Il existe 34 périodes de 7 chiffres pour n/239 en base 10.

Pour toutes les fractions de n/239 en base 10, la période de 1/239 revient alors 7 fois (en orange)

1/239=0,0041841...

2/239=0,0083682...

3/239=0,0125523...

4/239=0,0167364...

5/239=0,0209205...

6/239=0,0251046...

7/239=0,0292887...

8/239=0,0334728...

9/239=0,0376569...

10/239=0,0418410...

11/239=0,0460251...

12/239=0,0502092...

13/239=0,0543933...

14/239=0,0585774...

15/239=0,0627615...

16/239=0,0669456...

17/239=0,0711297...

18/239=0,0753138...

19/239=0,0794979...

20/239=0,0836820...

21/239=0,0878661...

22/239=0,0920502...

23/239=0,0962343...

24/239=0,1004184...

25/239=0,1046025...

26/239=0,1087866...

27/239=0,1129707...

28/239=0,1171548...

29/239=0,1213389...

30/239=0,1255230...

31/239=0,1297071...

32/239=0,1338912...

33/239=0,1380753...

34/239=0,1422594...

35/239=0,1464435...

36/239=0,1506276...

37/239=0,1548117...

38/239=0,1589958...

39/239=0,1631799...

40/239=0,1673640...

41/239=0,1715481...

42/239=0,1757322...

43/239=0,1799163...

44/239=0,1841004...

45/239=0,1882845...

46/239=0,1924686...

47/239=0,1966527...

48/239=0,2008368...

49/239=0,2050209...

50/239=0,2092050...

51/239=0,2133891...

52/239=0,2175732...

53/239=0,2217573...

54/239=0,2259414...

55/239=0,2301255...

56/239=0,2343096...

57/239=0,2384937...

58/239=0,2426778...

59/239=0,2468619...

60/239=0,2510460...

61/239=0,2552301...

62/239=0,2594142...

63/239=0,2635983...

64/239=0,2677824...

65/239=0,2719665...

66/239=0,2761506...

67/239=0,2803347...

68/239=0,2845188...

69/239=0,2887029...

70/239=0,2928870...

71/239=0,2970711...

72/239=0,3012552...

73/239=0,3054393...

74/239=0,3096234...

75/239=0,3138075...

76/239=0,3179916...

77/239=0,3221757...

78/239=0,3263598...

79/239=0,3305439...

80/239=0,3347280...

81/239=0,3389121...

82/239=0,3430962...

83/239=0,3472803...

84/239=0,3514644...

85/239=0,3556485...

86/239=0,3598326...

87/239=0,3640167...

88/239=0,3682008...

89/239=0,3723849...

90/239=0,3765690...

91/239=0,3807531...

92/239=0,3849372...

93/239=0,3891213...

94/239=0,3933054...

95/239=0,3974895...

96/239=0,4016736...

97/239=0,4058577...

98/239=0,4100418...

99/239=0,4142259...

100/239=0,4184100...

101/239=0,4225941...

102/239=0,4267782...

103/239=0,4309623...

104/239=0,4351464...

105/239=0,4393305...

106/239=0,4435146...

107/239=0,4476987...

108/239=0,4518828...

109/239=0,4560669...

110/239=0,4602510...

111/239=0,4644351...

112/239=0,4686192...

113/239=0,4728033...

114/239=0,4769874...

115/239=0,4811715...

116/239=0,4853556...

117/239=0,4895397...

118/239=0,4937238...

119/239=0,4979079...

120/239=0,5020920...

121/239=0,5062761...

122/239=0,5104602...

123/239=0,5146443...

124/239=0,5188284...

125/239=0,5230125...

126/239=0,5271966...

127/239=0,5313807...

128/239=0,5355648...

129/239=0,5397489...

130/239=0,5439330...

131/239=0,5481171...

132/239=0,5523012...

133/239=0,5564853...

134/239=0,5606694...

135/239=0,5648535...

136/239=0,5690376...

137/239=0,5732217...

138/239=0,5774058...

139/239=0,5815899...

140/239=0,5857740...

141/239=0,5899581...

142/239=0,5941422...

143/239=0,5983263...

144/239=0,6025104...

145/239=0,6066945...

146/239=0,6108786...

147/239=0,6150627...

148/239=0,6192468...

149/239=0,6234309...

150/239=0,6276150...

151/239=0,6317991...

152/239=0,6359832...

153/239=0,6401673...

154/239=0,6443514...

155/239=0,6485355...

156/239=0,6527196...

157/239=0,6569037...

158/239=0,6610878...

159/239=0,6652719...

160/239=0,6694560...

161/239=0,6736401...

162/239=0,6778242...

163/239=0,6820083...

164/239=0,6861924...

165/239=0,6903765...

166/239=0,6945606...

167/239=0,6987447...

168/239=0,7029288...

169/239=0,7071129...

170/239=0,7112970...

171/239=0,7154811...

172/239=0,7196652...

173/239=0,7238493...

174/239=0,7280334...

175/239=0,7322175...

176/239=0,7364016...

177/239=0,7405857...

178/239=0,7447698...

179/239=0,7489539...

180/239=0,7531380...

181/239=0,7573221...

182/239=0,7615062...

183/239=0,7656903...

184/239=0,7698744...

185/239=0,7740585...

186/239=0,7782426...

187/239=0,7824267...

188/239=0,7866108...

189/239=0,7907949...

190/239=0,7949790...

191/239=0,7991631...

192/239=0,8033472...

193/239=0,8075313...

194/239=0,8117154...

195/239=0,8158995...

196/239=0,8200836...

197/239=0,8242677...

198/239=0,8284518...

199/239=0,8326359...

200/239=0,8368200...

201/239=0,8410041...

202/239=0,8451882...

203/239=0,8493723...

204/239=0,8535564...

205/239=0,8577405...

206/239=0,8619246...

207/239=0,8661087...

208/239=0,8702928...

209/239=0,8744769...

210/239=0,8786610...

211/239=0,8828451...

212/239=0,8870292...

213/239=0,8912133...

214/239=0,8953974...

215/239=0,8995815...

216/239=0,9037656...

217/239=0,9079497...

218/239=0,9121338...

219/239=0,9163179...

220/239=0,9205020...

221/239=0,9246861...

222/239=0,9288702...

223/239=0,9330543...

224/239=0,9372384...

225/239=0,9414225...

226/239=0,9456066...

227/239=0,9497907...

228/239=0,9539748...

229/239=0,9581589...

230/239=0,9623430...

231/239=0,9665271...

232/239=0,9707112...

233/239=0,9748953...

234/239=0,9790794...

235/239=0,9832635...

236/239=0,9874476...

237/239=0,9916317...

238/239=0,9958158...

On remarque que le produit du nombre de périodes (34) et de leurs longueurs (7) est égal à 238 et donc au premier -1.