Il existe 10 périodes de 24 chiffres pour n/241 en base 2.

Pour toutes les fractions de n/241 en base 2, la période de 1/241 revient alors 24 fois (en orange)

1/241=0,000000010000111111101111...

2/241=0,000000100001111111011110...

3/241=0,000000110010111111001101...

4/241=0,000001000011111110111100...

5/241=0,000001010100111110101011...

6/241=0,000001100101111110011010...

7/241=0,000001110110111110001001...

8/241=0,000010000111111101111000...

9/241=0,000010011000111101100111...

10/241=0,000010101001111101010110...

11/241=0,000010111010111101000101...

12/241=0,000011001011111100110100...

13/241=0,000011011100111100100011...

14/241=0,000011101101111100010010...

15/241=0,000011111110111100000001...

16/241=0,000100001111111011110000...

17/241=0,000100100000111011011111...

18/241=0,000100110001111011001110...

19/241=0,000101000010111010111101...

20/241=0,000101010011111010101100...

21/241=0,000101100100111010011011...

22/241=0,000101110101111010001010...

23/241=0,000110000110111001111001...

24/241=0,000110010111111001101000...

25/241=0,000110101000111001010111...

26/241=0,000110111001111001000110...

27/241=0,000111001010111000110101...

28/241=0,000111011011111000100100...

29/241=0,000111101100111000010011...

30/241=0,000111111101111000000010...

31/241=0,001000001110110111110001...

32/241=0,001000011111110111100000...

33/241=0,001000110000110111001111...

34/241=0,001001000001110110111110...

35/241=0,001001010010110110101101...

36/241=0,001001100011110110011100...

37/241=0,001001110100110110001011...

38/241=0,001010000101110101111010...

39/241=0,001010010110110101101001...

40/241=0,001010100111110101011000...

41/241=0,001010111000110101000111...

42/241=0,001011001001110100110110...

43/241=0,001011011010110100100101...

44/241=0,001011101011110100010100...

45/241=0,001011111100110100000011...

46/241=0,001100001101110011110010...

47/241=0,001100011110110011100001...

48/241=0,001100101111110011010000...

49/241=0,001101000000110010111111...

50/241=0,001101010001110010101110...

51/241=0,001101100010110010011101...

52/241=0,001101110011110010001100...

53/241=0,001110000100110001111011...

54/241=0,001110010101110001101010...

55/241=0,001110100110110001011001...

56/241=0,001110110111110001001000...

57/241=0,001111001000110000110111...

58/241=0,001111011001110000100110...

59/241=0,001111101010110000010101...

60/241=0,001111111011110000000100...

61/241=0,010000001100101111110011...

62/241=0,010000011101101111100010...

63/241=0,010000101110101111010001...

64/241=0,010000111111101111000000...

65/241=0,010001010000101110101111...

66/241=0,010001100001101110011110...

67/241=0,010001110010101110001101...

68/241=0,010010000011101101111100...

69/241=0,010010010100101101101011...

70/241=0,010010100101101101011010...

71/241=0,010010110110101101001001...

72/241=0,010011000111101100111000...

73/241=0,010011011000101100100111...

74/241=0,010011101001101100010110...

75/241=0,010011111010101100000101...

76/241=0,010100001011101011110100...

77/241=0,010100011100101011100011...

78/241=0,010100101101101011010010...

79/241=0,010100111110101011000001...

80/241=0,010101001111101010110000...

81/241=0,010101100000101010011111...

82/241=0,010101110001101010001110...

83/241=0,010110000010101001111101...

84/241=0,010110010011101001101100...

85/241=0,010110100100101001011011...

86/241=0,010110110101101001001010...

87/241=0,010111000110101000111001...

88/241=0,010111010111101000101000...

89/241=0,010111101000101000010111...

90/241=0,010111111001101000000110...

91/241=0,011000001010100111110101...

92/241=0,011000011011100111100100...

93/241=0,011000101100100111010011...

94/241=0,011000111101100111000010...

95/241=0,011001001110100110110001...

96/241=0,011001011111100110100000...

97/241=0,011001110000100110001111...

98/241=0,011010000001100101111110...

99/241=0,011010010010100101101101...

100/241=0,011010100011100101011100...

101/241=0,011010110100100101001011...

102/241=0,011011000101100100111010...

103/241=0,011011010110100100101001...

104/241=0,011011100111100100011000...

105/241=0,011011111000100100000111...

106/241=0,011100001001100011110110...

107/241=0,011100011010100011100101...

108/241=0,011100101011100011010100...

109/241=0,011100111100100011000011...

110/241=0,011101001101100010110010...

111/241=0,011101011110100010100001...

112/241=0,011101101111100010010000...

113/241=0,011110000000100001111111...

114/241=0,011110010001100001101110...

115/241=0,011110100010100001011101...

116/241=0,011110110011100001001100...

117/241=0,011111000100100000111011...

118/241=0,011111010101100000101010...

119/241=0,011111100110100000011001...

