Base 30: 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 steps20 → 1S → Q3M7EF0TS1Q3
317 max steps100 → 0TT → ST1 → RT2 → QT3 → PT4 → OT5 → NT6 → MT7 → LT8 → KT9 → JTA → ITB → HTC → GTD → FTE → ETFETF
411 max steps400B → B3PJ → M7L8 → FCGF → 3TTQ → Q2Q4 → OL76 → IDFC61ROQHB4M5N8IDFC
518 max steps10000 → 0TTTT → STTT1 → S0TS2 → TPT31 → SPT32 → ROT43 → QMT64 → PJT95 → OFTD6 → NATI7 → MCTG8 → L9TJ9 → KBTHA → J8TKB → L8TK9 → LBTH9 → K9TJAK9TJA
6105 max steps500055 → 554OOP → LJIAA9 → C97LKI → EB5NIG → I71RMC → QF5NE4 → MI0SB8 → SE6MF2 → QG0SD4 → SM2Q72 → QOEE54 → MITTA8 → LJ3PA9 → MC8KH8 → EC4OHG → K51ROA → QJ9JA4 → MA8KJ8 → EC8KHG → C51ROI → QJ5NA4 → MI8KB8 → EC6MHG → G51ROE → QJ1RA4 → QM8K74 → MFBHE8 → E60SNG → SH1RC2 → RP4O43 → OLJ986 → ID9JGC → A62QNK → OH9JC6 → IA4OJC → K95NKA → IB9JIC → A75NMK → IF9JEC → A60SNK → SH9JC2 → QA4OJ4 → MK8K98 → ECAIHG → 851ROM → QJDFA4 → M91RK8 → QEAIF4 → M80SL8 → SECGF2 → Q40SP4 → SMK872 → QFBHE4 → M60SN8 → SHDFC2 → Q51RO4 → QMIA74 → MF7LE8FD0SGFS2TTQ2RR1R23QPN544MLHB88ED5NGGI31RQCQN5N64MIGCB8E73PMGMF1RE8QE0SF4SM0S72SQEE32QMTT64PN3P65MKGC98EB3PIGM71RM8QFDFE4M20SR8SPDF42QL1R84QMCG74MF3PE8ME0SF8SE0SF2SQ0S32SQM632QNFD64MH1RC8QE4OF4MK0S98SEAIF2Q80SL4SMCG72QF3PE4NL0S87SGCGD2Q42QP4OMK876IFBHEC750SONSJFDA2Q91RK4QMAI74MF7LE8
725 max steps1000000 → 0TTTTTT → STTTTT1 → S0TTTS2 → TR0TS21 → TSPT311 → SSOT412 → SQNT532 → RPKT843 → QNGTC64 → PKATI95 → OG9TJD6 → NF5TNE7 → OG8TKD6 → NG6TMD7 → NG8TKD7 → MF6TME8 → NE7TLF7 → MG6TMD8 → NE8TKF7 → MF5TNE8 → OF7TLE6NH6TMC7NG9TJD7ME5TNF8OF7TLE6
8143 max steps90000000 → 8TTTTTTL → L7TTTTL9 → MK87LL98 → FDDAIGGF → 832TTQQM → RQI3PB33 → ONM6M766 → IHGEEDCC → 652TTQOO → ROJTT953 → QOI4OB54 → MKJ6MA98 → GEB8KIFE → C720SRMI → SPF5NE42 → QLI0SB84 → SMD6MG72 → QGF2QED4 → OM30SQ76 → SNIEEB62 → QH6TTMC4 → PNE4OF65 → LJH0SCA9 → SC94OKH2 → QKB4OI94 → MKB6MI98 → GEB6MIFE → G720SRME → SPF1RE42 → RPL0S843 → SOLCG852 → QJD3PGA4 → NL92QK87 → OGDAIGD6 → I832QQLC → OND5NG66 → JHH2QCCB → O854OOL6 → KJICGBAA → A973PMKK → MFB9JIE8 → EA70SMJG → SF91RKE2 → RPB0SI43 → SOL6M852 → QJGCGDA4 → M942QPK8 → OLEAIF86 → ID80SLGC → SD62QNG2 → QOH2QC54 → OMJ4OA76 → KIF8KEBA → CA70SMJI → SF95NKE2 → QIB0SIB4 → SM76MM72 → QGFEEED4 → M30TTSQ8 → TQK3P931 → SNMAI762 → QHF7LEC4 → ME50SOF8 → SJE0SFA2 → SQ90SK32 → SQNAI632 → QNH7LC64 → MHE4OFC8 → KE50SOFA → SJA0SJA2 → SQ98KK32 → QNCAIH64 → MH84OLC8 → KED4OGFA → KA30SQJA → SNA8KJ62 → QHC8KHC4 → MC54OOH8 → KJE4OFAA → KA90SKJA → SBA8KJI2 → QC96MKH4 → MGB4OID8 → KE72QMFA → OFA0SJE6 → SI90SKB2 → SQB6MI32 → QNG6MD64 → MHG2QDC8 → OE52QOF6 → OJI0SBA6 → SI96MKB2 → QGB6MID4 → MG72QMD8 → OFE2QFE6 → OI10SSB6 → SRI6MB22 → QPG6MD44 → MLG2QD88 → OED2QGF6 → OI30SQB6 → SNI6MB62 → QHG6MDC4 → MG52QOD8 → OJE2QFA6 → OI90SKB6 → SIB6MIB2 → QG76MMD4 → MGF2QED8 → OE30SQF6 → SNI0SB62 → SQH6MC32 → QNG4OD64 → MKH2QC98 → OEB4OIF6 → KI70SMBA → SFA6MJE2 → QG90SKD4 → SMB2QI72 → QOF6ME54 → MJG0SDA8 → SE92QKF2 → QOB0SI54 → SMJ6MA72 → QGF8KED4 → MC30SQH8 → SNE4OF62 → QKH0SC94 → SMB4OI72 → QKF6ME94 → MGB0SID8 → SE72QMF2 → QOF0SE54SMJ0SA72SQF8KE32QNC0SH64SMH4OC72QKF4OE94MKB0SI98SEB6MIF2QG70SMD4SMF2QE72QOF0SE54
937 max steps100000006 → 60TTTTTSO → TN50TSO61 → TSNHTB611 → SSMBTH712 → SQLATI832 → RPIATIB43 → QNF6TME64 → PKH7TLC95 → OIC7TLHB6 → NHA5TNJC7 → OGD6TMGD6 → NI92TQKB7 → RJE8TKFA3 → QJA4TOJA4 → PME8TKF75 → OIE5TNFB6 → OIC3TPHB6 → QJD5TNGA4 → PLD5TNG85 → OKF7TLE96 → NHC5TNHC7 → OGB4TOID6 → PID4TOGB5 → PKD4TOG95 → PKF6TME95 → OJD5TNGA6 → OID5TNGB6 → OIC4TOHB6 → PID5TNGB5 → OKC4TOH96 → PIF7TLEB5 → OIA3TPJB6 → QJE7TLFA4 → PJB4TOIA5 → PKE7TLF95 → OIC5TNHB6OIC5TNHB6
10197 max steps300000CCDR → RDCC2QHHG3 → PN552QOO65 → OKJJGCAA96 → IB993PKKIC → MBB75NMII8 → IFE76MMFEC → GF610SSNEE → SRH20SRC22 → SQPP4O4432 → QNLLJ98864 → MHDD9JGGC8 → EA532QQOJG → ONJ91RKA66 → QIHB8KICB4 → MC774OMMH8 → KFFE4OFEEA → KA110SSSJA → SRRA8KJ222 → QPPC8KH444 → MLLC4OH888 → KEDD4OGGFA → KA330SQQJA → SNNA8KJ662 → QHHC8KHCC4 → MC554OOOH8 → KJJE4OFAAA → KA990SKKJA → SBBA8KJII2 → QC976MMKH4 → MGFB4OIED8 → KE730SQMFA → SNFA0SJE62 → SQH90SKC32 → SQNB4OI632 → QNKH6MC964 → MHGB4OIDC8 → KE752QOMFA → OJFA0SJEA6 → SI990SKKB2 → SQBB6MII32 → QNG76MMD64 → MHGF2QEDC8 → OE530SQOF6 → SNJI0SBA62 → SQH96MKC32 → QNGB4OID64 → MKH72QMC98 → OFEB4OIFE6 → KI710SSMBA → SRFA6MJE22 → QPG90SKD44 → SMLB2QI872 → QOFD6MGE54 → MJG30SQDA8 → SNE92QKF62 → QOHB0SIC54 → SMJ74OMA72 → QKFF8KEE94 → MCB10SSIH8 → SRE74OMF22 → QPKF0SE944 → SMLB0SI872 → SQFD6MGE32 → QNG30SQD64 → SNMH2QC762 → QOHF4OEC54 → MKJ50SOA98 → SJEB8KIFA2 → QC970SMKH4 → SMFB4OIE72 → QKF70SME94 → SMFB0SIE72 → SQF70SME32 → SQNF0SE632 → SQNH0SC632 → SQNH4OC632 → QNKH4OC964 → MKHB4OIC98 → KEB74OMIFA → KFA70SMJEA → SFA90SKJE2 → SQB90SKI32 → SQNB6MI632 → QNHG6MDC64 → MHG52QODC8 → OJE52QOFA6 → OJI90SKBA6 → SIB96MKIB2 → QGB76MMID4 → MGF72QMED8 → OFE30SQFE6 → SNI10SSB62 → SRQH6MC322 → QPNG4OD644 → MLKH2QC988 → OEDB4OIGF6 → KI730SQMBA → SNFA6MJE62 → QHG90SKDC4 → SMB52QOI72 → QOJF6MEA54 → MJG90SKDA8 → SEB92QKIF2 → QOB70SMI54 → SMJF6MEA72 → QGF90SKED4 → SMB30SQI72SQNF6ME632QNHG0SDC64SMH52QOC72QOJF4OEA54MKJ90SKA98SEBB8KIIF2QC770SMMH4SMFF4OEE72QKF10SSE94SRMB0SI722SQPF6ME432QNLG0SD864SMHD2QGC72QOF52QOE54OMJJ0SAA76SIF98KKEB2QCB70SMIH4SMF74OME72QKFF0SEE94SMB10SSI72SRQF6ME322QPNG0SD644SMLH2QC872QOFD4OGE54MKJ30SQA98SNEB8KIF62QHC70SMHC4SMF54OOE72QKJF0SEA94SMB90SKI72SQFB6MIE32QNG70SMD64SMHF2QEC72QOF50SOE54SMJJ0SAA72SQF98KKE32QNCB0SIH64SMH74OMC72QKFF4OEE94MKB10SSI98SREB6MIF22QPG70SMD44SMLF2QE872QOFD0SGE54SMJ30SQA72SQNF8KE632QNHC0SHC64SMH54OOC72QKJF4OEA94MKB90SKI98SEBB6MIIF2QG770SMMD4SMFF2QEE72QOF10SSE54SRMJ0SA722SQPF8KE432QNLC0SH864SMHD4OGC72QKF52QOE94OMJB0SIA76SIF96MKEB2QGB70SMID4SMF72QME72QOFF0SEE54SMJ10SSA72SRQF8KE322QPNC0SH644SMLH4OC872QKFD4OGE94MKB30SQI98SNEB6MIF62QHG70SMDC4SMF52QOE72QOJF0SEA54SMJ90SKA72SQFB8KIE32QNC70SMH64SMHF4OEC72QKF50SOE94SMJB0SIA72SQF96MKE32QNGB0SID64SMH72QMC72QOFF4OEE54MKJ10SSA98SREB8KIF22QPC70SMH44SMLF4OE872QKFD0SGE94SMB30SQI72
1173 max steps5000000EPPT → TPPE4TOF441 → SPLL9TJ8842 → ROHDBTHGC53 → QMD53TPOG74 → QMKH8TKC974 → PJEB7TLIFA5 → OIB83TPLIB6 → QJGA6TMJDA4 → PKC95TNKH95 → OKEB7TLIF96 → NHC93TPKHC7 → QIE84TOLFB4 → PMGA3TPJD75 → QKIC5TNHB94 → PLE95TNKF85 → OKFC5TNHE96 → OIE82TQLFB6 → RKGA3TPJD93 → QOGA5TNJD54 → PLJD5TNGA85 → OKFB5TNIE96 → OIE93TPKFB6 → QJF93TPKEA4 → QMGA4TOJD74 → PMHC5TNHC75 → OKGA4TOJD96 → PIFA5TNJEB5 → OKD83TPLG96 → QJGC6TMHDA4 → PKC73TPMH95 → QKID7TLGB94 → PJC94TOKHA5 → PKFA6TMJE95 → OJDA4TOJGA6 → PIE95TNKFB5 → OKE93TPKF96 → QJFB5TNIEA4 → PLD83TPLG85 → QKHD7TLGC94 → PJC83TPLHA5 → QKHB6TMIC94 → PKD95TNKG95 → OKEB6TMIF96 → NID93TPKGB7 → QIE94TOKFB4 → PMF93TPKE75 → QKID5TNGB94 → PLE94TOKF85PKGC5TNHD95OKE83TPLF96QJGC5TNHDA4PLD73TPMG85QKIE7TLFB94PJC93TPKHA5QKGA6TMJD94PKDA5TNJG95OKEA5TNJF96OIEA4TOJFB6PIE83TPLFB5QKHA3TPJC94QMGA6TMJD74PKFC5TNHE95OKE82TQLF96RKGC5TNHD93QME83TPLF74QMIE6TMFB74PKFB3TPIE95QKG93TPKD94QMGB6TMID74PKFB4TOIE95PKF93TPKE95QKGB5TNID94PLE94TOKF85
