Il existe 2 périodes de 68 chiffres pour n/137 en base 2.

Pour toutes les fractions de n/137 en base 2, la période de 1/137 revient alors 68 fois (en orange)

1/137=0,00000001110111100101110101101110001111111000100001101000101001000111...

2/137=0,00000011101111001011101011011100011111110001000011010001010010001110...

3/137=0,00000101100110110001100001001010101111101001100100111001111011010101...

4/137=0,00000111011110010111010110111000111111100010000110100010100100011100...

5/137=0,00001001010101111101001100100111001111011010101000001011001101100011...

6/137=0,00001011001101100011000010010101011111010011001001110011110110101010...

7/137=0,00001101000101001000111000000011101111001011101011011100011111110001...

8/137=0,00001110111100101110101101110001111111000100001101000101001000111000...

9/137=0,00010000110100010100100011100000001110111100101110101101110001111111...

10/137=0,00010010101011111010011001001110011110110101010000010110011011000110...

11/137=0,00010100100011100000001110111100101110101101110001111111000100001101...

12/137=0,00010110011011000110000100101010111110100110010011100111101101010100...

13/137=0,00011000010010101011111010011001001110011110110101010000010110011011...

14/137=0,00011010001010010001110000000111011110010111010110111000111111100010...

15/137=0,00011100000001110111100101110101101110001111111000100001101000101001...

16/137=0,00011101111001011101011011100011111110001000011010001010010001110000...

17/137=0,00011111110001000011010001010010001110000000111011110010111010110111...

18/137=0,00100001101000101001000111000000011101111001011101011011100011111110...

19/137=0,00100011100000001110111100101110101101110001111111000100001101000101...

20/137=0,00100101010111110100110010011100111101101010100000101100110110001100...

21/137=0,00100111001111011010101000001011001101100011000010010101011111010011...

22/137=0,00101001000111000000011101111001011101011011100011111110001000011010...

23/137=0,00101010111110100110010011100111101101010100000101100110110001100001...

24/137=0,00101100110110001100001001010101111101001100100111001111011010101000...

25/137=0,00101110101101110001111111000100001101000101001000111000000011101111...

26/137=0,00110000100101010111110100110010011100111101101010100000101100110110...

27/137=0,00110010011100111101101010100000101100110110001100001001010101111101...

28/137=0,00110100010100100011100000001110111100101110101101110001111111000100...

29/137=0,00110110001100001001010101111101001100100111001111011010101000001011...

30/137=0,00111000000011101111001011101011011100011111110001000011010001010010...

31/137=0,00111001111011010101000001011001101100011000010010101011111010011001...

32/137=0,00111011110010111010110111000111111100010000110100010100100011100000...

33/137=0,00111101101010100000101100110110001100001001010101111101001100100111...

34/137=0,00111111100010000110100010100100011100000001110111100101110101101110...

35/137=0,01000001011001101100011000010010101011111010011001001110011110110101...

36/137=0,01000011010001010010001110000000111011110010111010110111000111111100...

37/137=0,01000101001000111000000011101111001011101011011100011111110001000011...

38/137=0,01000111000000011101111001011101011011100011111110001000011010001010...

39/137=0,01001000111000000011101111001011101011011100011111110001000011010001...

40/137=0,01001010101111101001100100111001111011010101000001011001101100011000...

41/137=0,01001100100111001111011010101000001011001101100011000010010101011111...

42/137=0,01001110011110110101010000010110011011000110000100101010111110100110...

43/137=0,01010000010110011011000110000100101010111110100110010011100111101101...

44/137=0,01010010001110000000111011110010111010110111000111111100010000110100...

45/137=0,01010100000101100110110001100001001010101111101001100100111001111011...

46/137=0,01010101111101001100100111001111011010101000001011001101100011000010...

47/137=0,01010111110100110010011100111101101010100000101100110110001100001001...

48/137=0,01011001101100011000010010101011111010011001001110011110110101010000...

49/137=0,01011011100011111110001000011010001010010001110000000111011110010111...

50/137=0,01011101011011100011111110001000011010001010010001110000000111011110...

51/137=0,01011111010011001001110011110110101010000010110011011000110000100101...

52/137=0,01100001001010101111101001100100111001111011010101000001011001101100...

53/137=0,01100011000010010101011111010011001001110011110110101010000010110011...

54/137=0,01100100111001111011010101000001011001101100011000010010101011111010...

55/137=0,01100110110001100001001010101111101001100100111001111011010101000001...

56/137=0,01101000101001000111000000011101111001011101011011100011111110001000...

57/137=0,01101010100000101100110110001100001001010101111101001100100111001111...

58/137=0,01101100011000010010101011111010011001001110011110110101010000010110...

59/137=0,01101110001111111000100001101000101001000111000000011101111001011101...

60/137=0,01110000000111011110010111010110111000111111100010000110100010100100...

61/137=0,01110001111111000100001101000101001000111000000011101111001011101011...

62/137=0,01110011110110101010000010110011011000110000100101010111110100110010...

63/137=0,01110101101110001111111000100001101000101001000111000000011101111001...

64/137=0,01110111100101110101101110001111111000100001101000101001000111000000...

65/137=0,01111001011101011011100011111110001000011010001010010001110000000111...

66/137=0,01111011010101000001011001101100011000010010101011111010011001001110...

67/137=0,01111101001100100111001111011010101000001011001101100011000010010101...

