Il existe 16 périodes de 16 chiffres pour n/257 en base 8.

Pour toutes les fractions de n/257 en base 8, la période de 1/257 revient alors 16 fois (en orange)

1/257=0,0017740077600377...

2/257=0,0037700177400776...

3/257=0,0057640277201375...

4/257=0,0077600377001774...

5/257=0,0117540476602373...

6/257=0,0137500576402772...

7/257=0,0157440676203371...

8/257=0,0177400776003770...

9/257=0,0217341075604367...

10/257=0,0237301175404766...

11/257=0,0257241275205365...

12/257=0,0277201375005764...

13/257=0,0317141474606363...

14/257=0,0337101574406762...

15/257=0,0357041674207361...

16/257=0,0377001774007760...

17/257=0,0416742073610357...

18/257=0,0436702173410756...

19/257=0,0456642273211355...

20/257=0,0476602373011754...

21/257=0,0516542472612353...

22/257=0,0536502572412752...

23/257=0,0556442672213351...

24/257=0,0576402772013750...

25/257=0,0616343071614347...

26/257=0,0636303171414746...

27/257=0,0656243271215345...

28/257=0,0676203371015744...

29/257=0,0716143470616343...

30/257=0,0736103570416742...

31/257=0,0756043670217341...

32/257=0,0776003770017740...

33/257=0,1015744067620337...

34/257=0,1035704167420736...

35/257=0,1055644267221335...

36/257=0,1075604367021734...

37/257=0,1115544466622333...

38/257=0,1135504566422732...

39/257=0,1155444666223331...

40/257=0,1175404766023730...

41/257=0,1215345065624327...

42/257=0,1235305165424726...

43/257=0,1255245265225325...

44/257=0,1275205365025724...

45/257=0,1315145464626323...

46/257=0,1335105564426722...

47/257=0,1355045664227321...

48/257=0,1375005764027720...

49/257=0,1414746063630317...

50/257=0,1434706163430716...

51/257=0,1454646263231315...

52/257=0,1474606363031714...

53/257=0,1514546462632313...

54/257=0,1534506562432712...

55/257=0,1554446662233311...

56/257=0,1574406762033710...

57/257=0,1614347061634307...

58/257=0,1634307161434706...

59/257=0,1654247261235305...

60/257=0,1674207361035704...

61/257=0,1714147460636303...

62/257=0,1734107560436702...

63/257=0,1754047660237301...

64/257=0,1774007760037700...

65/257=0,2013750057640277...

66/257=0,2033710157440676...

67/257=0,2053650257241275...

68/257=0,2073610357041674...

69/257=0,2113550456642273...

70/257=0,2133510556442672...

71/257=0,2153450656243271...

72/257=0,2173410756043670...

73/257=0,2213351055644267...

74/257=0,2233311155444666...

75/257=0,2253251255245265...

76/257=0,2273211355045664...

77/257=0,2313151454646263...

78/257=0,2333111554446662...

79/257=0,2353051654247261...

80/257=0,2373011754047660...

81/257=0,2412752053650257...

82/257=0,2432712153450656...

83/257=0,2452652253251255...

84/257=0,2472612353051654...

85/257=0,2512552452652253...

86/257=0,2532512552452652...

87/257=0,2552452652253251...

88/257=0,2572412752053650...

89/257=0,2612353051654247...

90/257=0,2632313151454646...

91/257=0,2652253251255245...

92/257=0,2672213351055644...

93/257=0,2712153450656243...

94/257=0,2732113550456642...

95/257=0,2752053650257241...

96/257=0,2772013750057640...

97/257=0,3011754047660237...

98/257=0,3031714147460636...

99/257=0,3051654247261235...

100/257=0,3071614347061634...

101/257=0,3111554446662233...

102/257=0,3131514546462632...

103/257=0,3151454646263231...

104/257=0,3171414746063630...

105/257=0,3211355045664227...

106/257=0,3231315145464626...

107/257=0,3251255245265225...

108/257=0,3271215345065624...

109/257=0,3311155444666223...

110/257=0,3331115544466622...

111/257=0,3351055644267221...

112/257=0,3371015744067620...

113/257=0,3410756043670217...

114/257=0,3430716143470616...

115/257=0,3450656243271215...

116/257=0,3470616343071614...

117/257=0,3510556442672213...

118/257=0,3530516542472612...

119/257=0,3550456642273211...

120/257=0,3570416742073610...

121/257=0,3610357041674207...

122/257=0,3630317141474606...

123/257=0,3650257241275205...

124/257=0,3670217341075604...

125/257=0,3710157440676203...

126/257=0,3730117540476602...

127/257=0,3750057640277201...

