La base 4 est un carré parfait, ces bases (c'est une conjecture pour les carrés parfaits) ne génèrent aucune période unique pour tous les premiers inférieurs à 300000.

Il est tentant d'étendre à l'infini cette propriété, mais je n'ai jamais rien lu sur le sujet.

1/3=0,1...

1/5=0,03...

1/7=0,021...

1/11=0,01131...

1/13=0,010323...

1/17=0,0033...

1/19=0,003113211...

1/23=0,00230201121...

1/29=0,00203103313023...

1/31=0,00201...

1/37=0,001232230332101103...

1/41=0,0012033213...

1/43=0,0011331...

1/47=0,00111302120200223210301...

1/53=0,00103110201303323022313203...

1/59=0,00101112301321133131102130031...

1/61=0,001003021130110332330312203223...

1/67=0,000331020212031113320112323032111...

1/71=0,00032123002231010200130312011122021...

1/73=0,000320013...

1/79=0,000303312101310222020012132302032211101...

1/83=0,00030111211302013231133213110310123300211...

1/89=0,00023200113...

1/97=0,000222032200333111301133...

1/101=0,00022020313300302230112303331131302003303110322103...

1/103=0,000213301011211321302111020010332020230233032102221...

1/107=0,00021210133012211011120201133230313001302311311032331...

1/109=0,000211210333122123...

1/113=0,00021003331233...

1/127=0,0002001...

1/131=0,00013310101211213210221002130111133300113130310300312231323013111...

1/137=0,0001313211311232033320201220221013...

1/139=0,000131131323121110232002300303210113330110100210311122033221321203131...

1/149=0,00012313311230033131220303202302223303332102002210330020211303013103111003...

1/151=0,000123020003121...

1/157=0,00012201123103332113221023...

1/163=0,000121020033231021310032020220311121201113330312332002112301132032322321110303311...

1/167=0,00012020123211330022232300102121102301310200030100313023320111131200210302211203221...

1/173=0,00011322310202002032003230300311101120302103332201102313133130133010303302223221303123...

1/179=0,00011232013313122310030313301230230111130331133310203300101022113212100130212213111012011...

1/181=0,000112220103303101110313022100100332032312130333221113230030232223020311233233001301021203...

1/191=0,00011113013231033011001223032122020231210201200200022232033122132022003112130310101123021003001...

1/193=0,000111032100211020331000333222301233122313002333...

1/197=0,00011030222320201302112233123213103310103133200303332230311101313203122110021012023002323020013303...

1/199=0,000110211103213203230231001212322202011302133201020002210222130330131211220030313110100232103330021...

1/211=0,000103122120313303313200131013211103231303100223223113331210230321001201003330113003111202101211322202211...

1/223=0,0001021132020213002000210233010103201...

1/227=0,00010200231013003012133000312020131110211031310022021211133312332211301321303001332103233011112311210113223230311...

1/229=0,00010132023233032303332320131010030103...

1/233=0,00010121101103200020302202213...

1/239=0,00010102031120321311310300030312220022231201132100212203320200020210122301303223221200121231100111123002330201031013301...

1/241=0,000100333233...

1/251=0,0001001101211333133113031...

1/257=0,00003333...