Il existe 3 périodes de 76 chiffres pour n/229 en base 2.

Pour toutes les fractions de n/229 en base 2, la période de 1/229 revient alors 76 fois (en orange)

1/229=0,0000000100011110001011101111001110110011111110111000011101000100001100010011...

2/229=0,0000001000111100010111011110011101100111111101110000111010001000011000100110...

3/229=0,0000001101011010100011001101101100011011111100101001010111001100100100111001...

4/229=0,0000010001111000101110111100111011001111111011100001110100010000110001001100...

5/229=0,0000010110010110111010101100001010000011111010011010010001010100111101011111...

6/229=0,0000011010110101000110011011011000110111111001010010101110011001001001110010...

7/229=0,0000011111010011010010001010100111101011111000001011001011011101010110000101...

8/229=0,0000100011110001011101111001110110011111110111000011101000100001100010011000...

9/229=0,0000101000001111101001101001000101010011110101111100000101100101101110101011...

10/229=0,0000101100101101110101011000010100000111110100110100100010101001111010111110...

11/229=0,0000110001001100000001000111100010111011110011101100111111101110000111010001...

12/229=0,0000110101101010001100110110110001101111110010100101011100110010010011100100...

13/229=0,0000111010001000011000100110000000100011110001011101111001110110011111110111...

14/229=0,0000111110100110100100010101001111010111110000010110010110111010101100001010...

15/229=0,0001000011000100110000000100011110001011101111001110110011111110111000011101...

16/229=0,0001000111100010111011110011101100111111101110000111010001000011000100110000...

17/229=0,0001001100000001000111100010111011110011101100111111101110000111010001000011...

18/229=0,0001010000011111010011010010001010100111101011111000001011001011011101010110...

19/229=0,0001010100111101011111000001011001011011101010110000101000001111101001101001...

20/229=0,0001011001011011101010110000101000001111101001101001000101010011110101111100...

21/229=0,0001011101111001110110011111110111000011101000100001100010011000000010001111...

22/229=0,0001100010011000000010001111000101110111100111011001111111011100001110100010...

23/229=0,0001100110110110001101111110010100101011100110010010011100100000011010110101...

24/229=0,0001101011010100011001101101100011011111100101001010111001100100100111001000...

25/229=0,0001101111110010100101011100110010010011100100000011010110101000110011011011...

26/229=0,0001110100010000110001001100000001000111100010111011110011101100111111101110...

27/229=0,0001111000101110111100111011001111111011100001110100010000110001001100000001...

28/229=0,0001111101001101001000101010011110101111100000101100101101110101011000010100...

29/229=0,0010000001101011010100011001101101100011011111100101001010111001100100100111...

30/229=0,0010000110001001100000001000111100010111011110011101100111111101110000111010...

31/229=0,0010001010100111101011111000001011001011011101010110000101000001111101001101...

32/229=0,0010001111000101110111100111011001111111011100001110100010000110001001100000...

33/229=0,0010010011100100000011010110101000110011011011000110111111001010010101110011...

34/229=0,0010011000000010001111000101110111100111011001111111011100001110100010000110...

35/229=0,0010011100100000011010110101000110011011011000110111111001010010101110011001...

36/229=0,0010100000111110100110100100010101001111010111110000010110010110111010101100...

37/229=0,0010100101011100110010010011100100000011010110101000110011011011000110111111...

38/229=0,0010101001111010111110000010110010110111010101100001010000011111010011010010...

39/229=0,0010101110011001001001110010000001101011010100011001101101100011011111100101...

40/229=0,0010110010110111010101100001010000011111010011010010001010100111101011111000...

41/229=0,0010110111010101100001010000011111010011010010001010100111101011111000001011...

42/229=0,0010111011110011101100111111101110000111010001000011000100110000000100011110...

43/229=0,0011000000010001111000101110111100111011001111111011100001110100010000110001...

44/229=0,0011000100110000000100011110001011101111001110110011111110111000011101000100...

