Base 34: 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 → 1W → U3Q7IF2VS5MBANCL8PGH0XW1U3
319 max steps100 → 0XX → WX1 → VX2 → UX3 → TX4 → SX5 → RX6 → QX7 → PX8 → OX9 → NXA → MXB → LXC → KXD → JXE → IXF → HXG → GXHGXH
411 max steps400D → D3TL → Q7P8 → JGGF → 3XXU → U2U4 → SP76 → MHFCA1VOUDJ4Q5R8MHFC
518 max steps30000 → 2XXXV → V1XV3 → WRX52 → VQX63 → UOX84 → TLXB5 → SHXF6 → RCXK7 → QEXI8 → PBXL9 → ODXJA → NAXMB → NBXLB → MBXLC → M9XNCOAXMANDXJBM9XNC
6110 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 → OD1VKAUE6QJ4QK4SD8OI6QFAKE2UJES64SR6OMKCBAEB7PMKIB5RMGMB1VMCUB9NM4QEAMJ8IC4SLGO91VOAUFDJI4Q62UR8SLHFC6M91VOCUF9NI4QE2UJ8SI4SF6OM2UBASEAMJ6MC4SLCOA8ONAGECKJI851VSQUNHFA4QD1VK8UI6QF4QK2UD8SI6QF6MK2UDCSA6QN6MKCKDCA86QPOKHDJGE750WSRWNJDA2UD5RK4QM6QB8KIAMFEC62URMSL9NC6ME8OJCGA4SNIOD1VKA
728 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 → RH8XOG7QJ7XPE8QIAXMF8PG6XQH9RH8XOG7
8114 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 → UOLAMC94QFC8OLI8IG92UOHGSF20WVI6WTM2UB42USPAM854QNHBLGA8IDA0WNKGWD71VQK2VTJ6QE43SPK4SD86OMH6QGBAKEB0WMJEWB64SRM2UOLAMC94
947 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 → SMF7XPIB6RLE6XQJC7RKE6XQJD7RKD5XRKD7SKE6XQJD6RMD5XRKB7SKG8XOHD6RKB3XTMD7UMG8XOHB4TMD5XRKB5SOG8XOH96RKF7XPID7QKC4XSLD8TKE7XPJD5SMC5XRLB6SMG9XNHB6RJC5XRLE7SKF6XQID6RMD4XSKB7TLG8XOHC5SLC4XSLC6TMG8XOHB5SLD5XRKC6SMF7XPIB6
10171 max steps100000889G → G9880WPPOI → WHHF1VIGG2 → VT310WWU43 → WVSRO86522 → UTNLFHCA44 → QPD91VOK88 → UIHF6QIGF4 → QK330WUUD8 → WRRI6QF662 → ULLK2UDCC4 → SQ996QOO76 → MKJFEIIEDC → A7542UTSQO → SPNJDJEA86 → MHD64SRKGC → OLA70WQNCA → WJED8OKJE2 → UG754SSQH4 → QONJ0WEA98 → WIFD4SKIF2 → UO732UUQ94 → SRQJEIE766 → MLJ53TSECC → QNA94SONA8 → OIFDCKKIFA → E8732UUQPK → SRJH5RGE66 → NLL50WSCCB → WNC98OOLA2 → UGFD8OKIH4 → QG730WUQH8 → WRJI0WFE62 → WUL52USC32 → USRN8OA654 → QNLGCKHCA8 → ID980WPOKG → WHF71VQIG2 → VTJ30WUE43 → WSRP4S8652 → UONLGGCA94 → QFD8XXOKI8 → PPD91VOK89 → UHGF6QIHG4 → QK310WWUD8 → WVRI6QF622 → UTLK2UDC44 → SQP96QO876 → MKJHEIGEDC → A7540WTSQO → WPNJDJEA82 → UHD64SRKG4 → QOL70WQC98 → WJIF8OIFE2 → UG532UUSH4 → SRQN0WA766 → WMLJCKECB2 → UB984SPOM4 → QOHFAMIG98 → IFC30WULIG → WR931VUO62 → VTRLEIC643 → SPL93TOC86 → QMHF8OIGB8 → IGB30WUMHG → WRB20WVM62 → WUTLAMC432 → URPC8OL864 → QLHG8OHGC8 → IG910WWOHG → WVF20WVI22 → WUTT2U4432 → USRPO88654 → QNLHFHGCA8 → ID920WVOKG → WTF71VQI42 → VTPJ2UE843 → TRPH4SG865 → PNLH0WGCA9 → WGD90WOKH2 → WUF70WQI32 → WURJ2UE632 → USRL4SC654 → QONL8OCA98 → IGFD8OKIHG → G7320WVUQI → WTRJ1VE642 → VTPL4SC843 → SPOH8OG986 → MHGF0WIHGC → WA310WWUN2 → WVURCK6322 → UTRL7PC644 → QPLI8OFC88 → IHG92UOHGG → SF210WWVI6 → WVTM2UB422 → UTSPAM8544 → QPNHBLGA88 → IHDA0WNKGG → WD720WVQK2 → WUTJ6QE432 → URPK4SD864 → QOLH6QGC98 → KIF90WOIFE → WF632UURI2 → USRL2UC654 → SQNL8OCA76 → MJGD8OKHEC → GA750WSQNI → WNJD1VKEA2 → VTD74SQK43 → SPOJ6QE986 → MKHF4SIGDC → OA730WUQNA → WRJECKJE62 → UL854SSPC4 → QONH8OGA98IGFD0WKIHGW7320WVUQ2WUTRIE6432URPL3TC864RPLH8OGC87KHG90WOHGEWF610WWRI2WVUL2UC322UTSR8O6544QPNLFHCA88IHD91VOKGGUF720WVQI4WTQJ2UE742USPJ4SE854QONH4SGA98OIFD0WKIFAWE732UUQJ2USRJ4SE654QONL4SCA98OIFD8OKIFAGE732UUQJISRJ51VSE66UNML4SCBA4QODB8OMK98IGFB6QMIHGKB320WVUMEWTRB5RM642UPMLAMCB84QHCB8OMLG8IGB90WOMHGWFB20WVMI2WUTB2UM432USRPAM8654QNLHBLGCA8IDA90WONKGWFD71VQKI2VTJ72UQE43TRPJ4SE865PNLH4SGCA9OGD90WOKHAWFE70WQJI2WUJ52USE32USRN4SA654QONLCKCA98IFD97POKIGIF731VUQIGURJ31VUE64URQL4SC764QOLJ8OEC98IGF94SOIHGOF320WVUIAWTRE2UJ642USPL4SC854QONH8OGA98
11107 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 → 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