Il existe 6 périodes de 37 chiffres pour n/223 en base 2.

Pour toutes les fractions de n/223 en base 2, la période de 1/223 revient alors 37 fois (en orange)

1/223=0,0000000100100101111000100010011100001...

2/223=0,0000001001001011110001000100111000010...

3/223=0,0000001101110001101001100111010100011...

4/223=0,0000010010010111100010001001110000100...

5/223=0,0000010110111101011010101100001100101...

6/223=0,0000011011100011010011001110101000110...

7/223=0,0000100000001001001011110001000100111...

8/223=0,0000100100101111000100010011100001000...

9/223=0,0000101001010100111100110101111101001...

10/223=0,0000101101111010110101011000011001010...

11/223=0,0000110010100000101101111010110101011...

12/223=0,0000110111000110100110011101010001100...

13/223=0,0000111011101100011110111111101101101...

14/223=0,0001000000010010010111100010001001110...

15/223=0,0001000100111000010000000100100101111...

16/223=0,0001001001011110001000100111000010000...

17/223=0,0001001110000100000001001001011110001...

18/223=0,0001010010101001111001101011111010010...

19/223=0,0001010111001111110010001110010110011...

20/223=0,0001011011110101101010110000110010100...

21/223=0,0001100000011011100011010011001110101...

22/223=0,0001100101000001011011110101101010110...

23/223=0,0001101001100111010100011000000110111...

24/223=0,0001101110001101001100111010100011000...

25/223=0,0001110010110011000101011100111111001...

26/223=0,0001110111011000111101111111011011010...

27/223=0,0001111011111110110110100001110111011...

28/223=0,0010000000100100101111000100010011100...

29/223=0,0010000101001010100111100110101111101...

30/223=0,0010001001110000100000001001001011110...

31/223=0,0010001110010110011000101011100111111...

32/223=0,0010010010111100010001001110000100000...

33/223=0,0010010111100010001001110000100000001...

34/223=0,0010011100001000000010010010111100010...

35/223=0,0010100000101101111010110101011000011...

36/223=0,0010100101010011110011010111110100100...

37/223=0,0010101001111001101011111010010000101...

38/223=0,0010101110011111100100011100101100110...

39/223=0,0010110011000101011100111111001000111...

40/223=0,0010110111101011010101100001100101000...

41/223=0,0010111100010001001110000100000001001...

42/223=0,0011000000110111000110100110011101010...

43/223=0,0011000101011100111111001000111001011...

44/223=0,0011001010000010110111101011010101100...

45/223=0,0011001110101000110000001101110001101...

46/223=0,0011010011001110101000110000001101110...

47/223=0,0011010111110100100001010010101001111...

48/223=0,0011011100011010011001110101000110000...

49/223=0,0011100001000000010010010111100010001...

50/223=0,0011100101100110001010111001111110010...

51/223=0,0011101010001100000011011100011010011...

52/223=0,0011101110110001111011111110110110100...

53/223=0,0011110011010111110100100001010010101...

54/223=0,0011110111111101101101000011101110110...

55/223=0,0011111100100011100101100110001010111...

56/223=0,0100000001001001011110001000100111000...

57/223=0,0100000101101111010110101011000011001...

58/223=0,0100001010010101001111001101011111010...

59/223=0,0100001110111011000111101111111011011...

60/223=0,0100010011100001000000010010010111100...

61/223=0,0100011000000110111000110100110011101...

62/223=0,0100011100101100110001010111001111110...

63/223=0,0100100001010010101001111001101011111...

64/223=0,0100100101111000100010011100001000000...

65/223=0,0100101010011110011010111110100100001...

66/223=0,0100101111000100010011100001000000010...

67/223=0,0100110011101010001100000011011100011...

68/223=0,0100111000010000000100100101111000100...

69/223=0,0100111100110101111101001000010100101...

70/223=0,0101000001011011110101101010110000110...

71/223=0,0101000110000001101110001101001100111...

72/223=0,0101001010100111100110101111101001000...

