Il existe 8 périodes de 29 chiffres pour n/233 en base 8.

Pour toutes les fractions de n/233 en base 8, la période de 1/233 revient alors 29 fois (en orange)

1/233=0,00214505160043121234010624247...

2/233=0,00431212340106242470021450516...

3/233=0,00645717520151363724032274765...

4/233=0,01062424700214505160043121234...

5/233=0,01277132060257626414053745503...

6/233=0,01513637240322747650064571752...

7/233=0,01730344420366071104075416221...

8/233=0,02145051600431212340106242470...

9/233=0,02361556760474333574117066737...

10/233=0,02576264140537455030127713206...

11/233=0,03012771320602576264140537455...

12/233=0,03227476500645717520151363724...

13/233=0,03444203660711040754162210173...

14/233=0,03660711040754162210173034442...

15/233=0,04075416221017303444203660711...

16/233=0,04312123401062424700214505160...

17/233=0,04526630561125546134225331427...

18/233=0,04743335741170667370236155676...

19/233=0,05160043121234010624247002145...

20/233=0,05374550301277132060257626414...

21/233=0,05611255461342253314270452663...

22/233=0,06025762641405374550301277132...

23/233=0,06242470021450516004312123401...

24/233=0,06457175201513637240322747650...

25/233=0,06673702361556760474333574117...

26/233=0,07110407541622101730344420366...

27/233=0,07325114721665223164355244635...

28/233=0,07541622101730344420366071104...

29/233=0,07756327261773465654376715353...

30/233=0,10173034442036607110407541622...

31/233=0,10407541622101730344420366071...

32/233=0,10624247002145051600431212340...

33/233=0,11040754162210173034442036607...

34/233=0,11255461342253314270452663056...

35/233=0,11472166522316435524463507325...

36/233=0,11706673702361556760474333574...

37/233=0,12123401062424700214505160043...

38/233=0,12340106242470021450516004312...

39/233=0,12554613422533142704526630561...

40/233=0,12771320602576264140537455030...

41/233=0,13206025762641405374550301277...

42/233=0,13422533142704526630561125546...

43/233=0,13637240322747650064571752015...

44/233=0,14053745503012771320602576264...

45/233=0,14270452663056112554613422533...

46/233=0,14505160043121234010624247002...

47/233=0,14721665223164355244635073251...

48/233=0,15136372403227476500645717520...

49/233=0,15353077563272617734656543767...

50/233=0,15567604743335741170667370236...

51/233=0,16004312123401062424700214505...

52/233=0,16221017303444203660711040754...

53/233=0,16435524463507325114721665223...

54/233=0,16652231643552446350732511472...

55/233=0,17066737023615567604743335741...

56/233=0,17303444203660711040754162210...

57/233=0,17520151363724032274765006457...

58/233=0,17734656543767153530775632726...

59/233=0,20151363724032274765006457175...

60/233=0,20366071104075416221017303444...

61/233=0,20602576264140537455030127713...

62/233=0,21017303444203660711040754162...

63/233=0,21234010624247002145051600431...

64/233=0,21450516004312123401062424700...

65/233=0,21665223164355244635073251147...

66/233=0,22101730344420366071104075416...

67/233=0,22316435524463507325114721665...

68/233=0,22533142704526630561125546134...

69/233=0,22747650064571752015136372403...

70/233=0,23164355244635073251147216652...

71/233=0,23401062424700214505160043121...

72/233=0,23615567604743335741170667370...

73/233=0,24032274765006457175201513637...

74/233=0,24247002145051600431212340106...

75/233=0,24463507325114721665223164355...

76/233=0,24700214505160043121234010624...

77/233=0,25114721665223164355244635073...

78/233=0,25331427045266305611255461342...

79/233=0,25546134225331427045266305611...

80/233=0,25762641405374550301277132060...

81/233=0,26177346565437671535307756327...

82/233=0,26414053745503012771320602576...

83/233=0,26630561125546134225331427045...

84/233=0,27045266305611255461342253314...

85/233=0,27261773465654376715353077563...

86/233=0,27476500645717520151363724032...

87/233=0,27713206025762641405374550301...

88/233=0,30127713206025762641405374550...

89/233=0,30344420366071104075416221017...

90/233=0,30561125546134225331427045266...

91/233=0,30775632726177346565437671535...

92/233=0,31212340106242470021450516004...

93/233=0,31427045266305611255461342253...

94/233=0,31643552446350732511472166522...

95/233=0,32060257626414053745503012771...

96/233=0,32274765006457175201513637240...

97/233=0,32511472166522316435524463507...

98/233=0,32726177346565437671535307756...

99/233=0,33142704526630561125546134225...

100/233=0,33357411706673702361556760474...

101/233=0,33574117066737023615567604743...

102/233=0,34010624247002145051600431212...

103/233=0,34225331427045266305611255461...

104/233=0,34442036607110407541622101730...

105/233=0,34656543767153530775632726177...

106/233=0,35073251147216652231643552446...

107/233=0,35307756327261773465654376715...

108/233=0,35524463507325114721665223164...

109/233=0,35741170667370236155676047433...

110/233=0,36155676047433357411706673702...

111/233=0,36372403227476500645717520151...

112/233=0,36607110407541622101730344420...

113/233=0,37023615567604743335741170667...

114/233=0,37240322747650064571752015136...

115/233=0,37455030127713206025762641405...

