccZS → aR6VB3 → XPFMD6 → RC6VQC → PFDONE → CA7USR → NIENKG → 971aVU → ZOKHE4 → VA2ZS8 → XNHKF6 → R82ZUC → XMENG6 → R95WTC → RKENIC → F91aTO → ZK8TI4 → VL1aH8 → ZN3YF4 → WU7U87PNLGFEB84XUSTMGLGAJ64XWKTQ0bCAbJDOJ2ZAccR4YS7UA5TNHKFAJ82ZUKXM0bG6bR5WB2ZRFMB4VG6VM8PN5WFERB7URCNGENMG975WVUROKHECFA2ZSOXI8TK6RL1aHCZF3YN4WU7U87
743 max steps400000J → J3cccYK → ZJHcKJ4 → YI0cbK5 → cWFcM61 → bWGcL62 → aVFcM73 → ZTFcM94 → YQDcOC5 → XMCcPG6 → WL8cTH7 → VOBcQE8 → UKBcQI9 → TJ7cUJA → VK9cSI8 → UM9cSG9 → TLBcQHA → SI8cTKB → UI9cSK9 → TL9cSHA → TJAcRJA → SJ7cUJB → VJ8cTJ8 → UN9cSF9 → TLCcPHA → SH7cULB → VJAcRJ8 → UL7cUH9 → VLCcPH8 → UJ7cUJ9 → VLAcRH8 → UL9cSH9 → TLAcRHA → SJ9cSJB → TH8cTLA → UJBcQJ9TJ6cVJAWL9cSH7VNAcRF8ULBcQH9TJ8cTJAUJ9cSJ9TL8cTHAUJBcQJ9
8155 max stepsA0000Ebb → bbE9SO12 → aZJ9SJ33 → XWIccJ66 → WWFCPN67 → QPD7UPDD → NDCBQQPG → FEC6VQOO → PEA8TSOE → LIB9SRKI → JG31aZMK → ZW60bW64 → bVQPCC72 → ZOECPOE4 → VDA9SSP8 → NJIBQKJG → F71ccaVO → bVL6VH72 → ZPO3YED4 → WUC9SQ87 → PMJDOJGE → CA5ccWSR → XSK0bIA6 → bRI1aKB2 → aYG1aM43 → ZXU5W854 → VSRLGBA8 → NIG4XMKG → T761aWVA → ZQOIJEC4 → VEA0bSO8 → bNI9SKF2 → ZJ81aUJ4 → ZVLccG74 → YVJ9SJ75 → TOIccJEA → SOB4XREB → THG9SMLA → KI63YWKJ → VQ20baC8 → bYNDOF42 → ZUB7UR84 → VNMFMGF8 → N875WVUG → ROM6VGEC → PFA5WSNE → RIB7URKC → NGF1aNMG → Z875WVU4 → VROLGEB8 → NGA4XSMG → TI75WVKA → ROJ1aJEC → ZF9ccSN4 → YTK4XI95 → USK1aIA9 → ZLI1aKH4 → ZV41aY74 → ZVUNE874 → VOM8TGE8 → NLA5WSHG → RI73YVKC → VOF1aNE8 → ZNA7USF4 → VNI7UKF8 → OM81aUGF → ZM95WTG4 → VRK5WIB8 → RNG1aMFC → ZF85WUN4 → VRM7UGB8 → OMG5WMGF → R965WWTC → RQKENICC → FE91aTOO → ZKA8TSI4 → VLI1aKH8 → ZN41aYF4 → ZVU7U874 → VONLGFE8 → NA84XUSG → TMI6VKGA → PJ61aWJE → ZQAccRC4 → YSN0bFA5 → bTI7UK92 → ZNK1aIF4 → ZV81aU74 → ZVOLGE74 → VOA4XSE8 → TNI9SKFA → KI81aUKJ → ZM20baG4 → bYV5W742 → ZURNEB84 → VMG8TMG8 → NL65WWHG → RQ73YVCC → VOFDONE8 → NBA7USRG → NIG6VMKG → P761aWVE → ZQOAREC4 → VHE9SOL8 → NJA3YSJG → VI6ccVK8 → WUDARP87 → PMHBQLGE → FB63YWRO → VQG8TMC8 → NLE5WOHG → RA73YVSC → VOIENKE8 → NA91aTSG → ZKI6VKI4 → VP21aaD8 → ZYNBQF44 → VUF7UN88 → OMM7UGGF → N965WWTG → RQK6VICC → PFE1aONE → ZBA7USR4 → VNIFMKF8 → N871aVUG → ZOM6VGE4 → VPA5WSD8 → RNIBQKFC → GE81aUON → ZMA6VSG4 → VPI5WKD8 → RNC1aQFC → ZFE7UON4 → VNA7USF8 → OMI7UKGF → N961aWTG → ZQK6VIC4 → VPE1aOD8 → ZNC9SQF4 → VJE7UOJ8OM9ccSGFTNC1aQFAZJE7UOJ4VN9ccSF8UTG4XM99TLK5WIHARJ41aYJCZUEccN84YUL6VH85TPM3YGDAVJC5WQJ8RNDccOFCQPC0bQDDbEDBQPO2ZFC9SQN4VJE7UOJ8
