Il existe 6 périodes de 40 chiffres pour n/241 en base 5.

Pour toutes les fractions de n/241 en base 5, la période de 1/241 revient alors 40 fois (en orange)

1/241=0,0002244041113044142044422004033314003024...

2/241=0,0010043132231143334144344013122133011103...

3/241=0,0012342223344243031244321022211002014132...

4/241=0,0020141320012342223344243031244321022211...

5/241=0,0022440411130441420444220040333140030240...

6/241=0,0030240002244041113044142044422004033314...

7/241=0,0033034043412140310144114104010323041343...

8/241=0,0040333140030240002244041113044142044422...

9/241=0,0043132231143334144344013122133011103001...

10/241=0,0100431322311433341443440131221330111030...

11/241=0,0103230413430033034043412140310144114104...

12/241=0,0111030010043132231143334144344013122133...

13/241=0,0113324101211231423243311203432332130212...

14/241=0,0121123142324331120343233213021201133241...

15/241=0,0123422233442430312443210222110020141320...

16/241=0,0131221330111030010043132231143334144344...

17/241=0,0134020421224124202143104240232203202423...

18/241=0,0141320012342223344243031244321022211002...

19/241=0,0144114104010323041343003303404341214031...

20/241=0,0201413200123422233442430312443210222110...

21/241=0,0204212241242021431042402322032024230134...

22/241=0,0212011332410121123142324331120343233213...

23/241=0,0214310424023220320242301340204212241242...

24/241=0,0222110020141320012342223344243031244321...

25/241=0,0224404111304414204442200403331400302400...

26/241=0,0232203202423013402042122412420214310424...

27/241=0,0240002244041113044142044422004033314003...

28/241=0,0242301340204212241242021431042402322032...

29/241=0,0300100431322311433341443440131221330111...

30/241=0,0302400022440411130441420444220040333140...

31/241=0,0310144114104010323041343003303404341214...

32/241=0,0312443210222110020141320012342223344243...

33/241=0,0320242301340204212241242021431042402322...

34/241=0,0323041343003303404341214031014411410401...

35/241=0,0330340434121403101441141040103230413430...

36/241=0,0333140030240002244041113044142044422004...

37/241=0,0340434121403101441141040103230413430033...

38/241=0,0343233213021201133241012112314232433112...

39/241=0,0401032304134300330340434121403101441141...

40/241=0,0403331400302400022440411130441420444220...

41/241=0,0411130441420444220040333140030240002244...

42/241=0,0413430033034043412140310144114104010323...

43/241=0,0421224124202143104240232203202423013402...

44/241=0,0424023220320242301340204212241242021431...

45/241=0,0431322311433341443440131221330111030010...

46/241=0,0434121403101441141040103230413430033034...

47/241=0,0441420444220040333140030240002244041113...

48/241=0,0444220040333140030240002244041113044142...

49/241=0,1002014132001234222334424303124432102221...

50/241=0,1004313223114333414434401312213301110300...

51/241=0,1012112314232433112034323321302120113324...

52/241=0,1014411410401032304134300330340434121403...

53/241=0,1022211002014132001234222334424303124432...

54/241=0,1030010043132231143334144344013122133011...

55/241=0,1032304134300330340434121403101441141040...

56/241=0,1040103230413430033034043412140310144114...

57/241=0,1042402322032024230134020421224124202143...

58/241=0,1100201413200123422233442430312443210222...

59/241=0,1103001004313223114333414434401312213301...

60/241=0,1110300100431322311433341443440131221330...

61/241=0,1113044142044422004033314003024000224404...

62/241=0,1120343233213021201133241012112314232433...

63/241=0,1123142324331120343233213021201133241012...

64/241=0,1130441420444220040333140030240002244041...

65/241=0,1133241012112314232433112034323321302120...

66/241=0,1141040103230413430033034043412140310144...

67/241=0,1143334144344013122133011103001004313223...

68/241=0,1201133241012112314232433112034323321302...

69/241=0,1203432332130212011332410121123142324331...

70/241=0,1211231423243311203432332130212011332410...

71/241=0,1214031014411410401032304134300330340434...

72/241=0,1221330111030010043132231143334144344013...

73/241=0,1224124202143104240232203202423013402042...

74/241=0,1231423243311203432332130212011332410121...

75/241=0,1234222334424303124432102221100201413200...

76/241=0,1242021431042402322032024230134020421224...

77/241=0,1244321022211002014132001234222334424303...

78/241=0,1302120113324101211231423243311203432332...