45/229=0,0011001001001110010000001101011010100011001101101100011011111100101001010111...

46/229=0,0011001101101100011011111100101001010111001100100100111001000000110101101010...

47/229=0,0011010010001010100111101011111000001011001011011101010110000101000001111101...

48/229=0,0011010110101000110011011011000110111111001010010101110011001001001110010000...

49/229=0,0011011011000110111111001010010101110011001001001110010000001101011010100011...

50/229=0,0011011111100101001010111001100100100111001000000110101101010001100110110110...

51/229=0,0011100100000011010110101000110011011011000110111111001010010101110011001001...

52/229=0,0011101000100001100010011000000010001111000101110111100111011001111111011100...

53/229=0,0011101100111111101110000111010001000011000100110000000100011110001011101111...

54/229=0,0011110001011101111001110110011111110111000011101000100001100010011000000010...

55/229=0,0011110101111100000101100101101110101011000010100000111110100110100100010101...

56/229=0,0011111010011010010001010100111101011111000001011001011011101010110000101000...

57/229=0,0011111110111000011101000100001100010011000000010001111000101110111100111011...

58/229=0,0100000011010110101000110011011011000110111111001010010101110011001001001110...

59/229=0,0100000111110100110100100010101001111010111110000010110010110111010101100001...

60/229=0,0100001100010011000000010001111000101110111100111011001111111011100001110100...

61/229=0,0100010000110001001100000001000111100010111011110011101100111111101110000111...

62/229=0,0100010101001111010111110000010110010110111010101100001010000011111010011010...

63/229=0,0100011001101101100011011111100101001010111001100100100111001000000110101101...

64/229=0,0100011110001011101111001110110011111110111000011101000100001100010011000000...

65/229=0,0100100010101001111010111110000010110010110111010101100001010000011111010011...

66/229=0,0100100111001000000110101101010001100110110110001101111110010100101011100110...

67/229=0,0100101011100110010010011100100000011010110101000110011011011000110111111001...

68/229=0,0100110000000100011110001011101111001110110011111110111000011101000100001100...

69/229=0,0100110100100010101001111010111110000010110010110111010101100001010000011111...

70/229=0,0100111001000000110101101010001100110110110001101111110010100101011100110010...

71/229=0,0100111101011111000001011001011011101010110000101000001111101001101001000101...

72/229=0,0101000001111101001101001000101010011110101111100000101100101101110101011000...

73/229=0,0101000110011011011000110111111001010010101110011001001001110010000001101011...

74/229=0,0101001010111001100100100111001000000110101101010001100110110110001101111110...

75/229=0,0101001111010111110000010110010110111010101100001010000011111010011010010001...

76/229=0,0101010011110101111100000101100101101110101011000010100000111110100110100100...

77/229=0,0101011000010100000111110100110100100010101001111010111110000010110010110111...

78/229=0,0101011100110010010011100100000011010110101000110011011011000110111111001010...

79/229=0,0101100001010000011111010011010010001010100111101011111000001011001011011101...

80/229=0,0101100101101110101011000010100000111110100110100100010101001111010111110000...

81/229=0,0101101010001100110110110001101111110010100101011100110010010011100100000011...

82/229=0,0101101110101011000010100000111110100110100100010101001111010111110000010110...

83/229=0,0101110011001001001110010000001101011010100011001101101100011011111100101001...

84/229=0,0101110111100111011001111111011100001110100010000110001001100000001000111100...

85/229=0,0101111100000101100101101110101011000010100000111110100110100100010101001111...

86/229=0,0110000000100011110001011101111001110110011111110111000011101000100001100010...

87/229=0,0110000101000001111101001101001000101010011110101111100000101100101101110101...

88/229=0,0110001001100000001000111100010111011110011101100111111101110000111010001000...

89/229=0,0110001101111110010100101011100110010010011100100000011010110101000110011011...

90/229=0,0110010010011100100000011010110101000110011011011000110111111001010010101110...