73/223=0,0101001111001101011111010010000101001...

74/223=0,0101010011110011010111110100100001010...

75/223=0,0101011000011001010000010110111101011...

76/223=0,0101011100111111001000111001011001100...

77/223=0,0101100001100101000001011011110101101...

78/223=0,0101100110001010111001111110010001110...

79/223=0,0101101010110000110010100000101101111...

80/223=0,0101101111010110101011000011001010000...

81/223=0,0101110011111100100011100101100110001...

82/223=0,0101111000100010011100001000000010010...

83/223=0,0101111101001000010100101010011110011...

84/223=0,0110000001101110001101001100111010100...

85/223=0,0110000110010100000101101111010110101...

86/223=0,0110001010111001111110010001110010110...

87/223=0,0110001111011111110110110100001110111...

88/223=0,0110010100000101101111010110101011000...

89/223=0,0110011000101011100111111001000111001...

90/223=0,0110011101010001100000011011100011010...

91/223=0,0110100001110111011000111101111111011...

92/223=0,0110100110011101010001100000011011100...

93/223=0,0110101011000011001010000010110111101...

94/223=0,0110101111101001000010100101010011110...

95/223=0,0110110100001110111011000111101111111...

96/223=0,0110111000110100110011101010001100000...

97/223=0,0110111101011010101100001100101000001...

98/223=0,0111000010000000100100101111000100010...

99/223=0,0111000110100110011101010001100000011...

100/223=0,0111001011001100010101110011111100100...

101/223=0,0111001111110010001110010110011000101...

102/223=0,0111010100011000000110111000110100110...

103/223=0,0111011000111101111111011011010000111...

104/223=0,0111011101100011110111111101101101000...

105/223=0,0111100010001001110000100000001001001...

106/223=0,0111100110101111101001000010100101010...

107/223=0,0111101011010101100001100101000001011...

108/223=0,0111101111111011011010000111011101100...

109/223=0,0111110100100001010010101001111001101...

110/223=0,0111111001000111001011001100010101110...

111/223=0,0111111101101101000011101110110001111...

112/223=0,1000000010010010111100010001001110000...

113/223=0,1000000110111000110100110011101010001...

114/223=0,1000001011011110101101010110000110010...

115/223=0,1000010000000100100101111000100010011...

116/223=0,1000010100101010011110011010111110100...

117/223=0,1000011001010000010110111101011010101...

118/223=0,1000011101110110001111011111110110110...

119/223=0,1000100010011100001000000010010010111...

120/223=0,1000100111000010000000100100101111000...

121/223=0,1000101011100111111001000111001011001...

122/223=0,1000110000001101110001101001100111010...

123/223=0,1000110100110011101010001100000011011...

124/223=0,1000111001011001100010101110011111100...

125/223=0,1000111101111111011011010000111011101...

126/223=0,1001000010100101010011110011010111110...

127/223=0,1001000111001011001100010101110011111...

128/223=0,1001001011110001000100111000010000000...

129/223=0,1001010000010110111101011010101100001...

130/223=0,1001010100111100110101111101001000010...

131/223=0,1001011001100010101110011111100100011...

132/223=0,1001011110001000100111000010000000100...

133/223=0,1001100010101110011111100100011100101...

134/223=0,1001100111010100011000000110111000110...

135/223=0,1001101011111010010000101001010100111...

136/223=0,1001110000100000001001001011110001000...

137/223=0,1001110101000110000001101110001101001...

138/223=0,1001111001101011111010010000101001010...

139/223=0,1001111110010001110010110011000101011...

140/223=0,1010000010110111101011010101100001100...

141/223=0,1010000111011101100011110111111101101...

142/223=0,1010001100000011011100011010011001110...

143/223=0,1010010000101001010100111100110101111...

144/223=0,1010010101001111001101011111010010000...

145/223=0,1010011001110101000110000001101110001...

146/223=0,1010011110011010111110100100001010010...

147/223=0,1010100011000000110111000110100110011...

