Il existe 12 périodes de 20 chiffres pour n/241 en base 6.

Pour toutes les fractions de n/241 en base 6, la période de 1/241 revient alors 20 fois (en orange)

1/241=0,00052133205550342235...

2/241=0,00144310415541124514...

3/241=0,00240444025531511153...

4/241=0,00333021235522253432...

5/241=0,00425154445513040111...

6/241=0,00521332055503422350...

7/241=0,01013505305454205025...

8/241=0,01110042515444551304...

9/241=0,01202220125435333543...

10/241=0,01254353335430120222...

11/241=0,01350530545420502501...

12/241=0,01443104155411245140...

13/241=0,01535241405402031415...

14/241=0,02031415015352414054...

15/241=0,02123552225343200333...

16/241=0,02220125435333543012...

17/241=0,02312303045324325251...

18/241=0,02404440255315111530...

19/241=0,02501013505305454205...

20/241=0,02553151115300240444...

21/241=0,03045324325251023123...

22/241=0,03141501535241405402...

23/241=0,03234035145232152041...

24/241=0,03330212355222534320...

25/241=0,03422350005213320555...

26/241=0,03514523215204103234...

27/241=0,04011100425154445513...

28/241=0,04103234035145232152...

29/241=0,04155411245140014431...

30/241=0,04251544455130401110...

31/241=0,04344122105121143345...

32/241=0,04440255315111530024...

33/241=0,04532432525102312303...

34/241=0,05025010135053054542...

35/241=0,05121143345043441221...

36/241=0,05213320555034223500...

37/241=0,05305454205025010135...

38/241=0,05402031415015352414...

39/241=0,05454205025010135053...

40/241=0,05550342235000521332...

41/241=0,10042515444551304011...

42/241=0,10135053054542050250...

43/241=0,10231230304532432525...

44/241=0,10323403514523215204...

45/241=0,10415541124514001443...

46/241=0,10512114334504344122...

47/241=0,11004251544455130401...

48/241=0,11100425154445513040...

49/241=0,11153002404440255315...

50/241=0,11245140014431041554...

51/241=0,11341313224421424233...

52/241=0,11433450434412210512...

53/241=0,11530024044402553151...

54/241=0,12022201254353335430...

55/241=0,12114334504344122105...

56/241=0,12210512114334504344...

57/241=0,12303045324325251023...

58/241=0,12355222534320033302...

59/241=0,12451400144310415541...

60/241=0,12543533354301202220...

61/241=0,13040111004251544455...

62/241=0,13132244214242331134...

63/241=0,13224421424233113413...

64/241=0,13320555034223500052...

65/241=0,13413132244214242331...

66/241=0,13505305454205025010...

67/241=0,14001443104155411245...

68/241=0,14054020314150153524...

69/241=0,14150153524140540203...

70/241=0,14242331134131322442...

71/241=0,14334504344122105121...

72/241=0,14431041554112451400...

73/241=0,14523215204103234035...

74/241=0,15015352414054020314...

75/241=0,15111530024044402553...

76/241=0,15204103234035145232...

77/241=0,15300240444025531511...

78/241=0,15352414054020314150...

79/241=0,15444551304011100425...

80/241=0,15541124514001443104...

81/241=0,20033302123552225343...

82/241=0,20125435333543012022...

83/241=0,20222012543533354301...

84/241=0,20314150153524140540...

85/241=0,20410323403514523215...

86/241=0,20502501013505305454...

87/241=0,20555034223500052133...

88/241=0,21051211433450434412...

89/241=0,21143345043441221051...

90/241=0,21235522253432003330...

91/241=0,21332055503422350005...

92/241=0,21424233113413132244...

93/241=0,21520410323403514523...

94/241=0,22012543533354301202...

95/241=0,22105121143345043441...

96/241=0,22201254353335430120...

97/241=0,22253432003330212355...

98/241=0,22350005213320555034...

99/241=0,22442142423311341313...

100/241=0,22534320033302123552...

101/241=0,23030453243252510231...

102/241=0,23123030453243252510...

103/241=0,23215204103234035145...

104/241=0,23311341313224421424...

105/241=0,23403514523215204103...

106/241=0,23500052133205550342...

107/241=0,23552225343200333021...

108/241=0,24044402553151115300...

109/241=0,24140540203141501535...

110/241=0,24233113413132244214...

111/241=0,24325251023123030453...

112/241=0,24421424233113413132...

113/241=0,24514001443104155411...

114/241=0,25010135053054542050...

115/241=0,25102312303045324325...

116/241=0,25154445513040111004...

117/241=0,25251023123030453243...

118/241=0,25343200333021235522...

119/241=0,25435333543012022201...

