Base 38: 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
214 max steps20 → 1a → Y3U7MF6VODARGL4XS9IJ0ba1Y3
321 max steps100 → 0bb → ab1 → Zb2 → Yb3 → Xb4 → Wb5 → Vb6 → Ub7 → Tb8 → Sb9 → RbA → QbB → PbC → ObD → NbE → MbF → LbG → KbH → JbI → IbJIbJ
416 max steps500E → E4WO → S9RA → JGKJ → 3bbY → Y2Y4 → WT76 → QLFCE5VOQ9RCIDNKA1ZSYHJ4U1Z8YLF4U5V8QLFC
523 max stepsI0000 → HbbbK → KGbKI → L1bZH → aHbJ2 → ZIbI3 → YGbK4 → XHbJ5 → WFbL6 → VGbK7 → UEbM8 → TFbL9 → SDbNA → REbMB → QCbOC → PDbND → OBbPE → QAbQC → RDbNB → QDbNCPCbODPBbPDQBbPCQDbNC
6115 max steps3000IZ → ZI2YJ3 → XV0a65 → aSOC92 → YJBPI4 → UE0aN8 → aM8SF2 → YK6UH4 → UO2YD8 → WMAQF6 → QG6ULC → OE4WNE → SA8SRA → KIGKJI → 420aZY → aXT742 → YTLF84 → UL5VG8 → QM4WFC → SE6UNA → OI8SJE → KA0aRI → aH1ZK2 → ZX2Y43 → XVS865 → SPJHCA → ID1ZOK → YB1ZQ4 → YUEM74 → UN7TE8 → NL8SGF → K84WTI → SL1ZGA → YI4WJ4 → US0a98 → aMIIF2 → Y6bbU4 → XV3X65 → USOC98 → MJBPIG → E60aVO → aP9RC2 → YICOJ4 → UC0aP8 → aMCOF2 → YC6UP4 → UOCOD8 → MCAQPG → GD5VOM → QB5VQC → QFDNMC → EA6URO → OH9RKE → IA2YRK → WH1ZK6 → YQ2YB4 → WUEM76 → QN7TEC → ME8SNGK95VSIQJ1ZICYE0aN4aU8S72YNJHE4U91ZS8YMIIF4U6bbU8VSbb87UT2Y88WMKGF6Q73XUCUNDNE8MA8SRGKH5VKIQ31ZYCYVDN64UP9RC8MICOJGC60aVQaPDNC2YD9RO4UIAQJ8MG0aLGa64WV2YSOC94UJBPI8ME0aNGa95VS2YQIIB4UEbbM8TN7TE9MK8SHGK62YVIWP1ZC6YQCOB4UFBPM8ME6UNGO95VSEQJ9RICIE0aNKa91ZS2ZXII43WSbb86VT3X87UOKGD8MB3XQGUF5VM8QM6UFCOE6UNEOA8SREKH9RKII31ZYKYV1Z64YUOC74UNBPE8ME8SNG
730 max stepsJ00000M → MIbbbIG → LJIbIIH → K30baYI → bXFbL41 → aXHbJ42 → ZWFbL53 → YUGbK74 → XRDbNA5 → WNDbNE6 → VJ8bSI7 → UN9bRE8 → TLCbOG9 → SH7bTKA → UJAbQI8 → TK7bTH9 → UKBbPH8 → TJ7bTI9 → UKAbQH8 → TK8bSH9 → TKAbQH9 → SJ8bSIA → TI9bRJ9 → SK8bSHA → TIAbQJ9 → SJ7bTIA → UJ9bRI8TL8bSG9TKBbPH9SI7bTJAUJ9bRI8
