Base 36: Cycles Sequences: All Cycle Counts

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 # Full Cycles
(excluding zero)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
21 cycle 630×(max) 18 nodes⮎ 0Z → Y1 → W3 → S7 → KF → 4V → Q9 → GJ → 2X → U5 → OB → CN → AP → EL → 6T → MD → 8R → IH ⮌
31 cycle 8,400×(fixed) (max) 1 node ⮎ HZI ⮌
42 cycles45,549×(max) 3 nodes⮎ C3VO → SBN8 → KBNG ⮌
36,666×(max) 3 nodes⮎ K3VG → S3V8 → SJF8 ⮌
52 cycles656,642×(fixed) 1 node ⮎ OBZNC ⮌
1,330×(max) 2 nodes⮎ IGZII → IZZZH ⮌
65 cycles3,937,769×(max) 111 nodes⮎ A42WVQ → URFJ86 → OJ3VGC → SC2WN8 → UKAOF6 → OE4ULC → QC6SNA → MGAOJE → E82WRM → UJ7RG6 → OK2WFC → UC4UN6 → QOAOBA → GECMLK → A73VSQ → SLFJE8 → K73VSG → SL3VE8 → SK6SF8 → MK4UFE → Q84URA → QJFJGA → G42WVK → UR3V86 → SOIGB8 → KD1XMG → W93VQ4 → TRGI87 → MJ1XGE → W82WR4 → USIG76 → OL1XEC → WC6SN4 → SMAOD8 → KE8QLG → I73VSI → SKZZE8 → RL7RE9 → KI6SHG → M40YVE → YR7R82 → WKIGF4 → S51XU8 → WPJFA4 → SF3VK8 → SK4UF8 → QK4UFA → QG4UJA → QG2WJA → UG2WJ6 → UO2WB6 → UOCMB6 → OD9PMC → GC8QNK → IB3VOI → SCZZM8 → RN5TC9 → OIAOHC → EC0YNM → YB7RO2 → WKCMF4 → SA4UP8 → QKEKFA → G64UTK → QN3VCA → SGAOJ8 → KE2WLG → U73VS6 → SOKEB8 → KD5TMG → O93VQC → SHBNI8 → KC0YNG → YB3VO2 → WSCM74 → SL9PE8 → KG6SJG → M42WVE → UR7R86 → OKIGFC → C51XUO → WPBNA4 → SFBNK8 → KC4UNG → QB3VOA → SGCMJ8 → KA2WPG → UF3VK6 → SO4UB8 → QKCMFA → GA4UPK → QF3VKA → SG4UJ8 → QK2WFA → UG4UJ6 → QO2WBA → UGCMJ6 → OA2WPC → UFBNK6 → OC4UNC → QCAONA → GEAOLK → E73VSM → SL7RE8 → LJ6SGF → M62WTE → UN7RC6 → OKAOFC → EC4UNM → QB7ROA → KGCMJG ⮌
530,711×27 nodes⮎ C95TQO → OHBNIC → DB0YON → YD9PM2 → WG8QJ4 → SI2WH8 → UK0YF6 → YO4UB2 → WQCM94 → SH9PI8 → KG0YJG → Y42WV2 → WUQ854 → SPHHA8 → KEZZKG → LIZZGF → KJ2WGG → U42WV6 → URNB86 → OJBNGC → DB2WON → UD9PM6 → OG8QJC → IC2WNI → UAZZO6 → TP5TA7 → OMEKDC ⮌
14,000×3 nodes⮎ KF3VKG → S53VU8 → SPJFA8 ⮌
13,530×3 nodes⮎ C53VUO → SPBNA8 → KFBNKG ⮌
342×(fixed) 1 node ⮎ IHZZHI ⮌
72 cycles23,658,812×(max) 19 nodes⮎ QG7ZRJA → SH9ZPI8 → RJ7ZRG9 → SIAZOH8 → RI6ZSH9 → TJ9ZPG7 → SK8ZQF8 → RKAZOF9 → QH8ZQIA → RG8ZQJ9 → RI9ZPH9 → QI7ZRHA → SH8ZQI8 → RK8ZQF9 → RIAZOH9 → QH6ZSIA → TI8ZQH7 → SL8ZQE8 → RKBZNF9 ⮌
3,319,480×(fixed) 1 node ⮎ RI8ZQH9 ⮌
