Reciprocal expansions (1/n) in radix 3:

n₁₀	n	1/n	period

`1`	`1`	`1`	`0`
`2`	`2`	`0.(1)`	`1`
`3`	`10`	`0.1`	`0`
`4`	`11`	`0.(02)`	`2`
`5`	`12`	`0.(0121)`	`4`

`6`	`20`	`0.0(1)`	`1`
`7`	`21`	`0.(010212)`	`6`
`8`	`22`	`0.(01)`	`2`
`9`	`100`	`0.01`	`0`
`10`	`101`	`0.(0022)`	`4`

`11`	`102`	`0.(00211)`	`5`
`12`	`110`	`0.0(02)`	`2`
`13`	`111`	`0.(002)`	`3`
`14`	`112`	`0.(001221)`	`6`
`15`	`120`	`0.0(0121)`	`4`

`16`	`121`	`0.(0012)`	`4`
`17`	`122`	`0.(0011202122110201)`	`16`
`18`	`200`	`0.00(1)`	`1`
`19`	`201`	`0.(001102100221120122)`	`18`
`20`	`202`	`0.(0011)`	`4`

`21`	`210`	`0.0(010212)`	`6`
`22`	`211`	`0.(00102)`	`5`
`23`	`212`	`0.(00101120021)`	`11`
`24`	`220`	`0.0(01)`	`2`
`25`	`221`	`0.(00100201102212202112)`	`20`

`26`	`222`	`0.(001)`	`3`
`27`	`1000`	`0.001`	`0`
`28`	`1001`	`0.(000222)`	`6`
`29`	`1002`	`0.(0002210102011122200121202111)`	`28`
`30`	`1010`	`0.0(0022)`	`4`

`31`	`1011`	`0.(000212111221020222010111001202)`	`30`
`32`	`1012`	`0.(00021121)`	`8`
`33`	`1020`	`0.0(00211)`	`5`
`34`	`1021`	`0.(0002101022201212)`	`16`
`35`	`1022`	`0.(000202211101)`	`12`

`36`	`1100`	`0.00(02)`	`2`
`37`	`1101`	`0.(000201200222021022)`	`18`
`38`	`1102`	`0.(000201011222021211)`	`18`
`39`	`1110`	`0.0(002)`	`3`
`40`	`1111`	`0.(0002)`	`4`

`41`	`1112`	`0.(00012221)`	`8`
`42`	`1120`	`0.0(001221)`	`6`
`43`	`1121`	`0.(000121221202002111210222101001020220111012)`	`42`
`44`	`1122`	`0.(0001211201)`	`10`
`45`	`1200`	`0.00(0121)`	`4`

`46`	`1201`	`0.(00012021122)`	`11`
`47`	`1202`	`0.(00012011121002022001011)`	`23`
`48`	`1210`	`0.0(0012)`	`4`
`49`	`1211`	`0.(000112212200201211120222110010022021011102)`	`42`
`50`	`1212`	`0.(00011212012221101021)`	`20`

`51`	`1220`	`0.0(0011202122110201)`	`16`
`52`	`1221`	`0.(000112)`	`6`
`53`	`1222`	`0.(0001112021010120021122022122211102012121022011002001)`	`52`
`54`	`2000`	`0.000(1)`	`1`
`55`	`2001`	`0.(00011102021212001222)`	`20`

`56`	`2002`	`0.(000111)`	`6`
`57`	`2010`	`0.0(001102100221120122)`	`18`
`58`	`2011`	`0.(0001101201002022211210212202)`	`28`
`59`	`2012`	`0.(00011010012111021022200202121)`	`29`
`60`	`2020`	`0.0(0011)`	`4`

`61`	`2021`	`0.(0001022212)`	`10`
`62`	`2022`	`0.(000102202110121222120020112101)`	`30`
`63`	`2100`	`0.00(010212)`	`6`
`64`	`2101`	`0.(0001021011122022)`	`16`
`65`	`2102`	`0.(000102012211)`	`12`

`66`	`2110`	`0.0(00102)`	`5`
`67`	`2111`	`0.(0001012122022212101002)`	`22`
`68`	`2112`	`0.(0001012011100221)`	`16`
`69`	`2120`	`0.0(00101120021)`	`11`
`70`	`2121`	`0.(000101102012)`	`12`

`71`	`2122`	`0.(00010102102000202112110011120012201)`	`35`
`72`	`2200`	`0.00(01)`	`2`
`73`	`2201`	`0.(000100222122)`	`12`
`74`	`2202`	`0.(000100211222122011)`	`18`
`75`	`2210`	`0.0(00100201102212202112)`	`20`

`76`	`2211`	`0.(000100120222122102)`	`18`
`77`	`2212`	`0.(000100110121211102220220012021)`	`30`
`78`	`2220`	`0.0(001)`	`3`
`79`	`2221`	`0.(000100020011002201211012210212120201110222122202211220021011210012010102021112)`	`78`
`80`	`2222`	`0.(0001)`	`4`