79/241=0,1304414204442200403331400302400022440411...

80/241=0,1312213301110300100431322311433341443440...

81/241=0,1320012342223344243031244321022211002014...

82/241=0,1322311433341443440131221330111030010043...

83/241=0,1330111030010043132231143334144344013122...

84/241=0,1332410121123142324331120343233213021201...

85/241=0,1340204212241242021431042402322032024230...

86/241=0,1343003303404341214031014411410401032304...

87/241=0,1400302400022440411130441420444220040333...

88/241=0,1403101441141040103230413430033034043412...

89/241=0,1410401032304134300330340434121403101441...

90/241=0,1413200123422233442430312443210222110020...

91/241=0,1420444220040333140030240002244041113044...

92/241=0,1423243311203432332130212011332410121123...

93/241=0,1431042402322032024230134020421224124202...

94/241=0,1433341443440131221330111030010043132231...

95/241=0,1441141040103230413430033034043412140310...

96/241=0,1443440131221330111030010043132231143334...

97/241=0,2001234222334424303124432102221100201413...

98/241=0,2004033314003024000224404111304414204442...

99/241=0,2011332410121123142324331120343233213021...

100/241=0,2014132001234222334424303124432102221100...

101/241=0,2021431042402322032024230134020421224124...

102/241=0,2024230134020421224124202143104240232203...

103/241=0,2032024230134020421224124202143104240232...

104/241=0,2034323321302120113324101211231423243311...

105/241=0,2042122412420214310424023220320242301340...

106/241=0,2044422004033314003024000224404111304414...

107/241=0,2102221100201413200123422233442430312443...

108/241=0,2110020141320012342223344243031244321022...

109/241=0,2112314232433112034323321302120113324101...

110/241=0,2120113324101211231423243311203432332130...

111/241=0,2122412420214310424023220320242301340204...

112/241=0,2130212011332410121123142324331120343233...

113/241=0,2133011103001004313223114333414434401312...

114/241=0,2140310144114104010323041343003303404341...

115/241=0,2143104240232203202423013402042122412420...

116/241=0,2200403331400302400022440411130441420444...

117/241=0,2203202423013402042122412420214310424023...

118/241=0,2211002014132001234222334424303124432102...

119/241=0,2213301110300100431322311433341443440131...

120/241=0,2221100201413200123422233442430312443210...

121/241=0,2223344243031244321022211002014132001234...

122/241=0,2231143334144344013122133011103001004313...

123/241=0,2233442430312443210222110020141320012342...

124/241=0,2241242021431042402322032024230134020421...

125/241=0,2244041113044142044422004033314003024000...

126/241=0,2301340204212241242021431042402322032024...

127/241=0,2304134300330340434121403101441141040103...

128/241=0,2311433341443440131221330111030010043132...

129/241=0,2314232433112034323321302120113324101211...

130/241=0,2322032024230134020421224124202143104240...

131/241=0,2324331120343233213021201133241012112314...

132/241=0,2332130212011332410121123142324331120343...

133/241=0,2334424303124432102221100201413200123422...

134/241=0,2342223344243031244321022211002014132001...

135/241=0,2400022440411130441420444220040333140030...

136/241=0,2402322032024230134020421224124202143104...

137/241=0,2410121123142324331120343233213021201133...

138/241=0,2412420214310424023220320242301340204212...

139/241=0,2420214310424023220320242301340204212241...

140/241=0,2423013402042122412420214310424023220320...

141/241=0,2430312443210222110020141320012342223344...

142/241=0,2433112034323321302120113324101211231423...

143/241=0,2440411130441420444220040333140030240002...

144/241=0,2443210222110020141320012342223344243031...

145/241=0,3001004313223114333414434401312213301110...

146/241=0,3003303404341214031014411410401032304134...

147/241=0,3011103001004313223114333414434401312213...

148/241=0,3013402042122412420214310424023220320242...

149/241=0,3021201133241012112314232433112034323321...

150/241=0,3024000224404111304414204442200403331400...

151/241=0,3031244321022211002014132001234222334424...

152/241=0,3034043412140310144114104010323041343003...

153/241=0,3041343003303404341214031014411410401032...

154/241=0,3044142044422004033314003024000224404111...

155/241=0,3101441141040103230413430033034043412140...

156/241=0,3104240232203202423013402042122412420214...

157/241=0,3112034323321302120113324101211231423243...

158/241=0,3114333414434401312213301110300100431322...

159/241=0,3122133011103001004313223114333414434401...

