Il existe 30 périodes de 8 chiffres pour n/241 en base 8.

Pour toutes les fractions de n/241 en base 8, la période de 1/241 revient alors 8 fois (en orange)

1/241=0,00207757...

2/241=0,00417736...

3/241=0,00627715...

4/241=0,01037674...

5/241=0,01247653...

6/241=0,01457632...

7/241=0,01667611...

8/241=0,02077570...

9/241=0,02307547...

10/241=0,02517526...

11/241=0,02727505...

12/241=0,03137464...

13/241=0,03347443...

14/241=0,03557422...

15/241=0,03767401...

16/241=0,04177360...

17/241=0,04407337...

18/241=0,04617316...

19/241=0,05027275...

20/241=0,05237254...

21/241=0,05447233...

22/241=0,05657212...

23/241=0,06067171...

24/241=0,06277150...

25/241=0,06507127...

26/241=0,06717106...

27/241=0,07127065...

28/241=0,07337044...

29/241=0,07547023...

30/241=0,07757002...

31/241=0,10166761...

32/241=0,10376740...

33/241=0,10606717...

34/241=0,11016676...

35/241=0,11226655...

36/241=0,11436634...

37/241=0,11646613...

38/241=0,12056572...

39/241=0,12266551...

40/241=0,12476530...

41/241=0,12706507...

42/241=0,13116466...

43/241=0,13326445...

44/241=0,13536424...

45/241=0,13746403...

46/241=0,14156362...

47/241=0,14366341...

48/241=0,14576320...

49/241=0,15006277...

50/241=0,15216256...

51/241=0,15426235...

52/241=0,15636214...

53/241=0,16046173...

54/241=0,16256152...

55/241=0,16466131...

56/241=0,16676110...

57/241=0,17106067...

58/241=0,17316046...

59/241=0,17526025...

60/241=0,17736004...

61/241=0,20145763...

62/241=0,20355742...

63/241=0,20565721...

64/241=0,20775700...

65/241=0,21205657...

66/241=0,21415636...

67/241=0,21625615...

68/241=0,22035574...

69/241=0,22245553...

70/241=0,22455532...

71/241=0,22665511...

72/241=0,23075470...

73/241=0,23305447...

74/241=0,23515426...

75/241=0,23725405...

76/241=0,24135364...

77/241=0,24345343...

78/241=0,24555322...

79/241=0,24765301...

80/241=0,25175260...

81/241=0,25405237...

82/241=0,25615216...

83/241=0,26025175...

84/241=0,26235154...

85/241=0,26445133...

86/241=0,26655112...

87/241=0,27065071...

88/241=0,27275050...

89/241=0,27505027...

90/241=0,27715006...

91/241=0,30124765...

92/241=0,30334744...

93/241=0,30544723...

94/241=0,30754702...

95/241=0,31164661...

96/241=0,31374640...

97/241=0,31604617...

98/241=0,32014576...

99/241=0,32224555...

100/241=0,32434534...

101/241=0,32644513...

102/241=0,33054472...

103/241=0,33264451...

104/241=0,33474430...

105/241=0,33704407...

106/241=0,34114366...

107/241=0,34324345...

108/241=0,34534324...

109/241=0,34744303...

110/241=0,35154262...

111/241=0,35364241...

112/241=0,35574220...

113/241=0,36004177...

114/241=0,36214156...

115/241=0,36424135...

116/241=0,36634114...

117/241=0,37044073...

118/241=0,37254052...

119/241=0,37464031...

120/241=0,37674010...

121/241=0,40103767...

122/241=0,40313746...

123/241=0,40523725...

124/241=0,40733704...

125/241=0,41143663...

126/241=0,41353642...

127/241=0,41563621...

128/241=0,41773600...

129/241=0,42203557...

130/241=0,42413536...

131/241=0,42623515...

132/241=0,43033474...

133/241=0,43243453...

134/241=0,43453432...

135/241=0,43663411...

136/241=0,44073370...

137/241=0,44303347...

138/241=0,44513326...

139/241=0,44723305...

140/241=0,45133264...

141/241=0,45343243...

142/241=0,45553222...

143/241=0,45763201...

144/241=0,46173160...

145/241=0,46403137...

146/241=0,46613116...

147/241=0,47023075...

148/241=0,47233054...

149/241=0,47443033...

150/241=0,47653012...

151/241=0,50062771...

152/241=0,50272750...

153/241=0,50502727...

154/241=0,50712706...

155/241=0,51122665...

156/241=0,51332644...

157/241=0,51542623...

158/241=0,51752602...

159/241=0,52162561...

160/241=0,52372540...

161/241=0,52602517...

162/241=0,53012476...

163/241=0,53222455...

164/241=0,53432434...

165/241=0,53642413...

166/241=0,54052372...

167/241=0,54262351...

168/241=0,54472330...

169/241=0,54702307...

170/241=0,55112266...

171/241=0,55322245...

172/241=0,55532224...

173/241=0,55742203...

174/241=0,56152162...

175/241=0,56362141...

176/241=0,56572120...

177/241=0,57002077...

178/241=0,57212056...

179/241=0,57422035...

180/241=0,57632014...

181/241=0,60041773...

182/241=0,60251752...

183/241=0,60461731...

184/241=0,60671710...

185/241=0,61101667...

186/241=0,61311646...

187/241=0,61521625...

188/241=0,61731604...

189/241=0,62141563...

190/241=0,62351542...

191/241=0,62561521...

192/241=0,62771500...

193/241=0,63201457...

194/241=0,63411436...

195/241=0,63621415...

196/241=0,64031374...

197/241=0,64241353...

198/241=0,64451332...

199/241=0,64661311...

200/241=0,65071270...

201/241=0,65301247...

202/241=0,65511226...

203/241=0,65721205...

204/241=0,66131164...

205/241=0,66341143...

206/241=0,66551122...

207/241=0,66761101...

208/241=0,67171060...

209/241=0,67401037...

210/241=0,67611016...

211/241=0,70020775...

212/241=0,70230754...

213/241=0,70440733...

214/241=0,70650712...

215/241=0,71060671...

216/241=0,71270650...

217/241=0,71500627...

218/241=0,71710606...

219/241=0,72120565...

220/241=0,72330544...

221/241=0,72540523...

222/241=0,72750502...

223/241=0,73160461...

224/241=0,73370440...

225/241=0,73600417...

226/241=0,74010376...

227/241=0,74220355...

228/241=0,74430334...

229/241=0,74640313...

230/241=0,75050272...

231/241=0,75260251...

232/241=0,75470230...

233/241=0,75700207...

234/241=0,76110166...

235/241=0,76320145...

236/241=0,76530124...

237/241=0,76740103...

238/241=0,77150062...

239/241=0,77360041...

240/241=0,77570020...

On remarque que le produit du nombre de périodes (30) et de leurs longueurs (8) est égal à 240 et donc au premier -1.