85 cycles135,264,164×(max) 85 nodes⮎ C971XSQO → WLHBNIE4 → SC70YSN8 → YLKAOFE2 → WE74USL4 → SQL6SE98 → MKH6SIFE → M850YURE → YPJ7RGA2 → WKF2WKF4 → US54UU76 → QPOKEBAA → GFD5TMKK → O953VUQC → SPHBNIA8 → KFC0YNKG → YB53VUO2 → WSPCMA74 → SLF9PKE8 → KG74USJG → QL42WVEA → URG6SJ86 → OMJ2WGDC → UC92WQN6 → UOHAOIB6 → OED0YMLC → YC96SQN2 → WMHAOID4 → SE90YQL8 → YKH6SIF2 → WM50YUD4 → YSP8QA72 → WLIEKHE4 → S760YTS8 → YNLJFEC2 → WB73VSO4 → TRLCME87 → MJA6SPGE → MF82WRKE → UJ84URG6 → QOJ2WGBA → UGD2WMJ6 → UO92WQB6 → UOHCMIB6 → ODA0YPMC → YFC8QNK2 → WIB4UOH4 → SQD0YM98 → YKH8QIF2 → WI50YUH4 → YSP0YA72 → YWLEKE32 → WT75TS64 → SONKECB8 → KDB5TOMG → OD93VQMC → SHC8QNI8 → KIB0YOHG → YD40YVM2 → YWR8Q832 → WTJHHG64 → SN2ZZWC8 → XRK4UF83 → UQJ4UG96 → QOH2WIBA → UGD0YMJ6 → YO92WQB2 → WUHCMI54 → SPA0YPA8 → YKFEKKF2 → W654UUT4 → SQPMCA98 → KHF9PKIG → G540YVUK → YRP3VA82 → WSJEKG74 → SL62WTE8 → UNK6SFC6 → OMB4UODC → QDC8QNMA → IGB8QOJI → ID2ZZWMI → XME3VLD3 → US96SQ76 → OMLGIEDC ⮌
9,697,251×44 nodes⮎ C652WUTO → UPNBNCA6 → OFCAONKC → ECB4UONM → QDB7ROMA → KGD8QMJG → I942WVQI → URGZZI86 → TRE8QL87 → MJI6SHGE → M830YWRE → YTJ7RG62 → WNK2WFC4 → USB4UO76 → QOLCMEBA → GDA6SPMK → MF93VQKE → SH84URI8 → QKJ0YGFA → YG52WUJ2 → WUP2WA54 → USPEKA76 → OLF5TKEC → OC74USNC → QLCAONEA → GEB6SOLK → MD73VSME → SL97RQE8 → LJH6SIGF → M630YWTE → YTN7RC62 → WNKAOFC4 → SEB4UOL8 → QKD6SMFA → MG94UQJE → QH82WRIA → UJG0YJG6 → YO32WWB2 → WUTCM654 → SPN9PCA8 → KGFAOKJG → E542WVUM → URP7RA86 → OKJEKGFC ⮌
16,594×3 nodes⮎ KFF3VKKG → S553VUU8 → SPPJFAA8 ⮌
16,222×3 nodes⮎ C553VUUO → SPPBNAA8 → KFFBNKKG ⮌
14,246×(fixed) 1 node ⮎ ONBZZNCC ⮌
95 cycles410,995,162×(fixed) 1 node ⮎ TMF6ZSKD7 ⮌
148,496,202×6 nodes⮎ SMG6ZSJD8 → TKF5ZTKF7 → UME4ZULD6 → VOH7ZRIB5 → UOG6ZSJB6 → TOH7ZRIB7 ⮌
141,126,078×(max) 9 nodes⮎ SMC4ZUND8 → VMG9ZPJD5 → UMC5ZTND6 → UOH9ZPIB6 → TLE6ZSLE7 → TME6ZSLD7 → TMF7ZRKD7 → SME6ZSLD8 → TKF7ZRKF7 ⮌
8,312,688×2 nodes⮎ TMD5ZTMD7 → UMG8ZQJD6 ⮌
342×(fixed) 1 node ⮎ IIHZZZHHI ⮌
105 cycles2,927,719,379×(max) 163 nodes⮎ 65210YYXUU → YXVPNBA422 → WVRFBNK844 → SRJC4UNG88 → QKJB2WOGFA → UGD52WUMJ6 → UPO92WQBA6 → UOHFCMKIB6 → ODA50YUPMC → YPFC8QNKA2 → WIFB4UOKH4 → SQD50YUM98 → YPKH8QIFA2 → WIF50YUKH4 → YSP50YUA72 → YWPLEKEA32 → WTF75TSK64 → SONL4UECB8 → QKDB6SOMFA → MGD94UQMJE → QH982WRQIA → UJHG0YJIG6 → YO330YWWB2 → YWTTCM6632 → WTNN9PCC64 → SNGBAOOJC8 → KEDB2WOMLG → UD973VSQM6 → SOLH8QIEB8 → KID70YSMHG → YL940YVQE2 → YWRH6SI832 → WTMJ0YGD64 → YSN92WQC72 → WULHAOIE54 → SPE70YSLA8 → YLKF6SKFE2 → WM754UUSD4 → SQPL8QEA98 → KIHF6SKIHG → M5410YYVUE → YXRP7RA822 → WVKJEKGF44 → SR652WUT88 → UPNKIGFCA6 → OFB51XUOKC → WPDC4UNMA4 → SQFB8QOK98 → KIHD4UMIHG → Q9410YYVQA → YXRHFJI822 → WVJ40YVG44 → YSRR2W8872 → WULJIGGE54 → SP731XWSA8 → WTLKEKFE64 → SN764UTSC8 → QNLKAOFECA → GEB74USOLK → QLD73VSMEA → SLG96SQJE8 → MKH72WSIFE → UL850YURE6 → YPOJ6SGBA2 → WMFD2WMKD4 → US994UQQ76 → QOLHGIIEBA → GD720YXSMK → YVL93VQE42 → WSRH6SI874 → SMLJ0YGED8 → YK972WSQF2 → WULH4UIE54 → SQP70YSA98 → YLKHEKIFE2 → W7650YUTS4 → YSPNKECA72 → WLFB5TOKE4 → SOD74USMB8 → QLKD8QMFEA → IG974USQJI → QLH2ZZWIEA → XPI92WQHA3 → VTHF0YKI65 → YQN50YUC92 → YWPHAOIA32 → WTFE0YLK64 → YSN74USC72 → WQLLAOEE94 → SHE76SSLI8 → MLK70YSFEE → YL874USRE2 → WQLJ6SGE94 → SMH72WSID8 → ULK90YQFE6 → YOH74USIB2 → WQLD0YME94 → YSH96SQI72 → WMLH0YIED4 → YS970YSQ72 → YWLLGIEE32 → WT771XSS64 → WSNLKEEC74 → SLB75TSOE8 → OLKD6SMFEC → MC974USQNE → QLHB7ROIEA → KGD70YSMJG → YL942WVQE2 → WURH6SI854 → SPMJ0YGDA8 → YKF92WQKF2 → WUH54UUI54 → SQPP0YAA98 → YKHFEKKIF2 → W6550YUUT4 → YSPPMCAA72 → WLFF9PKKE4 → SG754UUSJ8 → QPLK2WFEAA → UGF74USKJ6 → QOL52WUEBA → UPGD6SMJA6 → OMF92WQKDC → UHC94UQNI6 → QOHB0YOIBA → YGDD0YMMJ2 → YW992WQQ32 → WUTHGII654 → SPN20YXCA8 → YVKFAOKF42 → WRE54UUL84 → SQPJ6SGA98 → MKHF2WKIFE → U8550YUUR6 → YPPOIGBAA2 → WFFD1XMKK4 → WS954UUQ74 → SQPLGIEA98 → KHF71XSKIG → WL540YVUE4 → YSRP6SA872 → WMLJEKGED4 → S9762WTSQ8 → UNLKGIFEC6 → OB751XUSOC → WPLDBNMEA4 → SFC96SQNK8 → MKHB4UOIFE → QD850YURMA → YPJG8QJGA2 → WIF32WWKH4 → UTS50YU766 → YPONKECBA2 → WFDB5TOMK4 → SOD94UQMB8 → QKHD8QMIFA → IG950YUQJI → YPH2ZZWIA2 → XXOF6SKB23 → VUMD4UMD55 → RPP98QQAA9 → JHHFEKKIIH ⮌
262,420,407×72 nodes⮎ GF764UTSKK → QNL53VUECA → SPGB6SOJA8 → MKFD2WMKFE → U9854UURQ6 → QPOJGIGBAA → GFD31XWMKK → WT953VUQ64 → TRPNGICA87 → MJFB1XOKGE → WD852WURM4 → USPJ8QGA76 → OLIF2WKHEC → UC750YUSN6 → YPOLAOEBA2 → WFED6SMLK4 → SM974USQD8 → QLKH8QIFEA → IG750YUSJI → YPL2ZZWEA2 → XXOI3VHB23 → VUSD0YM755 → YQPL8QEA92 → WIHF6SKIH4 → SM510YYUD8 → YXPK8QFA22 → WVIF4UKH44 → SRQ50YU988 → YPKJGIGFA2 → WF531XWUK4 → WTSP4UA764 → SQNLEKEC98 → KHB75TSOIG → OLD40YVMEC → YRC96SQN82 → WMJHAOIGD4 → SE930YWQL8 → YTKH6SIF62 → WNM50YUDC4 → YSPB8QOA72 → WLIFCMKHE4 → SA750YUSP8 → YPLKEKFEA2 → WF764UTSK4 → SQNL4UEC98 → QKHB6SOIFA → MGD50YUMJE → YP982WRQA2 → WUJHEKIG54 → SP630YWTA8 → YTNKEKFC62 → WNB64UTOC4 → SQNDAOMC98 → KHEB8QOLIG → ID740YVSMI → YRL8ZZQE82 → XRQD4UM983 → UQJH8QIG96 → OIH30YWIHC → YTC10YYN62 → YXWNAOC322 → WVTEAOL644 → SRNE6SLC88 → MKJB6SOGFE → MD852WURME → UPJ97RQGA6 → OKHF2WKIFC → UC550YUUN6 → YPPOAOBAA2 → WFFECMLKK4 → SA754UUSP8 → QPLKEKFEAA ⮌
19,986×3 nodes⮎ KFFF3VKKKG → S5553VUUU8 → SPPPJFAAA8 ⮌
19,378×3 nodes⮎ C5553VUUUO → SPPPBNAAA8 → KFFFBNKKKG ⮌
8,100×(fixed) 1 node ⮎ OOCBZZNNBC ⮌
11+---Not showing digit sets 11+ due to verbosity.