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 steps1 → 0 → 0
27 max steps10 → 0U → T1 → R3 → N7 → FF → 00 → 00
318 max steps100 → 0UU → TU1 → SU2 → RU3 → QU4 → PU5 → OU6 → NU7 → MU8 → LU9 → KUA → JUB → IUC → HUD → GUE → FUF → EUG → FUF
49 max stepsG000 → FUUF → FEFG → 1UUT → T0T2 → TQ32 → RM74 → NEF8 → F0TG → T0T2
518 max stepsF0000 → EUUUG → GDUGF → H0UTE → UEUF1 → TFUE2 → SEUF3 → RDUG4 → QDUG5 → PCUH6 → OCUH7 → NBUI8 → MBUI9 → LAUJA → KAUJB → K8ULB → M9UK9 → LCUHA → K8ULB
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 → SPUU43 → RQ2R44 → PNL876 → JGCHEC → 751SPO → RKGDA4 → NA2RK8 → PF9KF6 → JAUUJC → KHUUCB → JI2RCC → P75ON6 → KIFECB → 960TOM → TICHC2 → R64PO4 → NLHC98 → FC4PIG → L60TOA → TIAJC2 → R95OL4 → NJBIB8 → F86NMG → HE0TGE → T31SR2 → SQN643 → PMGD86 → JE2RGC → P71SN6 → RJFEB4 → N80TM8 → TFDGF2 → R2UUR4 → SPUU43
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 → OF9UKF7 → NF4UPF8 → QH7UMD5 → PJ8ULB6 → OH9UKD7 → NF6UNF8 → OF7UMF7 → NH6UND8 → OF9UKF7
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 → RNIBIC74 → NG75ONE8 → JGF1SFEC → R71UUSN4 → TQL3Q942 → RNMBI874 → NGE6NGE8 → HF21SSFE → RQ2UUR44 → SQN0T743 → TPMFE852 → RKE0TGA4 → TNA1SK72 → SQG9KE43 → PMB1SJ86 → RJE7MGB4 → NF81SMF8 → RFDUUGF4 → QHC0TID5 → TL63QO92 → RNIBIC74
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 → QLE5UOG95 → PLF6UNF96 → OJE5UOGB7 → PHD4UPHD6 → QJC3UQIB5 → RLF6UNF94 → QLE5UOG95
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 → RNGE1SGE74 → RNG21SSE74 → RQNG1SE744 → RNMG1SE874 → RNGE1SGE74
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 → QKD94UPLHA5 → QLGB6UNJE95 → PKEA4UPKGA6 → QJFA5UOKFB5 → PLE93UQLG96 → RKGC6UNIEA4 → QLD83UQMH95 → RLID7UMHC94 → QKD94UPLHA5