116/233=0,37671535307756327261773465654...

117/233=0,40106242470021450516004312123...

118/233=0,40322747650064571752015136372...

119/233=0,40537455030127713206025762641...

120/233=0,40754162210173034442036607110...

121/233=0,41170667370236155676047433357...

122/233=0,41405374550301277132060257626...

123/233=0,41622101730344420366071104075...

124/233=0,42036607110407541622101730344...

125/233=0,42253314270452663056112554613...

126/233=0,42470021450516004312123401062...

127/233=0,42704526630561125546134225331...

128/233=0,43121234010624247002145051600...

129/233=0,43335741170667370236155676047...

130/233=0,43552446350732511472166522316...

131/233=0,43767153530775632726177346565...

132/233=0,44203660711040754162210173034...

133/233=0,44420366071104075416221017303...

134/233=0,44635073251147216652231643552...

135/233=0,45051600431212340106242470021...

136/233=0,45266305611255461342253314270...

137/233=0,45503012771320602576264140537...

138/233=0,45717520151363724032274765006...

139/233=0,46134225331427045266305611255...

140/233=0,46350732511472166522316435524...

141/233=0,46565437671535307756327261773...

142/233=0,47002145051600431212340106242...

143/233=0,47216652231643552446350732511...

144/233=0,47433357411706673702361556760...

145/233=0,47650064571752015136372403227...

146/233=0,50064571752015136372403227476...

147/233=0,50301277132060257626414053745...

148/233=0,50516004312123401062424700214...

149/233=0,50732511472166522316435524463...

150/233=0,51147216652231643552446350732...

151/233=0,51363724032274765006457175201...

152/233=0,51600431212340106242470021450...

153/233=0,52015136372403227476500645717...

154/233=0,52231643552446350732511472166...

155/233=0,52446350732511472166522316435...

156/233=0,52663056112554613422533142704...

157/233=0,53077563272617734656543767153...

158/233=0,53314270452663056112554613422...

159/233=0,53530775632726177346565437671...

160/233=0,53745503012771320602576264140...

161/233=0,54162210173034442036607110407...

162/233=0,54376715353077563272617734656...

163/233=0,54613422533142704526630561125...

164/233=0,55030127713206025762641405374...

165/233=0,55244635073251147216652231643...

166/233=0,55461342253314270452663056112...

167/233=0,55676047433357411706673702361...

168/233=0,56112554613422533142704526630...

169/233=0,56327261773465654376715353077...

170/233=0,56543767153530775632726177346...

171/233=0,56760474333574117066737023615...

172/233=0,57175201513637240322747650064...

173/233=0,57411706673702361556760474333...

174/233=0,57626414053745503012771320602...

175/233=0,60043121234010624247002145051...

176/233=0,60257626414053745503012771320...

177/233=0,60474333574117066737023615567...

178/233=0,60711040754162210173034442036...

179/233=0,61125546134225331427045266305...

180/233=0,61342253314270452663056112554...

181/233=0,61556760474333574117066737023...

182/233=0,61773465654376715353077563272...

183/233=0,62210173034442036607110407541...

184/233=0,62424700214505160043121234010...

185/233=0,62641405374550301277132060257...

186/233=0,63056112554613422533142704526...

187/233=0,63272617734656543767153530775...

188/233=0,63507325114721665223164355244...

189/233=0,63724032274765006457175201513...

190/233=0,64140537455030127713206025762...

191/233=0,64355244635073251147216652231...

192/233=0,64571752015136372403227476500...

193/233=0,65006457175201513637240322747...

194/233=0,65223164355244635073251147216...

195/233=0,65437671535307756327261773465...

196/233=0,65654376715353077563272617734...

197/233=0,66071104075416221017303444203...

198/233=0,66305611255461342253314270452...

199/233=0,66522316435524463507325114721...

200/233=0,66737023615567604743335741170...

201/233=0,67153530775632726177346565437...

202/233=0,67370236155676047433357411706...

203/233=0,67604743335741170667370236155...

204/233=0,70021450516004312123401062424...

205/233=0,70236155676047433357411706673...

206/233=0,70452663056112554613422533142...

207/233=0,70667370236155676047433357411...

208/233=0,71104075416221017303444203660...

209/233=0,71320602576264140537455030127...

210/233=0,71535307756327261773465654376...

211/233=0,71752015136372403227476500645...

212/233=0,72166522316435524463507325114...

213/233=0,72403227476500645717520151363...

214/233=0,72617734656543767153530775632...

215/233=0,73034442036607110407541622101...

216/233=0,73251147216652231643552446350...

217/233=0,73465654376715353077563272617...

218/233=0,73702361556760474333574117066...

219/233=0,74117066737023615567604743335...

220/233=0,74333574117066737023615567604...

221/233=0,74550301277132060257626414053...

222/233=0,74765006457175201513637240322...

223/233=0,75201513637240322747650064571...

224/233=0,75416221017303444203660711040...

225/233=0,75632726177346565437671535307...

226/233=0,76047433357411706673702361556...

227/233=0,76264140537455030127713206025...

228/233=0,76500645717520151363724032274...

229/233=0,76715353077563272617734656543...

230/233=0,77132060257626414053745503012...

231/233=0,77346565437671535307756327261...

232/233=0,77563272617734656543767153530...

On remarque que le produit du nombre de périodes (8) et de leurs longueurs (29) est égal à 232 et donc au premier -1.