Base 35: 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 → 0Y → X1 → V3 → R7JF3VR7
320 max steps100 → 0YY → XY1 → WY2 → VY3 → UY4 → TY5 → SY6 → RY7 → QY8 → PY9 → OYA → NYB → MYC → LYD → KYE → JYF → IYG → HYHGYIHYH
416 max stepsI000 → HYYH → HGHI → 1YYX → X0X2XU32VQ74RIF8J2VGT2V6TMB6NANCDANMD8PMH8PIH0XIX0X2
521 max steps30000 → 2YYYW → W1YW3 → XSY52 → WRY63 → VPY84 → UMYB5 → TIYF6 → SDYK7 → REYJ8 → QCYL9 → PDYKA → OBYMB → NCYLC → MAYND → O9YOB → PCYLA → OCYLBNBYMCNAYNCOAYNBOCYLB
653 max steps40008T → T83UQ6 → RNHGB8 → JC0XMG → XA2VO2 → VTDK54 → RO6RA8 → LJDKFE → 863USR → RMIFC8 → JA2VOG → TE2VK6 → TN5SB6 → OMBMCB → DB9ONM → FC8PMK → HA4TOI → PE0XKA → XF5SJ2 → VN3UB4 → SQBM87 → LIANGE → D71WRM → VK8PE4 → RH5SH8 → NIYYFC → MJ4TFD → P93UPA → RGEJI8 → J51WTG → VO2VA4 → TRDK76 → NK6REC → LB5SNE → NC6RMC → LB9ONE → FC6RMK → LA4TOE → PE6RKA → LF5SJE → N73URC → RKANE8 → JD5SLG → N82VQC → TIANG6 → ND1WLC → VB7QN4 → RJBMF8JB3UNGRC2VM8TJ9OF6NF3UJCRB3UN8RJBMF8
742 max steps600000H → H5YYYSI → THFYIH6 → SE0YXK7 → YQDYK81 → XQCYL82 → WPDYK93 → VNBYMB4 → UKBYME5 → TJ7YQF6 → SMAYNC7 → RIAYNG8 → QH6YRH9 → SI8YPG7 → RK8YPE8 → QJAYNF9 → PG7YQIA → RG8YPI8 → QJ8YPF9 → QH9YOH9 → PH6YRHA → SH7YQH7 → RL8YPD8 → QJBYMF9 → PF6YRJA → SH9YOH7 → RJ6YRF8 → SJBYMF7 → RH6YRH8 → SJ9YOF7 → RJ8YPF8 → QJ9YOF9 → PH8YPHA → QF7YQJ9 → RHAYNH8QH5YSH9TJ8YPF6SL9YOD7RJAYNF8QH7YQH9RH8YPH8QJ7YQF9RHAYNH8
895 max steps10000000 → 0YYYYYYY → XYYYYYY1 → X0YYYYX2 → YW10XX21 → YWWT4221 → XUUO9442 → VQQEJ884 → RII4TGG8 → PJ21WWFA → VUF3UJ44 → SQQ3U887 → RLIHGGD8 → J820XWQG → XUI2VG42 → VTQ1W854 → VROHGA74 → RKE0XKE8 → XJ65SSF2 → VNM3UCB4 → SQC9OM87 → LIF9OJGE → F741WURK → VQK4TE84 → RPI5SG98 → NJG1WIFC → VB41WUN4 → VRQBM874 → RKIANGE8 → JD61WSLG → VM82VQC4 → TRI9OG76 → NKF1WJEC → VB63USN4 → SQMBMC87 → LIB9ONGE → FC71WRMK → VKA4TOE4 → RPE5SK98 → NJG5SIFC → NB41WUNC → VQCANM84 → RID9OLG8 → JF81WQJG → VI42VUG4 → TRQ1W876 → VNKHGEB4 → RC60XSM8 → XMJ9OFC2 → VFA3UOJ4 → SQE3UK87 → RLI5SGD8 → NJ81WQFC → VIB3UNG4 → SQC1WM87 → VLI9OGD4 → RF81WQJ8 → VJI3UGF4 → SQ41WU87 → VQLHGD84 → RI80XQG8 → XJI1WGF2 → WU41WU43 → VTQP8854 → ROIGHGA8 → JE20XWKG → XU62VS42 → VTQLC854 → ROI8PGA8 → JHE1WKHG → V62YYVS4 → WUP2V943 → USQFI865 → PMI2VGCA → TFA1WOJ6 → VNE3UKB4 → SQC5SM87 → NLI9OGDC → FB81WQNK → VIC4TMG4 → RPA1WO98 → VJGDKIF4 → R741WUR8 → VQKIFE84 → RI62VSG8 → TMJ1WFC6 → VNA3UOB4 → SQEBMK87 → LIB5SNGE → NC71WRMC → VKB9ONE4 → RFC5SMJ8 → NJA3UOFCREB3UNK8RJC5SMF8NJA3UOFC