128/257=0,3770017740077600...

129/257=0,4007760037700177...

130/257=0,4027720137500576...

131/257=0,4047660237301175...

132/257=0,4067620337101574...

133/257=0,4107560436702173...

134/257=0,4127520536502572...

135/257=0,4147460636303171...

136/257=0,4167420736103570...

137/257=0,4207361035704167...

138/257=0,4227321135504566...

139/257=0,4247261235305165...

140/257=0,4267221335105564...

141/257=0,4307161434706163...

142/257=0,4327121534506562...

143/257=0,4347061634307161...

144/257=0,4367021734107560...

145/257=0,4406762033710157...

146/257=0,4426722133510556...

147/257=0,4446662233311155...

148/257=0,4466622333111554...

149/257=0,4506562432712153...

150/257=0,4526522532512552...

151/257=0,4546462632313151...

152/257=0,4566422732113550...

153/257=0,4606363031714147...

154/257=0,4626323131514546...

155/257=0,4646263231315145...

156/257=0,4666223331115544...

157/257=0,4706163430716143...

158/257=0,4726123530516542...

159/257=0,4746063630317141...

160/257=0,4766023730117540...

161/257=0,5005764027720137...

162/257=0,5025724127520536...

163/257=0,5045664227321135...

164/257=0,5065624327121534...

165/257=0,5105564426722133...

166/257=0,5125524526522532...

167/257=0,5145464626323131...

168/257=0,5165424726123530...

169/257=0,5205365025724127...

170/257=0,5225325125524526...

171/257=0,5245265225325125...

172/257=0,5265225325125524...

173/257=0,5305165424726123...

174/257=0,5325125524526522...

175/257=0,5345065624327121...

176/257=0,5365025724127520...

177/257=0,5404766023730117...

178/257=0,5424726123530516...

179/257=0,5444666223331115...

180/257=0,5464626323131514...

181/257=0,5504566422732113...

182/257=0,5524526522532512...

183/257=0,5544466622333111...

184/257=0,5564426722133510...

185/257=0,5604367021734107...

186/257=0,5624327121534506...

187/257=0,5644267221335105...

188/257=0,5664227321135504...

189/257=0,5704167420736103...

190/257=0,5724127520536502...

191/257=0,5744067620337101...

192/257=0,5764027720137500...

193/257=0,6003770017740077...

194/257=0,6023730117540476...

195/257=0,6043670217341075...

196/257=0,6063630317141474...

197/257=0,6103570416742073...

198/257=0,6123530516542472...

199/257=0,6143470616343071...

200/257=0,6163430716143470...

201/257=0,6203371015744067...

202/257=0,6223331115544466...

203/257=0,6243271215345065...

204/257=0,6263231315145464...

205/257=0,6303171414746063...

206/257=0,6323131514546462...

207/257=0,6343071614347061...

208/257=0,6363031714147460...

209/257=0,6402772013750057...

210/257=0,6422732113550456...

211/257=0,6442672213351055...

212/257=0,6462632313151454...

213/257=0,6502572412752053...

214/257=0,6522532512552452...

215/257=0,6542472612353051...

216/257=0,6562432712153450...

217/257=0,6602373011754047...

218/257=0,6622333111554446...

219/257=0,6642273211355045...

220/257=0,6662233311155444...

221/257=0,6702173410756043...

222/257=0,6722133510556442...

223/257=0,6742073610357041...

224/257=0,6762033710157440...

225/257=0,7001774007760037...

226/257=0,7021734107560436...

227/257=0,7041674207361035...

228/257=0,7061634307161434...

229/257=0,7101574406762033...

230/257=0,7121534506562432...

231/257=0,7141474606363031...

232/257=0,7161434706163430...

233/257=0,7201375005764027...

234/257=0,7221335105564426...

235/257=0,7241275205365025...

236/257=0,7261235305165424...

237/257=0,7301175404766023...

238/257=0,7321135504566422...

239/257=0,7341075604367021...

240/257=0,7361035704167420...

241/257=0,7400776003770017...

242/257=0,7420736103570416...

243/257=0,7440676203371015...

244/257=0,7460636303171414...

245/257=0,7500576402772013...

246/257=0,7520536502572412...

247/257=0,7540476602373011...

248/257=0,7560436702173410...

249/257=0,7600377001774007...

250/257=0,7620337101574406...

251/257=0,7640277201375005...

252/257=0,7660237301175404...

253/257=0,7700177400776003...

254/257=0,7720137500576402...

255/257=0,7740077600377001...

256/257=0,7760037700177400...

On remarque que le produit du nombre de périodes (16) et de leurs longueurs (16) est égal à 256 et donc au premier -1.