148/223=0,1010100111100110101111101001000010100...

149/223=0,1010101100001100101000001011011110101...

150/223=0,1010110000110010100000101101111010110...

151/223=0,1010110101011000011001010000010110111...

152/223=0,1010111001111110010001110010110011000...

153/223=0,1010111110100100001010010101001111001...

154/223=0,1011000011001010000010110111101011010...

155/223=0,1011000111101111111011011010000111011...

156/223=0,1011001100010101110011111100100011100...

157/223=0,1011010000111011101100011110111111101...

158/223=0,1011010101100001100101000001011011110...

159/223=0,1011011010000111011101100011110111111...

160/223=0,1011011110101101010110000110010100000...

161/223=0,1011100011010011001110101000110000001...

162/223=0,1011100111111001000111001011001100010...

163/223=0,1011101100011110111111101101101000011...

164/223=0,1011110001000100111000010000000100100...

165/223=0,1011110101101010110000110010100000101...

166/223=0,1011111010010000101001010100111100110...

167/223=0,1011111110110110100001110111011000111...

168/223=0,1100000011011100011010011001110101000...

169/223=0,1100001000000010010010111100010001001...

170/223=0,1100001100101000001011011110101101010...

171/223=0,1100010001001110000100000001001001011...

172/223=0,1100010101110011111100100011100101100...

173/223=0,1100011010011001110101000110000001101...

174/223=0,1100011110111111101101101000011101110...

175/223=0,1100100011100101100110001010111001111...

176/223=0,1100101000001011011110101101010110000...

177/223=0,1100101100110001010111001111110010001...

178/223=0,1100110001010111001111110010001110010...

179/223=0,1100110101111101001000010100101010011...

180/223=0,1100111010100011000000110111000110100...

181/223=0,1100111111001000111001011001100010101...

182/223=0,1101000011101110110001111011111110110...

183/223=0,1101001000010100101010011110011010111...

184/223=0,1101001100111010100011000000110111000...

185/223=0,1101010001100000011011100011010011001...

186/223=0,1101010110000110010100000101101111010...

187/223=0,1101011010101100001100101000001011011...

188/223=0,1101011111010010000101001010100111100...

189/223=0,1101100011110111111101101101000011101...

190/223=0,1101101000011101110110001111011111110...

191/223=0,1101101101000011101110110001111011111...

192/223=0,1101110001101001100111010100011000000...

193/223=0,1101110110001111011111110110110100001...

194/223=0,1101111010110101011000011001010000010...

195/223=0,1101111111011011010000111011101100011...

196/223=0,1110000100000001001001011110001000100...

197/223=0,1110001000100111000010000000100100101...

198/223=0,1110001101001100111010100011000000110...

199/223=0,1110010001110010110011000101011100111...

200/223=0,1110010110011000101011100111111001000...

201/223=0,1110011010111110100100001010010101001...

202/223=0,1110011111100100011100101100110001010...

203/223=0,1110100100001010010101001111001101011...

204/223=0,1110101000110000001101110001101001100...

205/223=0,1110101101010110000110010100000101101...

206/223=0,1110110001111011111110110110100001110...

207/223=0,1110110110100001110111011000111101111...

208/223=0,1110111011000111101111111011011010000...

209/223=0,1110111111101101101000011101110110001...

210/223=0,1111000100010011100001000000010010010...

211/223=0,1111001000111001011001100010101110011...

212/223=0,1111001101011111010010000101001010100...

213/223=0,1111010010000101001010100111100110101...

214/223=0,1111010110101011000011001010000010110...

215/223=0,1111011011010000111011101100011110111...

216/223=0,1111011111110110110100001110111011000...

217/223=0,1111100100011100101100110001010111001...

218/223=0,1111101001000010100101010011110011010...

219/223=0,1111101101101000011101110110001111011...

220/223=0,1111110010001110010110011000101011100...

221/223=0,1111110110110100001110111011000111101...

222/223=0,1111111011011010000111011101100011110...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (37) est égal à 222 et donc au premier -1.