8243 max steps700000CG → GC6bbUPM → VPE2YNC7 → WOD8SOD6 → QKBAQQHC → GFE2YNMM → W975VUS6 → RPNIIECB → GD8bbSOM → TOC1ZPD9 → YKDAQOH4 → UGB2YQL8 → WMF4WMF6 → SQ76UUBA → ONIEMJEE → A980aTSS → aLJHJIG2 → Y520aZW4 → aXUQA742 → YTNFLE84 → UL95VSG8 → QMJ4WIFC → SE70aUNA → aNI8SJE2 → YK90aSH4 → aUJ2YI72 → YWN0aE54 → aUR8SA72 → YNKGKHE4 → U942YXS8 → WTMIIF86 → QL6bbUGC → VPE4WNC7 → SOD8SODA → KIBAQQJI → GF20aZMM → aX75VU42 → YTQMEB84 → ULF7TMG8 → NL74WUGF → SN84WTEA → SLI8SJGA → KI50aWJI → aR20aZA2 → aYXGK432 → YVT3X864 → VTPKGC87 → OLD3XOGE → UBA4WRQ8 → SMHEMKFA → I872YUTK → WNL1ZGE6 → YQ94WSB4 → USJEMI98 → MJ80aTIG → aL60aVG2 → aYP4WC32 → YVSCO964 → UPJBPIC8 → MED0aONG → aB95VSQ2 → YQJEMIB4 → UF80aTM8 → aML6UGF2 → YO74WUD4 → USNAQE98 → MJG8SLIG → K650aWVI → aRP1ZCA2 → ZXHCOK43 → WTC2YP86 → WQLCOGB6 → QFC4WPMC → SED6UONA → OIB8SQJE → KFA0aRMI → aH71ZUK2 → ZXN2YE43 → XVT8S865 → SPLJHGCA → ID51ZWOK → YRB1ZQA4 → YUHEMK74 → UN82YTE8 → WML8SGF6 → QK74WUHC → SNE2YNEA → WI98SSJ6 → QKJ0aIHC → aE30aYN2 → aYV8S632 → YVPJHC64 → UPD1ZOC8 → YMDAQOF4 → UGB6UQL8 → OMF4WMFE → SA76UURA → ONIGKJEE → A940aXSS → aTJHJI82 → YL20aZG4 → aXU4W742 → YTSME984 → ULJ7TIG8 → NL50aWGF → aR84WTA2 → YSLGKG94 → UJ53XWI8 → URM0aFA8 → aMH6UKF2 → YO72YUD4 → WUNAQE76 → QNG8SLEC → KE94WSNI → SJ91ZSIA → YJI0aJI4 → aU10aa72 → aZYME322 → YXV7T644 → UTPLFC88 → MLD5VOGG → QB64WVQC → SPFDNMCA → IDA6UROK → OHB1ZQKE → YFA2YRM4 → WUH6UK76 → QON2YEDC → WEB8SQN6 → QKF8SMHC → KE72YUNI → WN91ZSE6 → YQJ8SIB4 → UKF0aMH8 → aM72YUF2 → YWN6UE54 → URO8SDA8 → MKHAQKHG → G632YYVM → WVP5VC66 → RPPCOCCB → GDDBPOOM → EBB5VQQO → QFF9RMMC → IE76UUNK → ON91ZSEE → YJA8SRI4 → UKH0aKH8 → aM32YYF2 → YWV6U654 → URPNDCA8MHD9ROKGIB62YVQKWPF1ZMC6YQD6UOB4UOFAQMD8MGB6UQLGOF64WVMESPA6URCAOIHCOKJECA30aYRQaVHDNK62YPA2YRC4WUHCOK76QNC2YPECWED8SON6QKB8SQHCKFE2YNMIW971ZUS6YQNIIEB4UF8bbSM8TTF5VM89QLK6UHGCOE52YWNEWRA8SRA6QKHGKKHCE432YYXOWVT9R866QPLHJGCCED51ZWOOYRB9RQA4UIHEMKJ8M830aYTGaVL5VG62YQP4WCB4USFCOM98MJC6UPIGOD60aVOEaPB9RQC2YIFCOMJ4UC70aUP8aNMCOFE2YC96USP