958 max stepsJ000000TU → UTIcccJ99 → TTKAcRI9A → TJJ8cTJJA → UJ9cccSJ9 → TTJAcRJ9A → TJJ7cUJJA → VK9cccSI8 → UTKAcRI99 → TLJ8cTJHA → UJC1caQJ9 → bRI6cVKB2 → aVK8cTI73 → ZTNAcRF94 → YQJBcQJC5 → XNE6cVOF6 → WRH8cTLB7 → VOI9cSKE8 → UME5cWOG9 → XNG7cUMF6 → WQF6cVNC7 → WPJAcRJD7 → VME5cWOG8 → XOH7cULE6 → WQG6cVMC7 → WPJ9cSJD7 → VNF5cWNF8 → XOG7cUME6 → WQG7cUMC7 → VPI9cSKD8 → UMF6cVNG9 → WMF6cVNG7 → WPG6cVMD7 → WPI8cTKD7 → VOG6cVME8 → WNH7cULF7VPF5cWND8XOI9cSKE6WOE5cWOE7XPI9cSKD6WOF6cVNE7WPH8cTLD7VOG7cUME8VNG7cUMF8VNF6cVNF8WNG7cUMF7VPF6cVND8WNI9cSKF7VND4cXPF8YPI9cSKD5XPF6cVND6WRI9cSKB7VNH8cTLF8UNE5cWOF9XNG8cTMF6WPE6cVOD7WPIAcRKD7VME6cVOG8WNH7cULF7
10176 max steps40000099JU → UJ993YTTJ9 → VLKJccIIH8 → ULD30bZPH9 → bWLC3YQH62 → ZVQE3YOC74 → WUOE9SOE87 → PMJA9SSJGE → JIB5ccWRKK → XRE7ccUOB6 → WVMG2ZMG77 → XPO65WWED6 → SQQC9SQCCB → JHEEDOOOLK → BAA40bYSSS → bUIIGLKK82 → ZM521aaXG4 → ZYVS5WA744 → VUROHKEB88 → NMGA2ZSMGG → XI765WWVK6 → SQQO1aECCB → ZHEE9SOOL4 → VJAA3YSSJ8 → VNIHccKKF8 → UNE4ccXOF9 → YTJF0bNJ95 → bTK7ccUI92 → aVSC8TQA73 → XOLIDOKHE6 → RBA41aYSRC → ZUIGENMK84 → VM961aWTG8 → ZQNK5WIFC4 → VRE81aUOB8 → ZNMG9SMGF4 → VJ865WWUJ8 → RQNLccGFCC → QQCA1aSQCD → ZIEECPOOK4 → VDAA1aSSP8 → ZNIIBQKKF4 → VF821aaUN8 → ZYNM7UGF44 → VUN85WUF88 → RNMM7UGGFC → NF865WWUNG → RQM86VUGCC → PMFE5WONGE → RBA85WUSRC → RMIGENMKGC → F9661aWWTO → ZQQK8TICC4 → VLEE1aOOH8 → ZNAA3YSSF4 → WUII7UKK87 → PNM21aaGFE → ZYB85WUR44 → VURMFMGB88 → NMG75WVMGG → RO765WWVEC → RQOF9SNECC → JFEA7USONK → NIA80bUSKG → bMI71aVKG2 → aYO61aWE43 → ZXUQ9SC854 → VSMJDOJGA8 → NIB5ccWRKG → XRG92ZTMB6 → XRKG5WMIB6 → SQG61aWMCB → ZQHE5WOLC4 → VREA3YSOB8 → VNIG9SMKF8 → NJ861aWUJG → ZQM6ccVGC4 → YWNF3YNF65 → VTQ87UUC98 → OMMKDOIGGF → B9661aWWTS → ZQQKGLICC4 → VEE51aXOO8 → ZSNA9SSFA4 → VJII7UKKJ8 → OM21ccaaGF → baLK1aIH22 → aYY41aY443 → ZXUUT88854 → VSMMKHGGA8 → NI662ZWWKG → XQQ71aVCC6 → ZROEDOOEB4 → VGBA9SSRM8 → NJIG5WMKJG → R761ccaWVC → bWTK3YI962 → ZVQK1aIC74 → ZVOE1aOE74 → ZVOA9SSE74 → VOJI9SKJE8 → NJA1ccaSJG → bSK93YTIA2 → ZVKI1aKI74 → ZVO21aaE74 → ZYVO9SE744 → VUOJ9SJE88 → NMJ9ccSJGG → TMC42ZYQGA → XUJE5WOJ86 → SQM9ccSGCB → TRGC3YQMBA → VJGE5WOMJ8 → RNA5ccWSFC → XSKD3YPIA6 → VRIC1aQKB8 → ZNGE1aOMF4 → ZVA85WUS74 → VROMHKGEB8 → NGA62ZWSMG → XQI75WVKC6 → SQOE1aOECB → ZHEA9SSOL4 → VJIA3YSKJ8 → VNI1ccaKF8 → bULD2ZPH82 → ZXMC3YQG54 → WUSE5WOA87 → RPMI9SKGDC → JFC61aWQNK → ZQE80bUOC4 → bVME9SOG72 → ZOJA5WSJE4 → VRI9ccSKB8 → UTKA6VSI99 → PLKI1aKIHE → ZB421aaYR4 → ZYVUFM8744 → VUOM6VGE88 → PNMA5WSGFE → RIB85WURKC → RMGF1aNMGC → ZF865WWUN4 → VRQM7UGCB8 → OMGE5WOMGF → RA965WWTSC → RQKIENKICC → FE921aaTOO → ZYKA8TSI44 → VULI1aKH88 → ZNM41aYGF4 → ZVU85WU874 → VROMLGGEB8 → NGA64XWSMG → TQI75WVKCA → ROJE1aOJEC → ZFA9ccSSN4 → YTPD4XPD95USKCBQQIA9LIFE1aONKIZA831aZUS4ZWVMHKG764VQO62ZWEC8XQNE9SOFC6RJEA7USOJCNIF9ccSNKGTNC52ZXQFAXSJE7UOJA6RNI9ccSKFCTQD92ZTPCAXKJEBQOJI6RFA1ccaSNCbSOD3YPEA2ZVIC9SQK74VOJE1aOJE8ZNA9ccSSF4YTPD4XPD95