160/241=0,3124432102221100201413200123422233442430...

161/241=0,3132231143334144344013122133011103001004...

162/241=0,3140030240002244041113044142044422004033...

163/241=0,3142324331120343233213021201133241012112...

164/241=0,3200123422233442430312443210222110020141...

165/241=0,3202423013402042122412420214310424023220...

166/241=0,3210222110020141320012342223344243031244...

167/241=0,3213021201133241012112314232433112034323...

168/241=0,3220320242301340204212241242021431042402...

169/241=0,3223114333414434401312213301110300100431...

170/241=0,3230413430033034043412140310144114104010...

171/241=0,3233213021201133241012112314232433112034...

172/241=0,3241012112314232433112034323321302120113...

173/241=0,3243311203432332130212011332410121123142...

174/241=0,3301110300100431322311433341443440131221...

175/241=0,3303404341214031014411410401032304134300...

176/241=0,3311203432332130212011332410121123142324...

177/241=0,3314003024000224404111304414204442200403...

178/241=0,3321302120113324101211231423243311203432...

179/241=0,3324101211231423243311203432332130212011...

180/241=0,3331400302400022440411130441420444220040...

181/241=0,3334144344013122133011103001004313223114...

182/241=0,3341443440131221330111030010043132231143...

183/241=0,3344243031244321022211002014132001234222...

184/241=0,3402042122412420214310424023220320242301...

185/241=0,3404341214031014411410401032304134300330...

186/241=0,3412140310144114104010323041343003303404...

187/241=0,3414434401312213301110300100431322311433...

188/241=0,3422233442430312443210222110020141320012...

189/241=0,3430033034043412140310144114104010323041...

190/241=0,3432332130212011332410121123142324331120...

191/241=0,3440131221330111030010043132231143334144...

192/241=0,3442430312443210222110020141320012342223...

193/241=0,4000224404111304414204442200403331400302...

194/241=0,4003024000224404111304414204442200403331...

195/241=0,4010323041343003303404341214031014411410...

196/241=0,4013122133011103001004313223114333414434...

197/241=0,4020421224124202143104240232203202423013...

198/241=0,4023220320242301340204212241242021431042...

199/241=0,4031014411410401032304134300330340434121...

200/241=0,4033314003024000224404111304414204442200...

201/241=0,4041113044142044422004033314003024000224...

202/241=0,4043412140310144114104010323041343003303...

203/241=0,4101211231423243311203432332130212011332...

204/241=0,4104010323041343003303404341214031014411...

205/241=0,4111304414204442200403331400302400022440...

206/241=0,4114104010323041343003303404341214031014...

207/241=0,4121403101441141040103230413430033034043...

208/241=0,4124202143104240232203202423013402042122...

209/241=0,4132001234222334424303124432102221100201...

210/241=0,4134300330340434121403101441141040103230...

211/241=0,4142044422004033314003024000224404111304...

212/241=0,4144344013122133011103001004313223114333...

213/241=0,4202143104240232203202423013402042122412...

214/241=0,4204442200403331400302400022440411130441...

215/241=0,4212241242021431042402322032024230134020...

216/241=0,4220040333140030240002244041113044142044...

217/241=0,4222334424303124432102221100201413200123...

218/241=0,4230134020421224124202143104240232203202...

219/241=0,4232433112034323321302120113324101211231...

220/241=0,4240232203202423013402042122412420214310...

221/241=0,4243031244321022211002014132001234222334...

222/241=0,4300330340434121403101441141040103230413...

223/241=0,4303124432102221100201413200123422233442...

224/241=0,4310424023220320242301340204212241242021...

225/241=0,4313223114333414434401312213301110300100...

226/241=0,4321022211002014132001234222334424303124...

227/241=0,4323321302120113324101211231423243311203...

228/241=0,4331120343233213021201133241012112314232...

229/241=0,4333414434401312213301110300100431322311...

230/241=0,4341214031014411410401032304134300330340...

231/241=0,4344013122133011103001004313223114333414...

232/241=0,4401312213301110300100431322311433341443...

233/241=0,4404111304414204442200403331400302400022...

234/241=0,4411410401032304134300330340434121403101...

235/241=0,4414204442200403331400302400022440411130...

236/241=0,4422004033314003024000224404111304414204...

237/241=0,4424303124432102221100201413200123422233...

238/241=0,4432102221100201413200123422233442430312...

239/241=0,4434401312213301110300100431322311433341...

240/241=0,4442200403331400302400022440411130441420...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (40) est égal à 240 et donc au premier -1.