Liste des fractions de n/257 en base 4.

Il existe 32 périodes de 8 chiffres pour n/257 en base 4.

Pour toutes les fractions de n/257 en base 4, la période de 1/257 revient alors 8 fois (en orange)

1/257=0,00003333...

2/257=0,00013332...

3/257=0,00023331...

4/257=0,00033330...

5/257=0,00103323...

6/257=0,00113322...

7/257=0,00123321...

8/257=0,00133320...

9/257=0,00203313...

10/257=0,00213312...

11/257=0,00223311...

12/257=0,00233310...

13/257=0,00303303...

14/257=0,00313302...

15/257=0,00323301...

16/257=0,00333300...

17/257=0,01003233...

18/257=0,01013232...

19/257=0,01023231...

20/257=0,01033230...

21/257=0,01103223...

22/257=0,01113222...

23/257=0,01123221...

24/257=0,01133220...

25/257=0,01203213...

26/257=0,01213212...

27/257=0,01223211...

28/257=0,01233210...

29/257=0,01303203...

30/257=0,01313202...

31/257=0,01323201...

32/257=0,01333200...

33/257=0,02003133...

34/257=0,02013132...

35/257=0,02023131...

36/257=0,02033130...

37/257=0,02103123...

38/257=0,02113122...

39/257=0,02123121...

40/257=0,02133120...

41/257=0,02203113...

42/257=0,02213112...

43/257=0,02223111...

44/257=0,02233110...

45/257=0,02303103...

46/257=0,02313102...

47/257=0,02323101...

48/257=0,02333100...

49/257=0,03003033...

50/257=0,03013032...

51/257=0,03023031...

52/257=0,03033030...

53/257=0,03103023...

54/257=0,03113022...

55/257=0,03123021...

56/257=0,03133020...

57/257=0,03203013...

58/257=0,03213012...

59/257=0,03223011...

60/257=0,03233010...

61/257=0,03303003...

62/257=0,03313002...

63/257=0,03323001...

64/257=0,03333000...

65/257=0,10002333...

66/257=0,10012332...

67/257=0,10022331...

68/257=0,10032330...

69/257=0,10102323...

70/257=0,10112322...

71/257=0,10122321...

72/257=0,10132320...

73/257=0,10202313...

74/257=0,10212312...

75/257=0,10222311...

76/257=0,10232310...

77/257=0,10302303...

78/257=0,10312302...

79/257=0,10322301...

80/257=0,10332300...

81/257=0,11002233...

82/257=0,11012232...

83/257=0,11022231...

84/257=0,11032230...

85/257=0,11102223...

86/257=0,11112222...

87/257=0,11122221...

88/257=0,11132220...

89/257=0,11202213...

90/257=0,11212212...

91/257=0,11222211...

92/257=0,11232210...

93/257=0,11302203...

94/257=0,11312202...

95/257=0,11322201...

96/257=0,11332200...

97/257=0,12002133...

98/257=0,12012132...

99/257=0,12022131...

100/257=0,12032130...

101/257=0,12102123...

102/257=0,12112122...

103/257=0,12122121...

104/257=0,12132120...

105/257=0,12202113...

106/257=0,12212112...

107/257=0,12222111...

108/257=0,12232110...

109/257=0,12302103...

110/257=0,12312102...

111/257=0,12322101...

112/257=0,12332100...

113/257=0,13002033...

114/257=0,13012032...

115/257=0,13022031...

116/257=0,13032030...

117/257=0,13102023...

118/257=0,13112022...

119/257=0,13122021...

120/257=0,13132020...

121/257=0,13202013...

122/257=0,13212012...

123/257=0,13222011...

124/257=0,13232010...

125/257=0,13302003...

126/257=0,13312002...

127/257=0,13322001...

128/257=0,13332000...

129/257=0,20001333...

130/257=0,20011332...

131/257=0,20021331...

132/257=0,20031330...

133/257=0,20101323...

134/257=0,20111322...

135/257=0,20121321...

136/257=0,20131320...

137/257=0,20201313...

138/257=0,20211312...

139/257=0,20221311...

140/257=0,20231310...

141/257=0,20301303...

142/257=0,20311302...

143/257=0,20321301...

144/257=0,20331300...

145/257=0,21001233...

146/257=0,21011232...

147/257=0,21021231...

148/257=0,21031230...

149/257=0,21101223...

150/257=0,21111222...

151/257=0,21121221...

152/257=0,21131220...

153/257=0,21201213...

154/257=0,21211212...

155/257=0,21221211...

156/257=0,21231210...

157/257=0,21301203...

158/257=0,21311202...

159/257=0,21321201...

160/257=0,21331200...

161/257=0,22001133...

162/257=0,22011132...

163/257=0,22021131...

164/257=0,22031130...

165/257=0,22101123...

166/257=0,22111122...

167/257=0,22121121...

168/257=0,22131120...

169/257=0,22201113...

170/257=0,22211112...

171/257=0,22221111...

172/257=0,22231110...

173/257=0,22301103...

174/257=0,22311102...

175/257=0,22321101...

176/257=0,22331100...

177/257=0,23001033...

178/257=0,23011032...

179/257=0,23021031...

180/257=0,23031030...

181/257=0,23101023...

182/257=0,23111022...

183/257=0,23121021...

184/257=0,23131020...

185/257=0,23201013...

186/257=0,23211012...

187/257=0,23221011...

188/257=0,23231010...

189/257=0,23301003...

190/257=0,23311002...

191/257=0,23321001...

192/257=0,23331000...

193/257=0,30000333...

194/257=0,30010332...

195/257=0,30020331...

196/257=0,30030330...

197/257=0,30100323...

198/257=0,30110322...

199/257=0,30120321...

200/257=0,30130320...

201/257=0,30200313...

202/257=0,30210312...

203/257=0,30220311...

204/257=0,30230310...

205/257=0,30300303...

206/257=0,30310302...

207/257=0,30320301...

208/257=0,30330300...

209/257=0,31000233...

210/257=0,31010232...

211/257=0,31020231...

212/257=0,31030230...

213/257=0,31100223...

214/257=0,31110222...

215/257=0,31120221...

216/257=0,31130220...

217/257=0,31200213...

218/257=0,31210212...

219/257=0,31220211...

220/257=0,31230210...

221/257=0,31300203...

222/257=0,31310202...

223/257=0,31320201...

224/257=0,31330200...

225/257=0,32000133...

226/257=0,32010132...

227/257=0,32020131...

228/257=0,32030130...

229/257=0,32100123...

230/257=0,32110122...

231/257=0,32120121...

232/257=0,32130120...

233/257=0,32200113...

234/257=0,32210112...

235/257=0,32220111...

236/257=0,32230110...

237/257=0,32300103...

238/257=0,32310102...

239/257=0,32320101...

240/257=0,32330100...

241/257=0,33000033...

242/257=0,33010032...

243/257=0,33020031...

244/257=0,33030030...

245/257=0,33100023...

246/257=0,33110022...

247/257=0,33120021...

248/257=0,33130020...

249/257=0,33200013...

250/257=0,33210012...

251/257=0,33220011...

252/257=0,33230010...

253/257=0,33300003...

254/257=0,33310002...

255/257=0,33320001...

256/257=0,33330000...

On remarque que le produit du nombre de périodes (32) et de leurs longueurs (8) est égal à 256 et donc au premier -1.