120/241=0,25531511153002404440...

121/241=0,30024044402553151115...

122/241=0,30120222012543533354...

123/241=0,30212355222534320033...

124/241=0,30304532432525102312...

125/241=0,30401110042515444551...

126/241=0,30453243252510231230...

127/241=0,30545420502501013505...

128/241=0,31041554112451400144...

129/241=0,31134131322442142423...

130/241=0,31230304532432525102...

131/241=0,31322442142423311341...

132/241=0,31415015352414054020...

133/241=0,31511153002404440255...

134/241=0,32003330212355222534...

135/241=0,32055503422350005213...

136/241=0,32152041032340351452...

137/241=0,32244214242331134131...

138/241=0,32340351452321520410...

139/241=0,32432525102312303045...

140/241=0,32525102312303045324...

141/241=0,33021235522253432003...

142/241=0,33113413132244214242...

143/241=0,33205550342235000521...

144/241=0,33302123552225343200...

145/241=0,33354301202220125435...

146/241=0,33450434412210512114...

147/241=0,33543012022201254353...

148/241=0,34035145232152041032...

149/241=0,34131322442142423311...

150/241=0,34223500052133205550...

151/241=0,34320033302123552225...

152/241=0,34412210512114334504...

153/241=0,34504344122105121143...

154/241=0,35000521332055503422...

155/241=0,35053054542050250101...

156/241=0,35145232152041032340...

157/241=0,35241405402031415015...

158/241=0,35333543012022201254...

159/241=0,35430120222012543533...

160/241=0,35522253432003330212...

161/241=0,40014431041554112451...

162/241=0,40111004251544455130...

163/241=0,40203141501535241405...

164/241=0,40255315111530024044...

165/241=0,40351452321520410323...

166/241=0,40444025531511153002...

167/241=0,40540203141501535241...

168/241=0,41032340351452321520...

169/241=0,41124514001443104155...

170/241=0,41221051211433450434...

171/241=0,41313224421424233113...

172/241=0,41405402031415015352...

173/241=0,41501535241405402031...

174/241=0,41554112451400144310...

175/241=0,42050250101350530545...

176/241=0,42142423311341313224...

177/241=0,42235000521332055503...

178/241=0,42331134131322442142...

179/241=0,42423311341313224421...

180/241=0,42515444551304011100...

181/241=0,43012022201254353335...

182/241=0,43104155411245140014...

183/241=0,43200333021235522253...

184/241=0,43252510231230304532...

185/241=0,43345043441221051211...

186/241=0,43441221051211433450...

187/241=0,43533354301202220125...

188/241=0,44025531511153002404...

189/241=0,44122105121143345043...

190/241=0,44214242331134131322...

191/241=0,44310415541124514001...

192/241=0,44402553151115300240...

193/241=0,44455130401110042515...

194/241=0,44551304011100425154...

195/241=0,45043441221051211433...

196/241=0,45140014431041554112...

197/241=0,45232152041032340351...

198/241=0,45324325251023123030...

199/241=0,45420502501013505305...

200/241=0,45513040111004251544...

201/241=0,50005213320555034223...

202/241=0,50101350530545420502...

203/241=0,50153524140540203141...

204/241=0,50250101350530545420...

205/241=0,50342235000521332055...

206/241=0,50434412210512114334...

207/241=0,50530545420502501013...

208/241=0,51023123030453243252...

209/241=0,51115300240444025531...

210/241=0,51211433450434412210...

211/241=0,51304011100425154445...

212/241=0,51400144310415541124...

213/241=0,51452321520410323403...

214/241=0,51544455130401110042...

215/241=0,52041032340351452321...

216/241=0,52133205550342235000...

217/241=0,52225343200333021235...

218/241=0,52321520410323403514...

219/241=0,52414054020314150153...

220/241=0,52510231230304532432...

221/241=0,53002404440255315111...

222/241=0,53054542050250101350...

223/241=0,53151115300240444025...

224/241=0,53243252510231230304...

225/241=0,53335430120222012543...

226/241=0,53432003330212355222...

227/241=0,53524140540203141501...

228/241=0,54020314150153524140...

229/241=0,54112451400144310415...

230/241=0,54205025010135053054...

231/241=0,54301202220125435333...

232/241=0,54353335430120222012...

233/241=0,54445513040111004251...

234/241=0,54542050250101350530...

235/241=0,55034223500052133205...

236/241=0,55130401110042515444...

237/241=0,55222534320033302123...

238/241=0,55315111530024044402...

239/241=0,55411245140014431041...

240/241=0,55503422350005213320...

On remarque que le produit du nombre de périodes (12) et de leurs longueurs (20) est égal à 240 et donc au premier -1.