Liste des fractions de n/127 en base 2.

Il existe 18 périodes de 7 chiffres pour n/127 en base 2.

Pour toutes les fractions de n/127 en base 2, la période de 1/127 revient alors 7 fois (en orange)

1/127=0,0000001...

2/127=0,0000010...

3/127=0,0000011...

4/127=0,0000100...

5/127=0,0000101...

6/127=0,0000110...

7/127=0,0000111...

8/127=0,0001000...

9/127=0,0001001...

10/127=0,0001010...

11/127=0,0001011...

12/127=0,0001100...

13/127=0,0001101...

14/127=0,0001110...

15/127=0,0001111...

16/127=0,0010000...

17/127=0,0010001...

18/127=0,0010010...

19/127=0,0010011...

20/127=0,0010100...

21/127=0,0010101...

22/127=0,0010110...

23/127=0,0010111...

24/127=0,0011000...

25/127=0,0011001...

26/127=0,0011010...

27/127=0,0011011...

28/127=0,0011100...

29/127=0,0011101...

30/127=0,0011110...

31/127=0,0011111...

32/127=0,0100000...

33/127=0,0100001...

34/127=0,0100010...

35/127=0,0100011...

36/127=0,0100100...

37/127=0,0100101...

38/127=0,0100110...

39/127=0,0100111...

40/127=0,0101000...

41/127=0,0101001...

42/127=0,0101010...

43/127=0,0101011...

44/127=0,0101100...

45/127=0,0101101...

46/127=0,0101110...

47/127=0,0101111...

48/127=0,0110000...

49/127=0,0110001...

50/127=0,0110010...

51/127=0,0110011...

52/127=0,0110100...

53/127=0,0110101...

54/127=0,0110110...

55/127=0,0110111...

56/127=0,0111000...

57/127=0,0111001...

58/127=0,0111010...

59/127=0,0111011...

60/127=0,0111100...

61/127=0,0111101...

62/127=0,0111110...

63/127=0,0111111...

64/127=0,1000000...

65/127=0,1000001...

66/127=0,1000010...

67/127=0,1000011...

68/127=0,1000100...

69/127=0,1000101...

70/127=0,1000110...

71/127=0,1000111...

72/127=0,1001000...

73/127=0,1001001...

74/127=0,1001010...

75/127=0,1001011...

76/127=0,1001100...

77/127=0,1001101...

78/127=0,1001110...

79/127=0,1001111...

80/127=0,1010000...

81/127=0,1010001...

82/127=0,1010010...

83/127=0,1010011...

84/127=0,1010100...

85/127=0,1010101...

86/127=0,1010110...

87/127=0,1010111...

88/127=0,1011000...

89/127=0,1011001...

90/127=0,1011010...

91/127=0,1011011...

92/127=0,1011100...

93/127=0,1011101...

94/127=0,1011110...

95/127=0,1011111...

96/127=0,1100000...

97/127=0,1100001...

98/127=0,1100010...

99/127=0,1100011...

100/127=0,1100100...

101/127=0,1100101...

102/127=0,1100110...

103/127=0,1100111...

104/127=0,1101000...

105/127=0,1101001...

106/127=0,1101010...

107/127=0,1101011...

108/127=0,1101100...

109/127=0,1101101...

110/127=0,1101110...

111/127=0,1101111...

112/127=0,1110000...

113/127=0,1110001...

114/127=0,1110010...

115/127=0,1110011...

116/127=0,1110100...

117/127=0,1110101...

118/127=0,1110110...

119/127=0,1110111...

120/127=0,1111000...

121/127=0,1111001...

122/127=0,1111010...

123/127=0,1111011...

124/127=0,1111100...

125/127=0,1111101...

126/127=0,1111110...

On remarque que le produit du nombre de périodes (18) et de leurs longueurs (7) est égal à 126 et donc au premier -1.