`81`	`10000`	`0.0001`	`0`
`82`	`10001`	`0.(00002222)`	`8`
`83`	`10002`	`0.(00002221001022010120121120221101002021111)`	`41`
`84`	`10010`	`0.0(000222)`	`6`
`85`	`10011`	`0.(0000221201200202)`	`16`

`86`	`10012`	`0.(000022110212112202101222200112010110020121)`	`42`
`87`	`10020`	`0.0(0002210102011122200121202111)`	`28`
`88`	`10021`	`0.(0000220212)`	`10`
`89`	`10022`	`0.(0000220120110202000121101022111100101220212122220021021120202221011212001111221210020101)`	`88`
`90`	`10100`	`0.00(0022)`	`4`

`91`	`10101`	`0.(000022)`	`6`
`92`	`10102`	`0.(0000212202211121010211)`	`22`
`93`	`10110`	`0.0(000212111221020222010111001202)`	`30`
`94`	`10111`	`0.(00002120210112122112002)`	`23`
`95`	`10112`	`0.(000021200012010010102002021101111221)`	`36`

`96`	`10120`	`0.0(00021121)`	`8`
`97`	`10121`	`0.(000021111220202212122210222201111002020010100012)`	`48`
`98`	`10122`	`0.(000021102211212102021222201120011010120201)`	`42`
`99`	`10200`	`0.00(00211)`	`5`
`100`	`10201`	`0.(00002102121110200122)`	`20`

`101`	`10202`	`0.(0000210122122101011021111002200011210220212020221122220121001001212112011112200222110120020102020011)`	`100`
`102`	`10210`	`0.0(0002101022201212)`	`16`
`103`	`10211`	`0.(0000210020021212022220122022010102)`	`34`
`104`	`10212`	`0.(000021)`	`6`
`105`	`10220`	`0.0(000202211101)`	`12`

`106`	`10221`	`0.(0000202122001210010211011022220201002210122120112112)`	`52`
`107`	`10222`	`0.(00002021022120122102002202221111010021120101121011001)`	`53`
`108`	`11000`	`0.000(02)`	`2`
`109`	`11001`	`0.(000020200120121100102010222)`	`27`
`110`	`11002`	`0.(00002012122102112111)`	`20`

`111`	`11010`	`0.0(000201200222021022)`	`18`
`112`	`11011`	`0.(000020111202)`	`12`
`113`	`11012`	`0.(0000201100120001102201010002212102020012201211110102110122220211221022211200212122200101202022100210111121201121)`	`112`
`114`	`11020`	`0.0(000201011222021211)`	`18`
`115`	`11021`	`0.(00002010001102000221100121220102021021111212)`	`44`

`116`	`11022`	`0.(0000200212001011102101221101)`	`28`
`117`	`11100`	`0.00(002)`	`3`
`118`	`11101`	`0.(00002001121020122011100101022)`	`29`
`119`	`11102`	`0.(000020010101220001100202102100022011112112001211)`	`48`
`120`	`11110`	`0.0(0002)`	`4`

`121`	`11111`	`0.(00002)`	`5`
`122`	`11112`	`0.(0000122221)`	`10`
`123`	`11120`	`0.0(00012221)`	`8`
`124`	`11121`	`0.(000012212201210222210010021012)`	`30`
`125`	`11122`	`0.(0000122111101120202201212112200120112220102000102122221001111211020200210101100221021100021202221201)`	`100`

`126`	`11200`	`0.00(001221)`	`6`
`127`	`11201`	`0.(000012201222120112000211221221022002010101211202012022111121100222210021000102110222011001001200220212121011020210200111101122)`	`126`
`128`	`11202`	`0.(00001220020221221112010120211011)`	`32`
`129`	`11210`	`0.0(000121221202002111210222101001020220111012)`	`42`
`130`	`11211`	`0.(000012121102)`	`12`

`131`	`11212`	`0.(00001212002021012202211001102221202121111012011010022001000211021)`	`65`
`132`	`11220`	`0.0(0001211201)`	`10`
`133`	`11221`	`0.(000012110222210112)`	`18`
`134`	`11222`	`0.(0000121022122221012001)`	`22`
`135`	`12000`	`0.000(0121)`	`4`

`136`	`12001`	`0.(0000121002011222)`	`16`
`137`	`12002`	`0.(0000120222000101122100021002120011201201010011010202002202111101211122221020002221211001222012201022110210212122112120202200201111210111)`	`136`
`138`	`12010`	`0.0(00012021122)`	`11`
`139`	`12011`	`0.(000012020121022112202120221001112221211112101002201102110102122200020222210202101200110020102001221110001011110121220021120112120100022202)`	`138`
`140`	`12012`	`0.(000012012121)`	`12`

`141`	`12020`	`0.0(00012011121002022001011)`	`23`
`142`	`12021`	`0.(00001201012111212202201120210002212)`	`35`
`143`	`12022`	`0.(000012002122101)`	`15`
`144`	`12100`	`0.00(0012)`	`4`
`145`	`12101`	`0.(0000120002020022221022202022)`	`28`

