Base 34: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1W → U3
318 max steps100 → 0XX → WX1 → VX2 → UX3 → TX4 → SX5 → RX6 → QX7 → PX8 → OX9 → NXA → MXB → LXC → KXD → JXE → IXF → HXG → GXH
47 max steps400D → D3TL → Q7P8 → JGGF → 3XXU → U2U4 → SP76 → MHFC
515 max steps30000 → 2XXXV → V1XV3 → WRX52 → VQX63 → UOX84 → TLXB5 → SHXF6 → RCXK7 → QEXI8 → PBXL9 → ODXJA → NAXMB → NBXLB → MBXLC → M9XNC
664 max steps50008T → T84SP5 → PNGGA9 → GCXXKI → LH1VGD → U80WP4 → WQGG72 → UIXXE4 → TJBLE5 → OA4SNA → OECKJA → E84SPK → OH5RGA → ME0WJC → WA4SN2 → UOCK94 → QF7PI8 → JH2UGF → S40WT6 → WPLB82 → UH9NG4 → QE0WJ8 → WI4SF2 → UO2U94 → SQEI76 → MJ3TEC → QA4SN8 → OICKFA → E82UPK → SH5RG6 → NL0WCB → WC8OL2 → UG8OH4 → QG0WH8 → WI0WF2 → WU2U32 → USQ654 → QNJDA8 → ID5RKG → M71VQC → UJ9NE4 → QE4SJ8 → OI4SFA → OE2UJA → SE4SJ6 → OM4SBA → OEAMJA → EC4SLK → O95ROA → MFDJIC → A62URO → SLDJC6 → M95ROC → MF9NIC → EA2UNK → SD5RK6 → NL6QCB → KC8OLE → G95ROI → MF1VIC → UA2UN4 → SQCK76 → MJ7PEC → IA4SNG → OD1VKA
724 max steps50000FH → HF4XSIH → TD0XWK5 → XRFXH61 → WRBXL62 → VQFXH73 → UOAXM94 → TLDXJC5 → SH7XPG6 → RL8XOC7 → QJBXLE8 → PF6XQI9 → RH9XNG7 → QI6XQF8 → RIAXMF7 → QH6XQG8 → RI9XNF7 → QI7XPF8 → QI9XNF8 → PH7XPG9 → QG8XOH8 → PI7XPF9 → QG9XNH8 → PH6XQG9 → RH8XOG7
8100 max steps300003CD → DC32UULL → SR97PO66 → MLIEIFCC → A942UTOO → SPFDJI86 → MH62URGC → SLA0WNC6 → WMD8OKB2 → UGB6QMH4 → QKB0WMD8 → WIB6QMF2 → UKB2UMD4 → SQB6QM76 → MKJAMEDC → CA74SQNM → OJD9NKEA → FD74SQKJ → OJ73TQEA → QJE4SJE8 → OI54SSFA → ONE2UJAA → SED4SKJ6 → OM74SQBA → OJEAMJEA → EC54SSLK → ON95ROAA → MFECKJIC → A852USPO → SNHDJGA6 → MD60WRKC → WLA6QNC2 → UKD8OKD4 → QG76QQH8 → KJI0WFEE → W652USR2 → USNKCA54 → QND7PKA8 → JHD6QKGF → K740WTQE → WPJ5RE82 → UMH4SGB4 → QOB0WM98 → WIFAMIF2 → UC32UUL4 → SRQ8O766 → MLJFHECC → A951VSOO → UNFDJIA4 → QD62URK8 → SLI6QFC6 → MK92UODC → SFA6QNI6 → MKD2UKDC → SA76QQN6 → MKJCKEDC → A874SQPO → OJHDJGEA → E650WSRK → WNL5RCA2 → UMD8OKB4 → QGB6QMH8 → KIB0WMFE → WB62URM2 → USLAMC54 → QNC8OLA8 → IGD8OKHG → G720WVQI → WTJ1VE42 → VTP4S843 → SPOGG986 → MHEXXIGC → LJ60WRED → WL84SPC2 → UOH8OG94 → QGF0WIH8 → WI30WUF2 → WUR2U632 → USRKC654 → QNL7PCA8 → JHD8OKGF → G740WTQI → WPJ1VE82 → VTH4SG43 → SPO0W986 → WMHEIGB2 → UB40WTM4 → WQPAM872 → UJHBLGE4 → QA50WSN8 → WNICKFA2 → UD82UPK4 → SQH6QG76 → MKJ0WEDC → WA74SQN2 → UOJCKE94 → QF84SPI8 → OIH2UGFA → SE30WUJ6 → WRM4SB62 → UOLAMC94
924 max stepsC0000000C → CBXXXXXLM → MLCAXMLCC → NAA8XONNB → PEDBXLKJ9 → OE85XRPJA → SJF9XNIE6 → RJ93XTOE7 → UMI9XNFB4 → TLC6XQLC5 → SNE8XOJA6 → RKE8XOJD7 → QJB5XRME8 → SJF7XPIE6 → RLB3XTMC7 → UMG9XNHB4 → TLC5XRLC5 → SOF8XOI96 → RKF8XOID7 → QJB4XSME8 → TKF7XPID5 → SMC4XSLB6 → TMH9XNGB5 → SKC5XRLD6 → SMF7XPIB6
