Il existe 4 périodes de 28 chiffres pour n/113 en base 2.

Pour toutes les fractions de n/113 en base 2, la période de 1/113 revient alors 28 fois (en orange)

1/113=0,0000001001000011111101101111...

2/113=0,0000010010000111111011011110...

3/113=0,0000011011001011111001001101...

4/113=0,0000100100001111110110111100...

5/113=0,0000101101010011110100101011...

6/113=0,0000110110010111110010011010...

7/113=0,0000111111011011110000001001...

8/113=0,0001001000011111101101111000...

9/113=0,0001010001100011101011100111...

10/113=0,0001011010100111101001010110...

11/113=0,0001100011101011100111000101...

12/113=0,0001101100101111100100110100...

13/113=0,0001110101110011100010100011...

14/113=0,0001111110110111100000010010...

15/113=0,0010000111111011011110000001...

16/113=0,0010010000111111011011110000...

17/113=0,0010011010000011011001011111...

18/113=0,0010100011000111010111001110...

19/113=0,0010101100001011010100111101...

20/113=0,0010110101001111010010101100...

21/113=0,0010111110010011010000011011...

22/113=0,0011000111010111001110001010...

23/113=0,0011010000011011001011111001...

24/113=0,0011011001011111001001101000...

25/113=0,0011100010100011000111010111...

26/113=0,0011101011100111000101000110...

27/113=0,0011110100101011000010110101...

28/113=0,0011111101101111000000100100...

29/113=0,0100000110110010111110010011...

30/113=0,0100001111110110111100000010...

31/113=0,0100011000111010111001110001...

32/113=0,0100100001111110110111100000...

33/113=0,0100101011000010110101001111...

34/113=0,0100110100000110110010111110...

35/113=0,0100111101001010110000101101...

36/113=0,0101000110001110101110011100...

37/113=0,0101001111010010101100001011...

38/113=0,0101011000010110101001111010...

39/113=0,0101100001011010100111101001...

40/113=0,0101101010011110100101011000...

41/113=0,0101110011100010100011000111...

42/113=0,0101111100100110100000110110...

43/113=0,0110000101101010011110100101...

44/113=0,0110001110101110011100010100...

45/113=0,0110010111110010011010000011...

46/113=0,0110100000110110010111110010...

47/113=0,0110101001111010010101100001...

48/113=0,0110110010111110010011010000...

49/113=0,0110111100000010010000111111...

50/113=0,0111000101000110001110101110...

51/113=0,0111001110001010001100011101...

52/113=0,0111010111001110001010001100...

53/113=0,0111100000010010000111111011...

54/113=0,0111101001010110000101101010...

55/113=0,0111110010011010000011011001...

56/113=0,0111111011011110000001001000...

57/113=0,1000000100100001111110110111...

58/113=0,1000001101100101111100100110...

59/113=0,1000010110101001111010010101...

60/113=0,1000011111101101111000000100...

61/113=0,1000101000110001110101110011...

62/113=0,1000110001110101110011100010...

63/113=0,1000111010111001110001010001...

64/113=0,1001000011111101101111000000...

65/113=0,1001001101000001101100101111...

66/113=0,1001010110000101101010011110...

67/113=0,1001011111001001101000001101...

68/113=0,1001101000001101100101111100...

69/113=0,1001110001010001100011101011...

70/113=0,1001111010010101100001011010...

71/113=0,1010000011011001011111001001...

72/113=0,1010001100011101011100111000...

73/113=0,1010010101100001011010100111...

74/113=0,1010011110100101011000010110...

75/113=0,1010100111101001010110000101...

76/113=0,1010110000101101010011110100...

77/113=0,1010111001110001010001100011...

78/113=0,1011000010110101001111010010...

79/113=0,1011001011111001001101000001...

80/113=0,1011010100111101001010110000...

81/113=0,1011011110000001001000011111...

82/113=0,1011100111000101000110001110...

83/113=0,1011110000001001000011111101...

84/113=0,1011111001001101000001101100...

85/113=0,1100000010010000111111011011...

86/113=0,1100001011010100111101001010...

87/113=0,1100010100011000111010111001...

88/113=0,1100011101011100111000101000...

89/113=0,1100100110100000110110010111...

90/113=0,1100101111100100110100000110...

91/113=0,1100111000101000110001110101...

92/113=0,1101000001101100101111100100...

93/113=0,1101001010110000101101010011...

94/113=0,1101010011110100101011000010...

95/113=0,1101011100111000101000110001...

96/113=0,1101100101111100100110100000...

97/113=0,1101101111000000100100001111...

98/113=0,1101111000000100100001111110...

99/113=0,1110000001001000011111101101...

100/113=0,1110001010001100011101011100...

101/113=0,1110010011010000011011001011...

102/113=0,1110011100010100011000111010...

103/113=0,1110100101011000010110101001...

104/113=0,1110101110011100010100011000...

105/113=0,1110110111100000010010000111...

106/113=0,1111000000100100001111110110...

107/113=0,1111001001101000001101100101...

108/113=0,1111010010101100001011010100...

109/113=0,1111011011110000001001000011...

110/113=0,1111100100110100000110110010...

111/113=0,1111101101111000000100100001...

112/113=0,1111110110111100000010010000...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (28) est égal à 112 et donc au premier -1.