120/241=0,011111110111100000001000...

121/241=0,100000001000011111110111...

122/241=0,100000011001011111100110...

123/241=0,100000101010011111010101...

124/241=0,100000111011011111000100...

125/241=0,100001001100011110110011...

126/241=0,100001011101011110100010...

127/241=0,100001101110011110010001...

128/241=0,100001111111011110000000...

129/241=0,100010010000011101101111...

130/241=0,100010100001011101011110...

131/241=0,100010110010011101001101...

132/241=0,100011000011011100111100...

133/241=0,100011010100011100101011...

134/241=0,100011100101011100011010...

135/241=0,100011110110011100001001...

136/241=0,100100000111011011111000...

137/241=0,100100011000011011100111...

138/241=0,100100101001011011010110...

139/241=0,100100111010011011000101...

140/241=0,100101001011011010110100...

141/241=0,100101011100011010100011...

142/241=0,100101101101011010010010...

143/241=0,100101111110011010000001...

144/241=0,100110001111011001110000...

145/241=0,100110100000011001011111...

146/241=0,100110110001011001001110...

147/241=0,100111000010011000111101...

148/241=0,100111010011011000101100...

149/241=0,100111100100011000011011...

150/241=0,100111110101011000001010...

151/241=0,101000000110010111111001...

152/241=0,101000010111010111101000...

153/241=0,101000101000010111010111...

154/241=0,101000111001010111000110...

155/241=0,101001001010010110110101...

156/241=0,101001011011010110100100...

157/241=0,101001101100010110010011...

158/241=0,101001111101010110000010...

159/241=0,101010001110010101110001...

160/241=0,101010011111010101100000...

161/241=0,101010110000010101001111...

162/241=0,101011000001010100111110...

163/241=0,101011010010010100101101...

164/241=0,101011100011010100011100...

165/241=0,101011110100010100001011...

166/241=0,101100000101010011111010...

167/241=0,101100010110010011101001...

168/241=0,101100100111010011011000...

169/241=0,101100111000010011000111...

170/241=0,101101001001010010110110...

171/241=0,101101011010010010100101...

172/241=0,101101101011010010010100...

173/241=0,101101111100010010000011...

174/241=0,101110001101010001110010...

175/241=0,101110011110010001100001...

176/241=0,101110101111010001010000...

177/241=0,101111000000010000111111...

178/241=0,101111010001010000101110...

179/241=0,101111100010010000011101...

180/241=0,101111110011010000001100...

181/241=0,110000000100001111111011...

182/241=0,110000010101001111101010...

183/241=0,110000100110001111011001...

184/241=0,110000110111001111001000...

185/241=0,110001001000001110110111...

186/241=0,110001011001001110100110...

187/241=0,110001101010001110010101...

188/241=0,110001111011001110000100...

189/241=0,110010001100001101110011...

190/241=0,110010011101001101100010...

191/241=0,110010101110001101010001...

192/241=0,110010111111001101000000...

193/241=0,110011010000001100101111...

194/241=0,110011100001001100011110...

195/241=0,110011110010001100001101...

196/241=0,110100000011001011111100...

197/241=0,110100010100001011101011...

198/241=0,110100100101001011011010...

199/241=0,110100110110001011001001...

200/241=0,110101000111001010111000...

201/241=0,110101011000001010100111...

202/241=0,110101101001001010010110...

203/241=0,110101111010001010000101...

204/241=0,110110001011001001110100...

205/241=0,110110011100001001100011...

206/241=0,110110101101001001010010...

207/241=0,110110111110001001000001...

208/241=0,110111001111001000110000...

209/241=0,110111100000001000011111...

210/241=0,110111110001001000001110...

211/241=0,111000000010000111111101...

212/241=0,111000010011000111101100...

213/241=0,111000100100000111011011...

214/241=0,111000110101000111001010...

215/241=0,111001000110000110111001...

216/241=0,111001010111000110101000...

217/241=0,111001101000000110010111...

218/241=0,111001111001000110000110...

219/241=0,111010001010000101110101...

220/241=0,111010011011000101100100...

221/241=0,111010101100000101010011...

222/241=0,111010111101000101000010...

223/241=0,111011001110000100110001...

224/241=0,111011011111000100100000...

225/241=0,111011110000000100001111...

226/241=0,111100000001000011111110...

227/241=0,111100010010000011101101...

228/241=0,111100100011000011011100...

229/241=0,111100110100000011001011...

230/241=0,111101000101000010111010...

231/241=0,111101010110000010101001...

232/241=0,111101100111000010011000...

233/241=0,111101111000000010000111...

234/241=0,111110001001000001110110...

235/241=0,111110011010000001100101...

236/241=0,111110101011000001010100...

237/241=0,111110111100000001000011...

238/241=0,111111001101000000110010...

239/241=0,111111011110000000100001...

240/241=0,111111101111000000010000...

On remarque que le produit du nombre de périodes (10) et de leurs longueurs (24) est égal à 240 et donc au premier -1.