91/229=0,0110010110111010101100001010000011111010011010010001010100111101011111000001...

92/229=0,0110011011011000110111111001010010101110011001001001110010000001101011010100...

93/229=0,0110011111110111000011101000100001100010011000000010001111000101110111100111...

94/229=0,0110100100010101001111010111110000010110010110111010101100001010000011111010...

95/229=0,0110101000110011011011000110111111001010010101110011001001001110010000001101...

96/229=0,0110101101010001100110110110001101111110010100101011100110010010011100100000...

97/229=0,0110110001101111110010100101011100110010010011100100000011010110101000110011...

98/229=0,0110110110001101111110010100101011100110010010011100100000011010110101000110...

99/229=0,0110111010101100001010000011111010011010010001010100111101011111000001011001...

100/229=0,0110111111001010010101110011001001001110010000001101011010100011001101101100...

101/229=0,0111000011101000100001100010011000000010001111000101110111100111011001111111...

102/229=0,0111001000000110101101010001100110110110001101111110010100101011100110010010...

103/229=0,0111001100100100111001000000110101101010001100110110110001101111110010100101...

104/229=0,0111010001000011000100110000000100011110001011101111001110110011111110111000...

105/229=0,0111010101100001010000011111010011010010001010100111101011111000001011001011...

106/229=0,0111011001111111011100001110100010000110001001100000001000111100010111011110...

107/229=0,0111011110011101100111111101110000111010001000011000100110000000100011110001...

108/229=0,0111100010111011110011101100111111101110000111010001000011000100110000000100...

109/229=0,0111100111011001111111011100001110100010000110001001100000001000111100010111...

110/229=0,0111101011111000001011001011011101010110000101000001111101001101001000101010...

111/229=0,0111110000010110010110111010101100001010000011111010011010010001010100111101...

112/229=0,0111110100110100100010101001111010111110000010110010110111010101100001010000...

113/229=0,0111111001010010101110011001001001110010000001101011010100011001101101100011...

114/229=0,0111111101110000111010001000011000100110000000100011110001011101111001110110...

115/229=0,1000000010001111000101110111100111011001111111011100001110100010000110001001...

116/229=0,1000000110101101010001100110110110001101111110010100101011100110010010011100...

117/229=0,1000001011001011011101010110000101000001111101001101001000101010011110101111...

118/229=0,1000001111101001101001000101010011110101111100000101100101101110101011000010...

119/229=0,1000010100000111110100110100100010101001111010111110000010110010110111010101...

120/229=0,1000011000100110000000100011110001011101111001110110011111110111000011101000...

121/229=0,1000011101000100001100010011000000010001111000101110111100111011001111111011...

122/229=0,1000100001100010011000000010001111000101110111100111011001111111011100001110...

123/229=0,1000100110000000100011110001011101111001110110011111110111000011101000100001...

124/229=0,1000101010011110101111100000101100101101110101011000010100000111110100110100...

125/229=0,1000101110111100111011001111111011100001110100010000110001001100000001000111...

126/229=0,1000110011011011000110111111001010010101110011001001001110010000001101011010...

127/229=0,1000110111111001010010101110011001001001110010000001101011010100011001101101...

128/229=0,1000111100010111011110011101100111111101110000111010001000011000100110000000...

129/229=0,1001000000110101101010001100110110110001101111110010100101011100110010010011...

130/229=0,1001000101010011110101111100000101100101101110101011000010100000111110100110...

131/229=0,1001001001110010000001101011010100011001101101100011011111100101001010111001...

132/229=0,1001001110010000001101011010100011001101101100011011111100101001010111001100...

133/229=0,1001010010101110011001001001110010000001101011010100011001101101100011011111...

134/229=0,1001010111001100100100111001000000110101101010001100110110110001101111110010...

135/229=0,1001011011101010110000101000001111101001101001000101010011110101111100000101...

136/229=0,1001100000001000111100010111011110011101100111111101110000111010001000011000...