10156 max steps3000006GXX → XXG62URH01 → XWSL0WC511 → XVVN8OA221 → WTTGCKH442 → UPP80WP884 → WQHHGGGG72 → UJ10XXWWE4 → XWSIAMF511 → WVNC2ULA22 → UTSD8OK544 → QPNG6QHA88 → KIHD0WKGFE → W7630WURQ2 → WURLIEC632 → URL93TOC64 → RPLF8OIC87 → KHG92UOHGE → SF610WWRI6 → WVML2UCB22 → UTSB8OM544 → QPNGAMHA88 → IHDC0WLKGG → W9720WVQO2 → WUTJEIE432 → URP53TS864 → RPNLGGCA87 → KHD8XXOKGE → PKA42UTND9 → SPGD6QKH86 → MKH70WQGDC → WJA70WQNE2 → WUJD4SKE32 → URO74SQ964 → QOLJEIEC98 → IF953TSOIG → QNF31VUIA8 → URID2UKF64 → SQL72UQC76 → SMJJ8OEEB6 → MGB54SSMHC → ONBA0WNMAA → WEDDAMKKJ2 → UC774SQQL4 → QOJJ8OEE98 → IGF54SSIHG → ON320WVUAA → WTRECKJ642 → UPL84SPC84 → QOHH8OGG98 → IGF10WWIHG → WV320WVU22 → WUTTQ64432 → URPPJD8864 → QLHH5RGGC8 → MI910WWOFC → WVFA2UNI22 → UTSD2UK544 → SQPN6QA876 → MKJHCKGEDC → A8750WSQPO → WNJHDJGEA2 → UD650WSRK4 → WQNL6QCA72 → UKJD8OKED4 → QG774SQQH8 → OJJI0WFEEA → WE552USSJ2 → USNN4SAA54 → QONDCKKA98 → IFD86QPKIG → KH731VUQGE → URJ60WRE64 → WQLL4SCC72 → UOJ98OOE94 → QGFF4SIIH8 → OI330WUUFA → WRRE2UJ662 → USLL4SCC54 → QON98OOA98 → IGFFCKIIHG → 83320WVUUQ → WTRRHF6642 → UPLL1VCC84 → UQH98OOG74 → QJGF0WIHE8 → WI530WUSF2 → WURN2UA632 → USRLCKC654 → QNL97POCA8 → JHFD8OKIGF → G7430WUTQI → WRPJ1VE862 → VTLH4SGC43 → SPO90WO986 → WMHFEIIGB2 → UB430WUTM4 → WRQPAM8762 → ULJHBLGEC4 → QA950WSON8 → WNIFCKIFA2 → UD832UUPK4 → SRQH6QG766 → MLKJ0WEDCC → WA974SQON2 → UOJFCKIE94 → QF852USPI8 → SNIH2UGFA6 → SMD30WUKB6 → WRMB6QMB62 → ULKBAMMDC4 → QCB96QOML8 → KIFB8OMIFE → GB632UURMI → SRLB1VMC66 → UMLB8OMCB4 → QGBB8OMMH8 → IGBB0WMMHG → WBB20WVMM2 → WUTBAMM432 → URPCAML864 → QLHC8OLGC8 → IG990WOOHG → WFF20WVII2 → WUT32UU432 → USRRO86654 → QNLLFHCCA8 → ID991VOOKG → UFF71VQII4 → UQJ32UUE74 → SRQJ4SE766 → OMLJ4SECBA → OEB94SOMJA → OFEB4SMJIA → OEB52USMJA → SNEB4SMJA6 → OMDB4SMKBA → OEBB6QMMJA → KEBB4SMMJE → OBB64SRMMA → OLEBAMMJCA → ECB94SOMLK → OFB95ROMIA → MFEB2UMJIC → SBA52USNM6 → SNMDAMKBA6 → MDCB6QMLKC → KBA96QONME → KFDB5RMKIE → MB762URQMC → SLJB9NMEC6 → MEB94SOMJC → OFBA4SNMIA → OEDB2UMKJA → SEB74SQMJ6 → OMJB4SMEBA → OEBB4SMMJA
1157 max steps900000000GQ → QG8XXXXXOH8 → PPHG8XOHG89 → PHG80XWPHG9 → XOG90XWOH91 → XWNF7XPIA11 → WWPF7XPI812 → WUPH9XNG832 → VTMG6XQHB43 → URNF5XRIA64 → TPLH7XPGC85 → SMHD4XSKGB6 → TMH93XTOGB5 → UOKD5XRKD94 → TPIB6XQMF85 → SNIE6XQJFA6 → RMG93XTOHB7 → UMID5XRKFB4 → TPG94XSOH85 → TOKG7XPHD95 → SMGB3XTMHB6 → UNHB5XRMGA4 → TPHC5XRLG85 → SOJD4XSKE96 → TMJB5XRMEB5 → SOGB7XPMH96 → RLGD5XRKHC7 → SKF83XTPID6 → UNKC4XSLDA4 → TQIB7XPMF75 → SMJE6XQJEB6 → RMF84XSPIB7 → TLJE6XQJEC5 → SNE74XSQJA6 → TMLG8XOHCB5 → SLDA4XSNKC6 → TMIB7XPMFB5 → SMEB6XQMJB6 → RMFB7XPMIB7 → QKEB6XQMJD8 → RIF95XROIF7 → SKI92XUOFD6 → VOJB4XSME93 → URJD7XPKE64 → TOKC5XRLD95 → SOIC7XPLF96 → RLGC5XRLHC7 → SKF94XSOID6 → TMJB4XSMEB5 → TOHB7XPMG95 → SMGD5XRKHB6 → SMG93XTOHB6 → UNJD5XRKEA4 → TPHA5XRNG85 → SOJF6XQIE96 → RMHA3XTNGB7 → UMHC5XRLGB4 → TPGA4XSNH85