Il existe 14 périodes de 17 chiffres pour n/239 en base 6.

Pour toutes les fractions de n/239 en base 6, la période de 1/239 revient alors 17 fois (en orange)

1/239=0,00052311403151441...

2/239=0,00145023210343322...

3/239=0,00241335013535203...

4/239=0,00334050421131044...

5/239=0,00430402224322525...

6/239=0,00523114031514410...

7/239=0,01015425435110251...

8/239=0,01112141242302132...

9/239=0,01204453045454013...

10/239=0,01301204453045454...

11/239=0,01353520300241335...

12/239=0,01450232103433220...

13/239=0,01542543511025101...

14/239=0,02035255314220542...

15/239=0,02132011121412423...

16/239=0,02224322525004304...

17/239=0,02321034332200145...

18/239=0,02413350135352030...

19/239=0,02510101542543511...

20/239=0,03002413350135352...

21/239=0,03055125153331233...

22/239=0,03151441000523114...

23/239=0,03244152404114555...

24/239=0,03340504211310440...

25/239=0,03433220014502321...

26/239=0,03525531422054202...

27/239=0,04022243225250043...

28/239=0,04114555032441524...

29/239=0,04211310440033405...

30/239=0,04304022243225250...

31/239=0,04400334050421131...

32/239=0,04453045454013012...

33/239=0,04545401301204453...

34/239=0,05042113104400334...

35/239=0,05134424511552215...

36/239=0,05231140315144100...

37/239=0,05323452122335541...

38/239=0,05420203525531422...

39/239=0,05512515333123303...

40/239=0,10005231140315144...

41/239=0,10101542543511025...

42/239=0,10154254351102510...

43/239=0,10251010154254351...

44/239=0,10343322001450232...

45/239=0,10440033405042113...

46/239=0,10532345212233554...

47/239=0,11025101015425435...

48/239=0,11121412423021320...

49/239=0,11214124230213201...

50/239=0,11310440033405042...

51/239=0,11403151441000523...

52/239=0,11455503244152404...

53/239=0,11552215051344245...

54/239=0,12044530454540130...

55/239=0,12141242302132011...

56/239=0,12233554105323452...

57/239=0,12330305512515333...

58/239=0,12423021320111214...

59/239=0,12515333123303055...

60/239=0,13012044530454540...

61/239=0,13104400334050421...

62/239=0,13201112141242302...

63/239=0,13253423544434143...

64/239=0,13350135352030024...

65/239=0,13442451155221505...

66/239=0,13535203002413350...

67/239=0,14031514410005231...

68/239=0,14124230213201112...

69/239=0,14220542020352553...

70/239=0,14313253423544434...

71/239=0,14410005231140315...

72/239=0,14502321034332200...

73/239=0,14555032441524041...

74/239=0,15051344245115522...

75/239=0,15144100052311403...

76/239=0,15240411455503244...

77/239=0,15333123303055125...

78/239=0,15425435110251010...

79/239=0,15522150513442451...

80/239=0,20014502321034332...

81/239=0,20111214124230213...

82/239=0,20203525531422054...

83/239=0,20300241335013535...

84/239=0,20352553142205420...

85/239=0,20445304545401301...

86/239=0,20542020352553142...

87/239=0,21034332200145023...

88/239=0,21131044003340504...

89/239=0,21223355410532345...

90/239=0,21320111214124230...

91/239=0,21412423021320111...

92/239=0,21505134424511552...

93/239=0,22001450232103433...

94/239=0,22054202035255314...

95/239=0,22150513442451155...

96/239=0,22243225250043040...

97/239=0,22335541053234521...

98/239=0,22432252500430402...

99/239=0,22525004304022243...

100/239=0,23021320111214124...

101/239=0,23114031514410005...

102/239=0,23210343322001450...

103/239=0,23303055125153331...

104/239=0,23355410532345212...

105/239=0,23452122335541053...

106/239=0,23544434143132534...

107/239=0,24041145550324415...

108/239=0,24133501353520300...

109/239=0,24230213201112141...

110/239=0,24322525004304022...

111/239=0,24415240411455503...

112/239=0,24511552215051344...

113/239=0,25004304022243225...

114/239=0,25101015425435110...

115/239=0,25153331233030551...

116/239=0,25250043040222432...

117/239=0,25342354443414313...

118/239=0,25435110251010154...