4UOJCOID8MCB0aQPGaFD5VOM2YQB6UQB4UOFEMMD8MB86UTQGOLF5VMGEQA74WURCSNHDNKEAIA92YSRKWJH1ZKI6YQ30aYB4aVUEM762YPN7TEC4UMD8SOF8MKB6UQHGOF62YVMEWPA6URC6QOHCOKDCECB2YQPOWFD9ROM6QIB6UQJCOFE0aNMEaA96USR2YOJGKID4UB40aXQ8aTMEMF82YL86UTG4UOL4WGD8SMB4WQFASIF6UMJAOI70aUJEaNA0aRE2aYH8SK32YVK2YH64WUP2YC76WQNCOEB6QFC8SPMCKED6UONIOB91ZSQEYJF9RMI4UI70aUJ8aNM0aFE2aY96US32YVOIID64UPAbbQC8TRI0aJA9aKH0aKH2aY32YY32YWVU6654URPNDCA8
947 max stepsJ0000000R → RIbbbbbIB → QJJ9bRIIC → SF80baTMA → bSJCbOI91 → aSG5bVL92 → ZVMBbPF63 → YTK9bRH84 → XQK9bRHB5 → WOG8bSLD6 → VOF7bTMD7 → UOG8bSLD8 → TMF7bTMF9 → UKE6bUNH8 → VMG5bVLF7 → WOG5bVLD6 → WQI7bTJB6 → VPI7bTJC7 → UOH6bUKD8 → VMH6bUKF7 → VOF4bWMD7 → XPI8bSJC5 → WPG6bULC6 → VQI8bSJB7 → UNH7bTKE8 → UMF5bVMF8 → WNF6bUME6 → VQG7bTLB7 → UOI9bRJD8 → TLE5bVNG9 → WMF6bUMF6 → VQF6bUMB7 → VOJAbQID7 → ULD5bVOG8 → WNH7bTKE6 → VPF5bVMC7 → WOJ9bRID6 → VNE5bVNE7WOH8bSKD6VOF6bUMD7VOH8bSKD7UNF6bUME8VMG7bTLF7UOE5bVND8WNH9bRKE6VND5bVOE7WOI9bRJD6VNE5bVNE7
10374 max steps20000005Fb → bF51bbZWM1 → aaWK9RH512 → ZYRI2YJA33 → XVVH0aK665 → aSPP2YCC92 → YWJDCOOI54 → URCB0aQPA8 → aMHFCOMKF2 → YC772YUUP4 → WUNNCOEE76 → QNC98SSPEC → KJED8SONII → KB920aZSQI → aXJF1ZMI42 → ZXT70aU843 → aWTNKGE852 → YRL93XSGA4 → VTJH4WKI87 → SOL30aYGDA → aVIB4WQJ62 → YSPF0aMC94 → aUJD6UOI72 → YONB0aQED4 → aUFB8SQM72 → YNKF6UMHE4 → UO972YUSD8 → WNMJAQIFE6 → QG970aUSLC → aNJE4WNIE2 → YS990aSS94 → aUJJIIII72 → YN10bbaaE4 → baWMAQF511 → aZRG6ULA22 → YXOH4WKD44 → UTSB2YQ988 → WMLJEMIGF6 → Q8750aWUTC → aRNLDNGEA2 → YHA94WSRK4 → USJH2YKI98 → WMJ30aYIF6 → aVQ70aUB62 → aYPNEMEC32 → YVD97TSO64 → UPMJAQIFC8 → MGD70aUOLG → aNB64WVQE2 → YSPF8SMC94 → UKJD6UOIH8 → OMB30aYQFE → aVFA6URM62 → YPOH6UKDC4 → UODB2YQOD8 → WMFBAQQMF6 → QGF76UUMLC → ONE74WUNEE → SNA98SSREA → KJIH8SKJII → K3210aaZYI → aZXV1Z6422 → ZXXTOC8443 → WTTLBPG886 → QLLE4WNGGC → SE954WWSNA → SRJI8SJIAA → KIH10aaKJI → aZ320aZY22 → aYXXU64432 → YVTTND8864 → UPLL9RGGC8 → MID54WWOJG → SRB60aVQAA → aPIHEMKJC2 → YD830aYTO4 → aVULAQG762 → YPNG4WLEC4 → USD94WSO98 → SMJJAQIIFA → IG710aaULK → aZN51ZWE22 → ZXXR8SA443 → WTTKGKH886 → QLL42YXGGC → WTE54WWN86 → SRQL8SGBAA → KIHF4WMKJI → S7320aZYUA → aXVNHJE642 → YTP91ZSC84 → YULJCOIG74 → UNC50aWPE8 → aRMD8SOFA2 → YKHB6UQKH4 → UOF32YYMD8 → WVMB6UQF66 → QPOF6UMDCC → OEDB6UQONE → OFBA8SRQME → KHFA6URMKI → OH731ZYUKE → YVNA2YRE64 → WUPH8SKC76 → QNKD2YOHEC → WEB92YSQN6 → WQJF8SMIB6 → QKF70aUMHC → aNE72YUNE2 → YWN98SSE54 → URKJ8SIHA8 → MKH30aYKHG → aV632YYV62 → YWVPOCC654 → URPDBPOCA8 → MHEDAQONKG → GB962YVSQM → WPJF5VMIC6 → RPD70aUOCB → aNGDAQOLE2 → YGB94WSQL4 → USJF4WMI98 → SMJ70aUIFA → aNI70aUJE2 → aYN90aSE32 → aYVJ8SI632 → YVPK0aHC64 → aUPD2YOC72 → YWNDAQOE54 → URGB8SQLA8 → MKHF4WMKHG → S7632YYVUA → WVPNHJEC66 → QPD91ZSOCC → YJEDAQONI4 → UGB90aSQL8 → aMJF4WMIF2 → YS770aUU94 → aUNNIIEE72 → YN98bbSSE4 → XTPE4WNC85 → TRLD8SOGA9 → LJHB4WQKIH → SF430aYXMA → aVTI6UJ862 → YPOL0aGDC4 → aUDB4WQO72 → YSNFAQME94 → UJG96USLI8 → OMJ50aWIFE → aRA70aURA2 → aYNHGKKE32 → YV942YXS64 → WUTPIIC876 → QNLCbbOGEC → PPC81ZTPCD → YLDDBPOOG4 → UEBB4WQQN8 → SMFF8SMMFA → KI776UUUJI → ONN20aZEEE → aXA98SSR42 → YTKJGKIH84 → UL430aYXG8 → aVTM4WF862 → YSPL6UGC94 → UOJD4WOID8 → SMBB0aQQFA → aIFF6UMMJ2 → YO770aUUD4 → aUNNAQEE72 → YNG98SSLE4 → UKJ94WSIH8 → SMJ30aYIFA → aVI70aUJ62 → aYPN0aEC32 → aYVD8SO632 → YVPKAQHC64 → UPGD2YOLC8 → WMDB4WQOF6 → SQFB6UQMBA → OIFF6UMMJE → OA770aUURE → aNNH9RKEE2 → YI992YSSJ4 → WUJJ0aII76 → aQN10aaEB2 → aZYF8SM322 → YXVK6UH644 → UTPO2YDC88 → WMLDAQOGF6 → QGB74WUQLC → SNFE4WNMEA → SI996USSJA → OJJI0aJIIE → aA110aaaR2 → aZZYGK3222 → YXXV3X6444 → VTTTOC8887 → OLLLBPGGGE → EA554WWWRO → SRRH9RKAAA → JHHH2YKKKJ → W332bbYYY6 → ZYVS1Z9633 → YWVPIIC654 → URPCbbOCA8 → TRIF0aMJA9 → aKH70aUKH2 → aYN32YYE32 → YWVV8S6654 → URPPJHCCA8 → MHDD1ZOOKG → YBB62YVQQ4 → WUPFEMMC76 → QND86UTOEC → OLEB8SQNGE → KFA94WSRMI → SJH71ZUKIA → YNI30aYJE4 → aVU90aS762 → aYPNIIEC32 → YVD8bbSO64 → XVQI3XJB65 → USPF0aMC98 → aMJD6UOIF2 → YOB70aUQD4 → aUNFAQME72 → YNG96USLE4 → UOJ94WSID8 → SMJB0aQIFA → aIF70aUMJ2 → aYN70aUE32 → aYVN8SE632 → YVPK8SHC64 → UPKD2YOHC8 → WMDB2YQOF6 → WQFB6UQMB6 → QOFF6UMMDC → OEB76UUQNE → ONFA8SRMEE → KHA96USRKI → OJH31ZYKIE → YVA30aYR64 → aVUPGKC762 → YPND3XOEC4 → VTDB8SQO87 → OLKFAQMHGE → GA752YWURM → WRNH5VKEA6 → RPH92YSKCB → WJGD2YOLI6 → WQB50aWQB6 → aRQFEMMBA2 → YHF86UTMK4 → UOL72YUGD8 → WNMB4WQFE6 → SQF96USMBA → OJIF6UMJIE → OA710aaURE → aZNH9RKE22 → YXI92YSJ44 → WUTJ0aI876 → aQNL0aGEB2 → aYF94WSM32 → YVSJ6UI964 → UPOJ0aIDC8 → aMDB0aQOF2 → aYFB6UQM32 → YVOF6UMD64 → UPOB6UQDC8 → OMFDAQOMFE → GBA76UURQM → ONHF5VMKEE → QA972YUSRC → WNJHDNKIE6 → QA930aYSRC → aVJHDNKI62 → YPA30aYRC4 → aVUHCOK762 → YPNC2YPEC4 → WUDD8SOO76 → QNKBAQQHEC → GFE92YSNMM → WJ975VUSI6 → RPNJ0aIECB → aGD90aSOL2 → aYJB4WQI32 → YVSF0aM964 → aUPJ6UIC72 → YOND0aOED4 → aUBB8SQQ72 → YNKFEMMHE4 → U9872YUTS8 → WNMLIIGFE6 → Q974bbWUSC → XUNI1ZJE75 → YSN90aSE94aUJJ8SII72YNK10aaHE4aZU92YS722YXWNIIE544UTR8bbSA88TTMJ0aIF89aLK70aUHG2aYN52YWE32YWVR8SA654URPKGKHCA8MHD42YXOKGWTB62YVQ86WQPLEMGCB6QFD84WTOMCSLEB6UQNGAOIF94WSMJESJA70aURIAaNIH0aKJE2aY930aYS32aYVVII6632YVPObbCC64XVMJ0aIF65aSP70aUC92aYNJCOIE32YVC90aSP64aUPJCOIC72YNDC0aPOE4aUDB8SQO72YNKFAQMHE4UG972YUSL8WNMJ4WIFE6SQ970aUSBAaNJIEMJIE2Y9810aaTS4aZULIIG722YXN4bbWE44XXUJ8SI745TSNK0aHE99aKJ92YSIH2YWJ30aYI54aVUR0aA762aYPNGKEC32YVD93XSO64VTPJAQIC87OLGD0aOLGEaBA54WWRQ2YSRHEMKA94UJH82YTKI8WML30aYGF6aVQ74WUB62YSPNEMEC94UJD97TSOI8NLJB0aQIGFaF850aWTM2aYRL6UGA32YVOH4WKD64USPB2YQC98WMJFCOMIF6QC770aUUPCaNNECONEE2YC998SSSP4UKJJCOIIH8MC310aaYPGaZVD5VO622YXQPAQCB44UTGFCOML88MLC74WUPGGSND64WVOEASPIB8SQJCAKIFD0aOMJIaB720aZUQ2aYXNEME432YVT97TS864UPMLIIGFC8MD74bbWUOGXUJE1ZNI75YSN90aSE94