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 steps1 → 0 → 0
214 max steps20 → 1W → U3 → Q7 → IF → 2V → S5 → MB → AN → CL → 8P → GH → 0X → W1 → U3
319 max steps100 → 0XX → WX1 → VX2 → UX3 → TX4 → SX5 → RX6 → QX7 → PX8 → OX9 → NXA → MXB → LXC → KXD → JXE → IXF → HXG → GXH → GXH
411 max steps400D → D3TL → Q7P8 → JGGF → 3XXU → U2U4 → SP76 → MHFC → A1VO → UDJ4 → Q5R8 → MHFC
518 max steps30000 → 2XXXV → V1XV3 → WRX52 → VQX63 → UOX84 → TLXB5 → SHXF6 → RCXK7 → QEXI8 → PBXL9 → ODXJA → NAXMB → NBXLB → MBXLC → M9XNC → OAXMA → NDXJB → M9XNC
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 → OD1VKA → UE6QJ4 → QK4SD8 → OI6QFA → KE2UJE → S64SR6 → OMKCBA → EB7PMK → IB5RMG → MB1VMC → UB9NM4 → QEAMJ8 → IC4SLG → O91VOA → UFDJI4 → Q62UR8 → SLHFC6 → M91VOC → UF9NI4 → QE2UJ8 → SI4SF6 → OM2UBA → SEAMJ6 → MC4SLC → OA8ONA → GECKJI → 851VSQ → UNHFA4 → QD1VK8 → UI6QF4 → QK2UD8 → SI6QF6 → MK2UDC → SA6QN6 → MKCKDC → A86QPO → KHDJGE → 750WSR → WNJDA2 → UD5RK4 → QM6QB8 → KIAMFE → C62URM → SL9NC6 → ME8OJC → GA4SNI → OD1VKA
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 → RH8XOG7 → QJ7XPE8 → QIAXMF8 → PG6XQH9 → RH8XOG7
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 → UOLAMC94 → QFC8OLI8 → IG92UOHG → SF20WVI6 → WTM2UB42 → USPAM854 → QNHBLGA8 → IDA0WNKG → WD71VQK2 → VTJ6QE43 → SPK4SD86 → OMH6QGBA → KEB0WMJE → WB64SRM2 → UOLAMC94
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 → SMF7XPIB6 → RLE6XQJC7 → RKE6XQJD7 → RKD5XRKD7 → SKE6XQJD6 → RMD5XRKB7 → SKG8XOHD6 → RKB3XTMD7 → UMG8XOHB4 → TMD5XRKB5 → SOG8XOH96 → RKF7XPID7 → QKC4XSLD8 → TKE7XPJD5 → SMC5XRLB6 → SMG9XNHB6 → RJC5XRLE7 → SKF6XQID6 → RMD4XSKB7 → TLG8XOHC5 → SLC4XSLC6 → TMG8XOHB5 → SLD5XRKC6 → SMF7XPIB6
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 → QONH8OGA98 → IGFD0WKIHG → W7320WVUQ2 → WUTRIE6432 → URPL3TC864 → RPLH8OGC87 → KHG90WOHGE → WF610WWRI2 → WVUL2UC322 → UTSR8O6544 → QPNLFHCA88 → IHD91VOKGG → UF720WVQI4 → WTQJ2UE742 → USPJ4SE854 → QONH4SGA98 → OIFD0WKIFA → WE732UUQJ2 → USRJ4SE654 → QONL4SCA98 → OIFD8OKIFA → GE732UUQJI → SRJ51VSE66 → UNML4SCBA4 → QODB8OMK98 → IGFB6QMIHG → KB320WVUME → WTRB5RM642 → UPMLAMCB84 → QHCB8OMLG8 → IGB90WOMHG → WFB20WVMI2 → WUTB2UM432 → USRPAM8654 → QNLHBLGCA8 → IDA90WONKG → WFD71VQKI2 → VTJ72UQE43 → TRPJ4SE865 → PNLH4SGCA9 → OGD90WOKHA → WFE70WQJI2 → WUJ52USE32 → USRN4SA654 → QONLCKCA98 → IFD97POKIG → IF731VUQIG → URJ31VUE64 → URQL4SC764 → QOLJ8OEC98 → IGF94SOIHG → OF320WVUIA → WTRE2UJ642 → USPL4SC854 → QONH8OGA98
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 → TPGA4XSNH85 → TOKF6XQID95 → SNHB4XSMGA6 → TMIC5XRLFB5 → SOGA5XRNH96 → SMIE6XQJFB6 → RMF83XTPIB7 → UMJE6XQJEB4 → TOF84XSPI95 → TOKG8XOHD95 → SLFB3XTMIC6 → UNHA5XRNGA4 → TPHD6XQKG85 → SNIC3XTLFA6 → UNIB5XRMFA4 → TPHC6XQLG85 → SNID4XSKFA6 → TMIA4XSNFB5 → TOIC6XQLF95 → SNHC5XRLGA6 → SMHB4XSMGB6 → TMHB5XRMGB5 → SOGB5XRMH96 → SMID5XRKFB6 → SMG94XSOHB6 → TMJD5XRKEB5 → SOG95XROH96 → SMIF7XPIFB6 → RLE72XUQJC7 → VNKE6XQJDA3 → UPGA5XRNH84 → TPJF6XQIE85 → SNIB3XTMFA6 → UNIC6XQLFA4 → TOGB5XRMH95 → SOID5XRKF96 → SMIB4XSMFB6 → TMHB6XQMGB5 → SNFB5XRMIA6 → SMHC6XQLGB6 → RMFA4XSNIB7 → TLHC6XQLGC5 → SNE94XSOJA6 → TMJE8XOJEB5 → SLD84XSPKC6 → TMKD7XPKDB5 → SME96XQOJB6 → RMHD7XPKGB7 → QKE93XTOJD8 → ULHB5XRMGC4 → TPGA4XSNH85