119/239=0,25531422054202035...

120/239=0,30024133501353520...

121/239=0,30120445304545401...

122/239=0,30213201112141242...

123/239=0,30305512515333123...

124/239=0,30402224322525004...

125/239=0,30454540130120445...

126/239=0,30551251533312330...

127/239=0,31044003340504211...

128/239=0,31140315144100052...

129/239=0,31233030551251533...

130/239=0,31325342354443414...

131/239=0,31422054202035255...

132/239=0,31514410005231140...

133/239=0,32011121412423021...

134/239=0,32103433220014502...

135/239=0,32200145023210343...

136/239=0,32252500430402224...

137/239=0,32345212233554105...

138/239=0,32441524041145550...

139/239=0,32534235444341431...

140/239=0,33030551251533312...

141/239=0,33123303055125153...

142/239=0,33220014502321034...

143/239=0,33312330305512515...

144/239=0,33405042113104400...

145/239=0,33501353520300241...

146/239=0,33554105323452122...

147/239=0,34050421131044003...

148/239=0,34143132534235444...

149/239=0,34235444341431325...

150/239=0,34332200145023210...

151/239=0,34424511552215051...

152/239=0,34521223355410532...

153/239=0,35013535203002413...

154/239=0,35110251010154254...

155/239=0,35203002413350135...

156/239=0,35255314220542020...

157/239=0,35352030024133501...

158/239=0,35444341431325342...

159/239=0,35541053234521223...

160/239=0,40033405042113104...

161/239=0,40130120445304545...

162/239=0,40222432252500430...

163/239=0,40315144100052311...

164/239=0,40411455503244152...

165/239=0,40504211310440033...

166/239=0,41000523114031514...

167/239=0,41053234521223355...

168/239=0,41145550324415240...

169/239=0,41242302132011121...

170/239=0,41335013535203002...

171/239=0,41431325342354443...

172/239=0,41524041145550324...

173/239=0,42020352553142205...

174/239=0,42113104400334050...

175/239=0,42205420203525531...

176/239=0,42302132011121412...

177/239=0,42354443414313253...

178/239=0,42451155221505134...

179/239=0,42543511025101015...

180/239=0,43040222432252500...

181/239=0,43132534235444341...

182/239=0,43225250043040222...

183/239=0,43322001450232103...

184/239=0,43414313253423544...

185/239=0,43511025101015425...

186/239=0,44003340504211310...

187/239=0,44100052311403151...

188/239=0,44152404114555032...

189/239=0,44245115522150513...

190/239=0,44341431325342354...

191/239=0,44434143132534235...

192/239=0,44530454540130120...

193/239=0,45023210343322001...

194/239=0,45115522150513442...

195/239=0,45212233554105323...

196/239=0,45304545401301204...

197/239=0,45401301204453045...

198/239=0,45454013012044530...

199/239=0,45550324415240411...

200/239=0,50043040222432252...

201/239=0,50135352030024133...

202/239=0,50232103433220014...

203/239=0,50324415240411455...

204/239=0,50421131044003340...

205/239=0,50513442451155221...

206/239=0,51010154254351102...

207/239=0,51102510101542543...

208/239=0,51155221505134424...

209/239=0,51251533312330305...

210/239=0,51344245115522150...

211/239=0,51441000523114031...

212/239=0,51533312330305512...

213/239=0,52030024133501353...

214/239=0,52122335541053234...

215/239=0,52215051344245115...

216/239=0,52311403151441000...

217/239=0,52404114555032441...

218/239=0,52500430402224322...

219/239=0,52553142205420203...

220/239=0,53045454013012044...

221/239=0,53142205420203525...

222/239=0,53234521223355410...

223/239=0,53331233030551251...

224/239=0,53423544434143132...

225/239=0,53520300241335013...

226/239=0,54013012044530454...

227/239=0,54105323452122335...

228/239=0,54202035255314220...

229/239=0,54254351102510101...

230/239=0,54351102510101542...

231/239=0,54443414313253423...

232/239=0,54540130120445304...

233/239=0,55032441524041145...

234/239=0,55125153331233030...

235/239=0,55221505134424511...

236/239=0,55314220542020352...

237/239=0,55410532345212233...

238/239=0,55503244152404114...

On remarque que le produit du nombre de périodes (14) et de leurs longueurs (17) est égal à 238 et donc au premier -1.