137/229=0,1001100100100111001000000110101101010001100110110110001101111110010100101011...

138/229=0,1001101001000101010011110101111100000101100101101110101011000010100000111110...

139/229=0,1001101101100011011111100101001010111001100100100111001000000110101101010001...

140/229=0,1001110010000001101011010100011001101101100011011111100101001010111001100100...

141/229=0,1001110110011111110111000011101000100001100010011000000010001111000101110111...

142/229=0,1001111010111110000010110010110111010101100001010000011111010011010010001010...

143/229=0,1001111111011100001110100010000110001001100000001000111100010111011110011101...

144/229=0,1010000011111010011010010001010100111101011111000001011001011011101010110000...

145/229=0,1010001000011000100110000000100011110001011101111001110110011111110111000011...

146/229=0,1010001100110110110001101111110010100101011100110010010011100100000011010110...

147/229=0,1010010001010100111101011111000001011001011011101010110000101000001111101001...

148/229=0,1010010101110011001001001110010000001101011010100011001101101100011011111100...

149/229=0,1010011010010001010100111101011111000001011001011011101010110000101000001111...

150/229=0,1010011110101111100000101100101101110101011000010100000111110100110100100010...

151/229=0,1010100011001101101100011011111100101001010111001100100100111001000000110101...

152/229=0,1010100111101011111000001011001011011101010110000101000001111101001101001000...

153/229=0,1010101100001010000011111010011010010001010100111101011111000001011001011011...

154/229=0,1010110000101000001111101001101001000101010011110101111100000101100101101110...

155/229=0,1010110101000110011011011000110111111001010010101110011001001001110010000001...

156/229=0,1010111001100100100111001000000110101101010001100110110110001101111110010100...

157/229=0,1010111110000010110010110111010101100001010000011111010011010010001010100111...

158/229=0,1011000010100000111110100110100100010101001111010111110000010110010110111010...

159/229=0,1011000110111111001010010101110011001001001110010000001101011010100011001101...

160/229=0,1011001011011101010110000101000001111101001101001000101010011110101111100000...

161/229=0,1011001111111011100001110100010000110001001100000001000111100010111011110011...

162/229=0,1011010100011001101101100011011111100101001010111001100100100111001000000110...

163/229=0,1011011000110111111001010010101110011001001001110010000001101011010100011001...

164/229=0,1011011101010110000101000001111101001101001000101010011110101111100000101100...

165/229=0,1011100001110100010000110001001100000001000111100010111011110011101100111111...

166/229=0,1011100110010010011100100000011010110101000110011011011000110111111001010010...

167/229=0,1011101010110000101000001111101001101001000101010011110101111100000101100101...

168/229=0,1011101111001110110011111110111000011101000100001100010011000000010001111000...

169/229=0,1011110011101100111111101110000111010001000011000100110000000100011110001011...

170/229=0,1011111000001011001011011101010110000101000001111101001101001000101010011110...

171/229=0,1011111100101001010111001100100100111001000000110101101010001100110110110001...

172/229=0,1100000001000111100010111011110011101100111111101110000111010001000011000100...

173/229=0,1100000101100101101110101011000010100000111110100110100100010101001111010111...

174/229=0,1100001010000011111010011010010001010100111101011111000001011001011011101010...

175/229=0,1100001110100010000110001001100000001000111100010111011110011101100111111101...

176/229=0,1100010011000000010001111000101110111100111011001111111011100001110100010000...

177/229=0,1100010111011110011101100111111101110000111010001000011000100110000000100011...

178/229=0,1100011011111100101001010111001100100100111001000000110101101010001100110110...

179/229=0,1100100000011010110101000110011011011000110111111001010010101110011001001001...

180/229=0,1100100100111001000000110101101010001100110110110001101111110010100101011100...

181/229=0,1100101001010111001100100100111001000000110101101010001100110110110001101111...

182/229=0,1100101101110101011000010100000111110100110100100010101001111010111110000010...