957 max steps5000000FW → WF4YYYTJ3 → VUJCYLF44 → URI5YSG75 → TPLAYND96 → SKF9YOJE7 → RJA4YTOF8 → ULH8YPHD5 → TMC3YUMC6 → VOH9YOHA4 → UME6YRKC5 → TOF7YQJA6 → SMG8YPIC7 → RKD5YSLE8 → TKE6YRKE6 → SND5YSLB7 → TLH9YOHD6 → SKB3YUNE7 → VNH8YPHB4 → UNE5YSKB5 → TPH8YPH96 → SLG7YQID7 → RLD4YTLD8 → ULE7YQKD5 → TND6YRLB6 → SNG9YOIB7 → RJD6YRLF8 → SJE5YSKF7 → TLE4YTKD6 → UNG6YRIB5 → TOG6YRIA6 → SNH7YQHB7 → RLF5YSJD8 → TKE5YSKE6 → TNE5YSKB6 → TNH8YPHB6 → SLE5YSKD7TLF6YRJD6SNE5YSKB7TLH8YPHD6SLC3YUMD7VNG8YPIB4UNE6YRKB5TOG8YPIA6SLF7YQJD7RLD5YSLD8TKE7YQKE6SMC5YSMC7TLG9YOID6SKB4YTNE7UMH8YPHC5TMD4YTLC6UNH8YPHB5TME5YSKC6TNG7YQIB6SMF6YRJC7SLF6YRJD7SLE5YSKD7
10105 max stepsC00000PPYY → YYPPBM9901 → YXGGANII11 → XWD21WWL22 → WUUU7Q4443 → TQQQIF8886 → NIII2VGGGC → TB221WWWN6 → VUUNBMB444 → RQQCANM888 → JIID9OLGGG → F8321WWVQK → VUSI4TG644 → RQPM1WC988 → VJIG9OIGF4 → RF421WWUJ8 → VUQJ3UF844 → SQQI3UG887 → RLII1WGGD8 → VJ821WWQF4 → VURI3UG744 → SQQK1WE887 → VLII5SGGD4 → RN821WWQB8 → VUJIBMGF44 → RQB41WUN88 → VQJIBMGF84 → RIB41WUNG8 → VQJC1WMF84 → VRIA3UOG74 → SQKE1WKE87 → VLI65SSGD4 → RNM81WQCB8 → VJIC9OMGF4 → RFA41WUOJ8 → VQJE3UKF84 → SQI63USG87 → RMLI1WGDC8 → VJA81WQOF4 → VRIE3UKG74 → SQK61WSE87 → VMLI5SGDC4 → RNA81WQOB8 → VJIEBMKGF4 → RB641WUSN8 → VQMJBMFC84 → RIBA3UONG8 → RJEC1WMKF8 → VJA63USOF4 → SQME3UKC87 → RLIA5SOGD8 → NJE81WQKFC → VIB63USNG4 → SQMC1WMC87 → VLIA9OOGD4 → RFE81WQKJ8 → VJI63USGF4 → SQM41WUC87 → VQLI9OGD84 → RIF81WQJG8 → VJI41WUGF4 → VRQ41WU874 → VRQKHGE874 → RKI60XSGE8 → XMJ61WSFC2 → WUMA3UOC43 → TRQE9OK876 → NKIF5SJGEC → NB641WUSNC → VQMCANMC84 → RIDA9OOLG8 → JFE81WQKJG → VI642VUSG4 → TRQM1WC876 → VNKI9OGEB4 → RFC61WSMJ8 → VMJA3UOFC4 → SQEA3UOK87 → RLIE5SKGD8 → NJ861WSQFC → VMIB3UNGC4 → SQCA1WOM87 → VLIE9OKGD4 → RF861WSQJ8 → VMJI3UGFC4 → SQA41WUO87 → VQLIDKGD84 → RI871WRQG8 → VKJI1WGFE4 → VR641WUS74 → VRQMJEC874 → RKIA4TOGE8 → PJE61WSKFA → VMF63USJC4 → SQMA3UOC87 → RLIE9OKGD8 → JF861WSQJG → VMI42VUGC4 → TRQA1WO876 → VNKIDKGEB4 → RC761WSRM8 → VMKJ9OFEC4 → RFA63USOJ8 → RMJE3UKFC8RJA63USOF8RMJE3UKFC8