12196 max steps300000003CCJ → JCC32TTQQHHB → RQFE6TTMFE33 → QQLC7TTLH834 → QPJI93PKBA44 → NLLB96MKI887 → HFDDB6MIGGED → G74330SQQPME → SNNLF1RE8662 → RPHHD0SGCC43 → SOL552QOO852 → QOJJJCGAAA54 → MJ9993PKKKA8 → MEBBB8KIIIF8 → EC7770SMMMHG → SFFF51ROEEE2 → RPJ110SSSA43 → SRROL8K85222 → QPPJDBHGA444 → MLL962QNK888 → OHEDDAIGGFC6 → I85330SQQOLC → SNNJD5NGA662 → QIHH92QKCCB4 → OMB754OOMI76 → KJIFF6MEEBAA → GA9710SSMKJE → SRFB91RKIE22 → RPPB70SMI443 → SOLLF6ME8852 → QJGDD0SGGDA4 → SM9332QQQK72 → QONNFAIE6654 → MJHH80SLCCA8 → SED954OOKGF2 → QKJB30SQIA94 → SNMB96MKI762 → QHGFB6MIEDC4 → MG7530SQOMD8 → SNJFE2QFEA62 → QOH910SSKC54 → SRMJB4OIA722 → QPKF96MKE944 → MLGBB0SIID88 → SED772QMMGF2 → QOFF30SQEE54 → SNMJ10SSA762 → SRQHF8KEC322 → QPNC50SOH644 → SMLJH4OCA872 → QKFD94OKGE94 → MKBB30SQII98 → SNEB76MMIF62 → QHGF70SMEDC4 → SMF530SQOE72 → SQNJF0SEA632 → SQNH90SKC632 → SQNHB4OIC632 → QNKH74OMC964 → MKHFB4OIEC98 → KEB750SOMIFA → SJFA70SMJEA2 → SQF990SKKE32 → SQNBB0SII632 → SQNH76MMC632 → QNHGF4OEDC64 → MKH530SQOC98 → SNJEB4OIFA62 → QKH970SMKC94 → SMFBB4OIIE72 → QKF770SMME94 → SMFFB0SIEE72 → SQF710SSME32 → SRQNF0SE6322 → SQPNH0SC6432 → SQNLH4OC8632 → QNKHD4OGC964 → MKHB52QOIC98 → OJEB74OMIFA6 → KIF970SMKEBA → SFBA70SMJIE2 → SQF970SMKE32 → SQNFB0SIE632 → SQNH70SMC632 → SQNHF4OEC632 → QNKH50SOC964 → SMJHB4OICA72 → QKF974OMKE94 → MKFBB0SIIE98 → SEB770SMMIF2 → SQFF70SMEE32 → SQNF10SSE632 → SRQNH0SC6322 → SQPNH4OC6432 → QNLKH4OC9864 → MKHDB4OIGC98 → KEB752QOMIFA → OJFA70SMJEA6 → SIF990SKKEB2 → SQBB70SMII32 → SQNF76MME632 → QNHGF0SEDC64 → SMH530SQOC72 → SQNJF4OEA632 → QNKH90SKC964 → SMHBB4OIIC72 → QKF774OMME94 → MKFFB0SIEE98 → SEB710SSMIF2 → SRQF70SME322 → SQPNF0SE6432 → SQNLH0SC8632 → SQNHD4OGC632 → QNKH52QOC964 → OMJHB4OICA76 → KIF974OMKEBA → KFBA70SMJIEA → SFA970SMKJE2 → SQFB90SKIE32 → SQNB70SMI632 → SQNHF6MEC632 → QNHG50SODC64 → SMJH52QOCA72 → QOJF94OKEA54 → MKJB90SKIA98 → SEBB96MKIIF2 →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