183/229=0,1100110010010011100100000011010110101000110011011011000110111111001010010101...

184/229=0,1100110110110001101111110010100101011100110010010011100100000011010110101000...

185/229=0,1100111011001111111011100001110100010000110001001100000001000111100010111011...

186/229=0,1100111111101110000111010001000011000100110000000100011110001011101111001110...

187/229=0,1101000100001100010011000000010001111000101110111100111011001111111011100001...

188/229=0,1101001000101010011110101111100000101100101101110101011000010100000111110100...

189/229=0,1101001101001000101010011110101111100000101100101101110101011000010100000111...

190/229=0,1101010001100110110110001101111110010100101011100110010010011100100000011010...

191/229=0,1101010110000101000001111101001101001000101010011110101111100000101100101101...

192/229=0,1101011010100011001101101100011011111100101001010111001100100100111001000000...

193/229=0,1101011111000001011001011011101010110000101000001111101001101001000101010011...

194/229=0,1101100011011111100101001010111001100100100111001000000110101101010001100110...

195/229=0,1101100111111101110000111010001000011000100110000000100011110001011101111001...

196/229=0,1101101100011011111100101001010111001100100100111001000000110101101010001100...

197/229=0,1101110000111010001000011000100110000000100011110001011101111001110110011111...

198/229=0,1101110101011000010100000111110100110100100010101001111010111110000010110010...

199/229=0,1101111001110110011111110111000011101000100001100010011000000010001111000101...

200/229=0,1101111110010100101011100110010010011100100000011010110101000110011011011000...

201/229=0,1110000010110010110111010101100001010000011111010011010010001010100111101011...

202/229=0,1110000111010001000011000100110000000100011110001011101111001110110011111110...

203/229=0,1110001011101111001110110011111110111000011101000100001100010011000000010001...

204/229=0,1110010000001101011010100011001101101100011011111100101001010111001100100100...

205/229=0,1110010100101011100110010010011100100000011010110101000110011011011000110111...

206/229=0,1110011001001001110010000001101011010100011001101101100011011111100101001010...

207/229=0,1110011101100111111101110000111010001000011000100110000000100011110001011101...

208/229=0,1110100010000110001001100000001000111100010111011110011101100111111101110000...

209/229=0,1110100110100100010101001111010111110000010110010110111010101100001010000011...

210/229=0,1110101011000010100000111110100110100100010101001111010111110000010110010110...

211/229=0,1110101111100000101100101101110101011000010100000111110100110100100010101001...

212/229=0,1110110011111110111000011101000100001100010011000000010001111000101110111100...

213/229=0,1110111000011101000100001100010011000000010001111000101110111100111011001111...

214/229=0,1110111100111011001111111011100001110100010000110001001100000001000111100010...

215/229=0,1111000001011001011011101010110000101000001111101001101001000101010011110101...

216/229=0,1111000101110111100111011001111111011100001110100010000110001001100000001000...

217/229=0,1111001010010101110011001001001110010000001101011010100011001101101100011011...

218/229=0,1111001110110011111110111000011101000100001100010011000000010001111000101110...

219/229=0,1111010011010010001010100111101011111000001011001011011101010110000101000001...

220/229=0,1111010111110000010110010110111010101100001010000011111010011010010001010100...

221/229=0,1111011100001110100010000110001001100000001000111100010111011110011101100111...

222/229=0,1111100000101100101101110101011000010100000111110100110100100010101001111010...

223/229=0,1111100101001010111001100100100111001000000110101101010001100110110110001101...

224/229=0,1111101001101001000101010011110101111100000101100101101110101011000010100000...

225/229=0,1111101110000111010001000011000100110000000100011110001011101111001110110011...

226/229=0,1111110010100101011100110010010011100100000011010110101000110011011011000110...

227/229=0,1111110111000011101000100001100010011000000010001111000101110111100111011001...

228/229=0,1111111011100001110100010000110001001100000001000111100010111011110011101100...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (76) est égal à 228 et donc au premier -1.