68/137=0,01111111000100001101000101001000111000000011101111001011101011011100...

69/137=0,10000000111011110010111010110111000111111100010000110100010100100011...

70/137=0,10000010110011011000110000100101010111110100110010011100111101101010...

71/137=0,10000100101010111110100110010011100111101101010100000101100110110001...

72/137=0,10000110100010100100011100000001110111100101110101101110001111111000...

73/137=0,10001000011010001010010001110000000111011110010111010110111000111111...

74/137=0,10001010010001110000000111011110010111010110111000111111100010000110...

75/137=0,10001100001001010101111101001100100111001111011010101000001011001101...

76/137=0,10001110000000111011110010111010110111000111111100010000110100010100...

77/137=0,10001111111000100001101000101001000111000000011101111001011101011011...

78/137=0,10010001110000000111011110010111010110111000111111100010000110100010...

79/137=0,10010011100111101101010100000101100110110001100001001010101111101001...

80/137=0,10010101011111010011001001110011110110101010000010110011011000110000...

81/137=0,10010111010110111000111111100010000110100010100100011100000001110111...

82/137=0,10011001001110011110110101010000010110011011000110000100101010111110...

83/137=0,10011011000110000100101010111110100110010011100111101101010100000101...

84/137=0,10011100111101101010100000101100110110001100001001010101111101001100...

85/137=0,10011110110101010000010110011011000110000100101010111110100110010011...

86/137=0,10100000101100110110001100001001010101111101001100100111001111011010...

87/137=0,10100010100100011100000001110111100101110101101110001111111000100001...

88/137=0,10100100011100000001110111100101110101101110001111111000100001101000...

89/137=0,10100110010011100111101101010100000101100110110001100001001010101111...

90/137=0,10101000001011001101100011000010010101011111010011001001110011110110...

91/137=0,10101010000010110011011000110000100101010111110100110010011100111101...

92/137=0,10101011111010011001001110011110110101010000010110011011000110000100...

93/137=0,10101101110001111111000100001101000101001000111000000011101111001011...

94/137=0,10101111101001100100111001111011010101000001011001101100011000010010...

95/137=0,10110001100001001010101111101001100100111001111011010101000001011001...

96/137=0,10110011011000110000100101010111110100110010011100111101101010100000...

97/137=0,10110101010000010110011011000110000100101010111110100110010011100111...

98/137=0,10110111000111111100010000110100010100100011100000001110111100101110...

99/137=0,10111000111111100010000110100010100100011100000001110111100101110101...

100/137=0,10111010110111000111111100010000110100010100100011100000001110111100...

101/137=0,10111100101110101101110001111111000100001101000101001000111000000011...

102/137=0,10111110100110010011100111101101010100000101100110110001100001001010...

103/137=0,11000000011101111001011101011011100011111110001000011010001010010001...

104/137=0,11000010010101011111010011001001110011110110101010000010110011011000...

105/137=0,11000100001101000101001000111000000011101111001011101011011100011111...

106/137=0,11000110000100101010111110100110010011100111101101010100000101100110...

107/137=0,11000111111100010000110100010100100011100000001110111100101110101101...

108/137=0,11001001110011110110101010000010110011011000110000100101010111110100...

109/137=0,11001011101011011100011111110001000011010001010010001110000000111011...

110/137=0,11001101100011000010010101011111010011001001110011110110101010000010...

111/137=0,11001111011010101000001011001101100011000010010101011111010011001001...

112/137=0,11010001010010001110000000111011110010111010110111000111111100010000...

113/137=0,11010011001001110011110110101010000010110011011000110000100101010111...

114/137=0,11010101000001011001101100011000010010101011111010011001001110011110...

115/137=0,11010110111000111111100010000110100010100100011100000001110111100101...

116/137=0,11011000110000100101010111110100110010011100111101101010100000101100...

117/137=0,11011010101000001011001101100011000010010101011111010011001001110011...

118/137=0,11011100011111110001000011010001010010001110000000111011110010111010...

119/137=0,11011110010111010110111000111111100010000110100010100100011100000001...

120/137=0,11100000001110111100101110101101110001111111000100001101000101001000...

121/137=0,11100010000110100010100100011100000001110111100101110101101110001111...

122/137=0,11100011111110001000011010001010010001110000000111011110010111010110...

123/137=0,11100101110101101110001111111000100001101000101001000111000000011101...

124/137=0,11100111101101010100000101100110110001100001001010101111101001100100...

125/137=0,11101001100100111001111011010101000001011001101100011000010010101011...

126/137=0,11101011011100011111110001000011010001010010001110000000111011110010...

127/137=0,11101101010100000101100110110001100001001010101111101001100100111001...

128/137=0,11101111001011101011011100011111110001000011010001010010001110000000...

129/137=0,11110001000011010001010010001110000000111011110010111010110111000111...

130/137=0,11110010111010110111000111111100010000110100010100100011100000001110...

131/137=0,11110100110010011100111101101010100000101100110110001100001001010101...

132/137=0,11110110101010000010110011011000110000100101010111110100110010011100...

133/137=0,11111000100001101000101001000111000000011101111001011101011011100011...

134/137=0,11111010011001001110011110110101010000010110011011000110000100101010...

135/137=0,11111100010000110100010100100011100000001110111100101110101101110001...

136/137=0,11111110001000011010001010010001110000000111011110010111010110111000...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (68) est égal à 136 et donc au premier -1.