Base 31: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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 → 0U → T1 → R3 → N7 → FF → 0000
318 max steps100 → 0UU → TU1 → SU2 → RU3 → QU4 → PU5 → OU6 → NU7 → MU8 → LU9 → KUA → JUB → IUC → HUD → GUE → FUFEUGFUF
49 max stepsG000 → FUUF → FEFG → 1UUT → T0T2TQ32RM74NEF8F0TGT0T2
518 max stepsF0000 → EUUUG → GDUGF → H0UTE → UEUF1 → TFUE2 → SEUF3 → RDUG4 → QDUG5 → PCUH6 → OCUH7 → NBUI8 → MBUI9 → LAUJA → KAUJB → K8ULBM9UK9LCUHAK8ULB
668 max stepsD000UU → UUCH01 → UT4P11 → TSK922 → RQAJ44 → NM8L88 → FECHGG → 520TSQ → TQK942 → RMAJ84 → NE8LG8 → FD1SHG → R40TQ4 → TNL872 → RGCHE4 → N51SP8 → RKEFA4 → NA0TK8 → TF9KF2 → RAUUJ4 → QK7MA5 → LF9KFA → C9UUKJ → LI0TCA → TB5OJ2 → RJ7MB4 → NF7MF8 → GDUUGF → HEUUFE → GG1SEF → R20TS4 → TQM742 → RMEF84 → NE0TG8 → TF1SF2 → SPUU43RQ2R44PNL876JGCHEC751SPORKGDA4NA2RK8PF9KF6JAUUJCKHUUCBJI2RCCP75ON6KIFECB960TOMTICHC2R64PO4NLHC98FC4PIGL60TOATIAJC2R95OL4NJBIB8F86NMGHE0TGET31SR2SQN643PMGD86JE2RGCP71SN6RJFEB4N80TM8TFDGF2R2UUR4SPUU43
739 max steps800000Q → Q7UUUM5 → PN7UM76 → OIFUEC7 → NC3UQI8 → RIAUJC4 → QH6UND5 → PK9UKA6 → OG9UKE7 → NF5UOF8 → PG7UME6 → OI7UMC7 → NH9UKD8 → ME6UNG9 → OE7UMG7 → NH7UMD8 → NF8ULF8 → MF5UOF9 → PF6UNF6 → OJ7UMB7 → NHAUJD8 → MD5UOH9 → PF8ULF6 → OH5UOD7 → PHAUJD6 → OF5UOF7 → PH8ULD6 → OH7UMD7 → NH8ULD8 → MF7UMF9 → ND6UNH8 → OF9UKF7NF4UPF8QH7UMD5PJ8ULB6OH9UKD7NF6UNF8OF7UMF7NH6UND8OF9UKF7
8101 max steps10000DFK → KFD0THFB → T93UUQL2 → SRK4PA33 → POL9K966 → JICAJICC → 9765OONM → JIGCHECC → 7651SPOO → RKIGDCA4 → NA62ROK8 → PIF9KFC6 → JB5UUOJC → PJBUUIB6 → OJE0TGB7 → TH81SMD2 → SQE3QG43 → PNM1S876 → RJGDGEB4 → N831SRM8 → ROFDGF64 → NI2UURC8 → SMF4PF83 → PLDUUG96 → OLC4PI97 → LHC5OIDA → JB63QOJC → NI86NMC8 → HFE5OGFE → J31UUSRC → TRG7ME32 → ROF1SF64 → RNHUUC74 → QNF5OF75 → LJFUUEBA → KJ73QNBB → NG97MLE8 → GEC1SIGF → R620TSO4 → TQNHC742 → RMG4PE84 → NLE1SG98 → RFC1SIF4 → RN5UUO74 → QPK0TA55 → TLK9KA92 → RCB9KJI4 → NB85OMJ8 → JFE7MGFC → F71UUSNG → TND6NH72 → RHG3QED4 → OM41SQ87 → RMHDGD84 → NE42RQG8 → PMF1SF86 → RJDUUGB4 → QJE2RGB5 → PL81SM96 → RJEBIGB4 → N871SNM8 → RGFDGFE4 → N31UUSR8 → TRK3QA32 → RON9K764 → NIGAJEC8 → F961SOLG → RIC0TIC4 → TN65OO72 → RJIFECB4 → N860TOM8 → TIFDGFC2 → R62UURO4 → SQL2R943 → QOMBI865 → LIE6NGCA → HB61SOJE → RI82RMC4 → PNE5OG76 → KIG1SECB → R961SOL4 → RNIBIC74NG75ONE8JGF1SFECR71UUSN4TQL3Q942RNMBI874NGE6NGE8HF21SSFERQ2UUR44SQN0T743TPMFE852RKE0TGA4TNA1SK72SQG9KE43PMB1SJ86RJE7MGB4NF81SMF8RFDUUGF4QHC0TID5TL63QO92RNIBIC74
945 max stepsF00000FFL → LFFEUFFFA → K6UUUUUNB → OJA6UNKB7 → OHD8ULHD7 → NG83UQME8 → RIF7UMFC4 → QKA2URKA5 → SMG9UKE83 → RKD5UOHA4 → QME6UNG85 → PKF7UMFA6 → OIC4UPIC7 → QIC5UOIC5 → PLC5UOI96 → PJF8ULFB6 → OHA3UQKD7 → RJE6UNGB4 → QLC4UPI95 → QLG8ULE95 → PIC6UNIC6 → OJB5UOJB7 → PHD7UMHD6 → OI93UQLC7 → RJF8ULFB4 → QJA3UQKB5 → RLG8ULE94 → QJC6UNIB5 → PKC6UNIA6 → OJD7UMHB7 → NHB5UOJD8 → PGC5UOIE6 → PJC3UQIB6 → RKE6UNGA4 → QLD5UOH95 → PLF7UMF96 → OID5UOHC7 → PHC4UPID6 → QJD4UPHB5 → QLE5UOG95PLF6UNF96OJE5UOGB7PHD4UPHD6QJC3UQIB5RLF6UNF94QLE5UOG95
10140 max steps7000000DDM → MDD6UUNHH9 → OLA8UULK97 → NMFB0TJF88 → TFE7UUMGF2 → SNF70TNF73 → TPGFUUEE52 → SPFB0TJF53 → TPK7UUMA52 → SPMF1SF853 → RPKDUUGA54 → QPHC3QID55 → NLK63QOA98 → NIFC9KIFC8 → FB65UUOOJG → POD92RLH66 → PJIC3QICB6 → NJ865OOMB8 → JIFE7MGFCC → F761UUSONG → TOL96NL962 → RIHCBIIDC4 → N7663QOON8 → NIIGEFECC8 → F6620TSOOG → TQII0TCC42 → TRM65OO832 → ROJIDGCB64 → NI862ROMC8 → PIFE5OGFC6 → KI61UUSOCB → TOHC1SID62 → SQI63QOC43 → PNMI5OC876 → KIGE5OGECB → J9621SSOLC → RQIC6NIC44 → NMH65OOD88 → JIFE3QGFCC → N761UUSON8 → TOLFUUE962 → SOKA5OKA63 → PJIA9KKCB6 → JBA85OMKJC → JEA86NMKGC → HEA71SNKGE → RGA31SRKE4 → RONA1SK764 → RNIG9KEC74 → NGB61SOJE8 → RIF81SMFC4 → RNE5UUOG74 → QPKA6NKA55 → LKHA9KKDAA → CAAA3QKKKJ → NAAA6NKKK8 → HFAA9KKKFE → BAA2UURKKK → SKH8UULDA3 → RMI82RMC84 → PNEE5OGG76 → KIG21SSECB → RQ961SOL44 → RNMIBIC874 → NGE75ONGE8 → JGF21SSFEC → RQ71UUSN44 → TQOK2RA642 → RPMI9KC854 → NKEB5OJGA8 → JFA81SMKFC → REA6UUNKG4 → QOH93QLD65 → NLIC3QIC98 → NFC65OOIF8 → JIF5UUOFCC → PIC42RQIC6 → PMJ65OOB86 → KIIE7MGCCB → F9661SOOLG → RIIC0TICC4 → TN665OOO72 → RJIIFECCB4 → N8660TOOM8 → TIIFDGFCC2 → R662UUROO4 → SQLKUU9943 → RQJH0TDB44 → TNM83QM872 → RNGEDGGE74 → NG321SSRE8 → RQOF1SF644 → RNMHUUC874 → QNJB4PJB75 → MKG87MMEA9 → FEDA1SKHGG → RA420TSQK4 → TQNM9K8742 → RMGEAJGE84 → NE921SSLG8 → RQFC1SIF44 → RNM5UUO874 → QPKG0TEA55 → TLKA1SKA92 → SQCA9KKI43 → PMBA5OKJ86 → KIEA7MKGCB → FA961SOLKG → RICA0TKIC4 → TNA65OOK72 → RJIG9KECB4 → NB861SOMJ8 → RIFE7MGFC4 → NF61UUSOF8 → TOK97MLA62 → RIFC9KIFC4 → NB65UUOOJ8 → POGD3QHE66 → NJI41SQCB8 → RMF85OMF84 → NJEDUUGGB8 → MJA4UUPKB9 → QLFB0TJF95 → TLC7UUMI92 → SNKA2RKA73 → QOGA9KKE65 → LIBA1SKJCA → RBA85OMKJ4 → NJEA7MKGB8 → GEA81SMKGF → REA20TSKG4 → TQNA1SK742 → SQMG9KE843 → PMEB1SJG86 → RJE81SMGB4 → RNE81SMG74 → RNGE1SGE74RNG21SSE74RQNG1SE744RNMG1SE874RNGE1SGE74
1188 max steps10000000223 → 3220UUUTSSS → USSPUUU4221 → TSSQ2UR4222 → SRQQMU74433 → RPNMIUB8754 → QMIFAUJFC85 → PIC72URNIC6 → SLIB5UOJC93 → RNFA6UNKF74 → QLGD4UPHE95 → QLG82URME95 → SMID6UNHC83 → RMFA4UPKF84 → QNHC4UPID75 → QLIB4UPJC95 → QLGA6UNKE95 → PKEB5UOJGA6 → PJE94UPLGB6 → QJGA4UPKEB5 → QLF94UPLF95 → QLGC5UOIE95 → PLF93UQLF96 → RKGC5UOIEA4 → QME83UQMG85 → RLIE7UMGC94 → QKD93UQLHA5 → RLHB6UNJD94 → QLEA5UOKG95 → PLFB5UOJF96 → PJFA3UQKFB6 → RKF93UQLFA4 → RNHB4UPJD74 → QNIC5UOIC75 → PLHB5UOJD96 → PJFA5UOKFB6 → PJE93UQLGB6 → RKGA4UPKEA4 → QNFA5UOKF75 → PLHD4UPHD96 → QJG83UQMEB5 → RLIB4UPJC94 → QNGA6UNKE75 → PKGD5UOHEA6 → PJE72URNGB6 → SLIC4UPIC93 → ROG95UOLE64 → QMIF6UNFC85 → PKFA2URKFA6 → SLFA4UPKF93 → ROGB4UPJE64 → QNJD4UPHB75 → QLIC5UOIC95 → PLF95UOLF96 → PJFC5UOIFB6 → PJD72URNHB6 → SLIC5UOIC93 → RNF95UOLF74 → QMHE5UOGD85 → PLG92URLE96 → SLGC6UNIE93 → RME93UQLG84 → RNID6UNHC74 → QLGB4UPJE95 → QLGA4UPKE95 → QLGB5UOJE95 → PLFA4UPKF96 → QJGB4UPJEB5 → QLE84UPMG95 → QLHD6UNHD95 → PKE83UQMGA6 → RKHC5UOIDA4 → QME84UPMG85 → QLHE7UMGD95 → PJD82URMHB6 → SLHB5UOJD93 → RNFA5UOKF74 → QMHD4UPHD85 → QLH93UQLD95 → RLHC7UMID94 → QKD94UPLHA5QLGB6UNJE95PKEA4UPKGA6QJFA5UOKFB5PLE93UQLG96RKGC6UNIEA4QLD83UQMH95RLID7UMHC94QKD94UPLHA5