Il existe 20 périodes de 12 chiffres pour n/241 en base 4.

Pour toutes les fractions de n/241 en base 4, la période de 1/241 revient alors 12 fois (en orange)

1/241=0,000100333233...

2/241=0,000201333132...

3/241=0,000302333031...

4/241=0,001003332330...

5/241=0,001110332223...

6/241=0,001211332122...

7/241=0,001312332021...

8/241=0,002013331320...

9/241=0,002120331213...

10/241=0,002221331112...

11/241=0,002322331011...

12/241=0,003023330310...

13/241=0,003130330203...

14/241=0,003231330102...

15/241=0,003332330001...

16/241=0,010033323300...

17/241=0,010200323133...

18/241=0,010301323032...

19/241=0,011002322331...

20/241=0,011103322230...

21/241=0,011210322123...

22/241=0,011311322022...

23/241=0,012012321321...

24/241=0,012113321220...

25/241=0,012220321113...

26/241=0,012321321012...

27/241=0,013022320311...

28/241=0,013123320210...

29/241=0,013230320103...

30/241=0,013331320002...

31/241=0,020032313301...

32/241=0,020133313200...

33/241=0,020300313033...

34/241=0,021001312332...

35/241=0,021102312231...

36/241=0,021203312130...

37/241=0,021310312023...

38/241=0,022011311322...

39/241=0,022112311221...

40/241=0,022213311120...

41/241=0,022320311013...

42/241=0,023021310312...

43/241=0,023122310211...

44/241=0,023223310110...

45/241=0,023330310003...

46/241=0,030031303302...

47/241=0,030132303201...

48/241=0,030233303100...

49/241=0,031000302333...

50/241=0,031101302232...

51/241=0,031202302131...

52/241=0,031303302030...

53/241=0,032010301323...

54/241=0,032111301222...

55/241=0,032212301121...

56/241=0,032313301020...

57/241=0,033020300313...

58/241=0,033121300212...

59/241=0,033222300111...

60/241=0,033323300010...

61/241=0,100030233303...

62/241=0,100131233202...

63/241=0,100232233101...

64/241=0,100333233000...

65/241=0,101100232233...

66/241=0,101201232132...

67/241=0,101302232031...

68/241=0,102003231330...

69/241=0,102110231223...

70/241=0,102211231122...

71/241=0,102312231021...

72/241=0,103013230320...

73/241=0,103120230213...

74/241=0,103221230112...

75/241=0,103322230011...

76/241=0,110023223310...

77/241=0,110130223203...

78/241=0,110231223102...

79/241=0,110332223001...

80/241=0,111033222300...

81/241=0,111200222133...

82/241=0,111301222032...

83/241=0,112002221331...

84/241=0,112103221230...

85/241=0,112210221123...

86/241=0,112311221022...

87/241=0,113012220321...

88/241=0,113113220220...

89/241=0,113220220113...

90/241=0,113321220012...

91/241=0,120022213311...

92/241=0,120123213210...

93/241=0,120230213103...

94/241=0,120331213002...

95/241=0,121032212301...

96/241=0,121133212200...

97/241=0,121300212033...

98/241=0,122001211332...

99/241=0,122102211231...

100/241=0,122203211130...

101/241=0,122310211023...

102/241=0,123011210322...

103/241=0,123112210221...

104/241=0,123213210120...

105/241=0,123320210013...

106/241=0,130021203312...

107/241=0,130122203211...

108/241=0,130223203110...

109/241=0,130330203003...

110/241=0,131031202302...

111/241=0,131132202201...

112/241=0,131233202100...

113/241=0,132000201333...

114/241=0,132101201232...

115/241=0,132202201131...

116/241=0,132303201030...

117/241=0,133010200323...

118/241=0,133111200222...

119/241=0,133212200121...

120/241=0,133313200020...

121/241=0,200020133313...

122/241=0,200121133212...

123/241=0,200222133111...

124/241=0,200323133010...

125/241=0,201030132303...

126/241=0,201131132202...

127/241=0,201232132101...

128/241=0,201333132000...

129/241=0,202100131233...

130/241=0,202201131132...

131/241=0,202302131031...

132/241=0,203003130330...

133/241=0,203110130223...

134/241=0,203211130122...

135/241=0,203312130021...

136/241=0,210013123320...

137/241=0,210120123213...

138/241=0,210221123112...

139/241=0,210322123011...

140/241=0,211023122310...

141/241=0,211130122203...

142/241=0,211231122102...

143/241=0,211332122001...

144/241=0,212033121300...

145/241=0,212200121133...

146/241=0,212301121032...

147/241=0,213002120331...

148/241=0,213103120230...

149/241=0,213210120123...

150/241=0,213311120022...

151/241=0,220012113321...

152/241=0,220113113220...

153/241=0,220220113113...

154/241=0,220321113012...

155/241=0,221022112311...

156/241=0,221123112210...

157/241=0,221230112103...

158/241=0,221331112002...

159/241=0,222032111301...

160/241=0,222133111200...

161/241=0,222300111033...

162/241=0,223001110332...

163/241=0,223102110231...

164/241=0,223203110130...

165/241=0,223310110023...

166/241=0,230011103322...

167/241=0,230112103221...

168/241=0,230213103120...

169/241=0,230320103013...

170/241=0,231021102312...

171/241=0,231122102211...

172/241=0,231223102110...

173/241=0,231330102003...

174/241=0,232031101302...

175/241=0,232132101201...

176/241=0,232233101100...

177/241=0,233000100333...

178/241=0,233101100232...

179/241=0,233202100131...

180/241=0,233303100030...

181/241=0,300010033323...

182/241=0,300111033222...

183/241=0,300212033121...

184/241=0,300313033020...

185/241=0,301020032313...

186/241=0,301121032212...

187/241=0,301222032111...

188/241=0,301323032010...

189/241=0,302030031303...

190/241=0,302131031202...

191/241=0,302232031101...

192/241=0,302333031000...

193/241=0,303100030233...

194/241=0,303201030132...

195/241=0,303302030031...

196/241=0,310003023330...

197/241=0,310110023223...

198/241=0,310211023122...

199/241=0,310312023021...

200/241=0,311013022320...

201/241=0,311120022213...

202/241=0,311221022112...

203/241=0,311322022011...

204/241=0,312023021310...

205/241=0,312130021203...

206/241=0,312231021102...

207/241=0,312332021001...

208/241=0,313033020300...

209/241=0,313200020133...

210/241=0,313301020032...

211/241=0,320002013331...

212/241=0,320103013230...

213/241=0,320210013123...

214/241=0,320311013022...

215/241=0,321012012321...

216/241=0,321113012220...

217/241=0,321220012113...

218/241=0,321321012012...

219/241=0,322022011311...

220/241=0,322123011210...

221/241=0,322230011103...

222/241=0,322331011002...

223/241=0,323032010301...

224/241=0,323133010200...

225/241=0,323300010033...

226/241=0,330001003332...

227/241=0,330102003231...

228/241=0,330203003130...

229/241=0,330310003023...

230/241=0,331011002322...

231/241=0,331112002221...

232/241=0,331213002120...

233/241=0,331320002013...

234/241=0,332021001312...

235/241=0,332122001211...

236/241=0,332223001110...

237/241=0,332330001003...

238/241=0,333031000302...

239/241=0,333132000201...

240/241=0,333233000100...

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