`146`	`12102`	`0.(000011222211)`	`12`
`147`	`12110`	`0.0(000112212200201211120222110010022021011102)`	`42`
`148`	`12111`	`0.(000011220222211002)`	`18`
`149`	`12112`	`0.(0000112200022011011112022111221201202021222021102121010102221220122101200122221100222002112111102001110010210202010002011201012121200010021001210221)`	`148`
`150`	`12120`	`0.0(00011212012221101021)`	`20`

`151`	`12121`	`0.(00001121110011021212102102222110111221120101012012)`	`50`
`152`	`12122`	`0.(000011210111022201)`	`18`
`153`	`12200`	`0.00(0011202122110201)`	`16`
`154`	`12201`	`0.(000011201210220201110110002122)`	`30`
`155`	`12202`	`0.(000011200222122121000200210221121101002210020210102111102011)`	`60`

`156`	`12210`	`0.0(000112)`	`6`
`157`	`12211`	`0.(000011122100222022102112002202021220120222211100122000200120110220020201002102)`	`78`
`158`	`12212`	`0.(000011121120112212102002220102210100201222211101102110010120220002120012122021)`	`78`
`159`	`12220`	`0.0(0001112021010120021122022122211102012121022011002001)`	`52`
`160`	`12221`	`0.(00001112)`	`8`

`161`	`12222`	`0.(000011112020212122102220111002011212022101101201210022001100020001)`	`66`
`162`	`20000`	`0.0000(1)`	`1`
`163`	`20001`	`0.(000011110202101002211000211100202212112002011010210212100121101202201001022210000222211112020121220011222011122020010110220211212012010122101121020021221200012222)`	`162`
`164`	`20002`	`0.(00001111)`	`8`
`165`	`20010`	`0.0(00011102021212001222)`	`20`

`166`	`20011`	`0.(00001110112011001210022021222012001010202)`	`41`
`167`	`20012`	`0.(00001110021202112101111202001021220220020210100012211011001010120000222012011200121)`	`83`
`168`	`20020`	`0.0(000111)`	`6`
`169`	`20021`	`0.(000011022110121202221002020101112200212)`	`39`
`170`	`20022`	`0.(0000110212100101)`	`16`

`171`	`20100`	`0.00(001102100221120122)`	`18`
`172`	`20101`	`0.(000011020102202212200222211202120020010022)`	`42`
`173`	`20102`	`0.(0000110122022201222101010220100100211110210112111220000221021122110221202021210200201122221121002000210001212120021221220111120121101110022220012011001120010202010120220211)`	`172`
`174`	`20110`	`0.0(0001101201002022211210212202)`	`28`
`175`	`20111`	`0.(000011011110210202100212121100120021101221202200012112222002)`	`60`

`176`	`20112`	`0.(00001101021111221221)`	`20`
`177`	`20120`	`0.0(00011010012111021022200202121)`	`29`
`178`	`20121`	`0.(0000110021201212111210200122202011200221221022221122010210101110120221000202110220010012)`	`88`
`179`	`20122`	`0.(00001100122122111102110112000202100210201110100221210102022110001210212112022220021200201)`	`89`
`180`	`20200`	`0.00(0011)`	`4`

`181`	`20201`	`0.(000011000202010201200122110020021011022210122)`	`45`
`182`	`20202`	`0.(000011)`	`6`
`183`	`20210`	`0.0(0001022212)`	`10`
`184`	`20211`	`0.(0000102212220210120102)`	`22`
`185`	`20212`	`0.(000010221101122122210202010210110021)`	`36`

`186`	`20220`	`0.0(000102202110121222120020112101)`	`30`
`187`	`20221`	`0.(00001022002022101002212222010121110102021002000120121000201111021122121121022112)`	`80`
`188`	`20222`	`0.(0000102122002102220211211112210101202211021001)`	`46`
`189`	`21000`	`0.000(010212)`	`6`
`190`	`21001`	`0.(000010211121001120012112122012020222)`	`36`

`191`	`21002`	`0.(00001021100110201111201020002010020210012111212001010112102022100012002101212220000211220022111)`	`95`
`192`	`21010`	`0.0(0001021011122022)`	`16`
`193`	`21011`	`0.(0000102022221202)`	`16`
`194`	`21012`	`0.(000010202110101102211101222212020112121120011121)`	`48`
`195`	`21020`	`0.0(000102012211)`	`12`

`196`	`21021`	`0.(000010201102102201010222212021120120021212)`	`42`
`197`	`21022`	`0.(0000102002202000021101211100011221012220010021210221002012012121201110110202010222022111102122112122221202200202222011210111222110012100022122010120012202102101010211121120202120002001111201001101)`	`196`
`198`	`21100`	`0.00(00102)`	`5`
`199`	`21101`	`0.(000010122220120001121221220200201112111222022200110012200212012102112101022102010101120201221111200222212100002102221101001002022021110111000200022112210022010210120110121200120212121102021001111022)`	`198`
`200`	`21102`	`0.(00001012210201211211)`	`20`