Il existe 2 périodes de 48 chiffres pour n/97 en base 2.

Pour toutes les fractions de n/97 en base 2, la période de 1/97 revient alors 48 fois (en orange)

1/97=0,000000101010001110100000111111010101110001011111...

2/97=0,000001010100011101000001111110101011100010111110...

3/97=0,000001111110101011100010111110000001010100011101...

4/97=0,000010101000111010000011111101010111000101111100...

5/97=0,000011010011001000100100111100101100110111011011...

6/97=0,000011111101010111000101111100000010101000111010...

7/97=0,000100100111100101100110111011011000011010011001...

8/97=0,000101010001110100000111111010101110001011111000...

9/97=0,000101111100000010101000111010000011111101010111...

10/97=0,000110100110010001001001111001011001101110110110...

11/97=0,000111010000011111101010111000101111100000010101...

12/97=0,000111111010101110001011111000000101010001110100...

13/97=0,001000100100111100101100110111011011000011010011...

14/97=0,001001001111001011001101110110110000110100110010...

15/97=0,001001111001011001101110110110000110100110010001...

16/97=0,001010100011101000001111110101011100010111110000...

17/97=0,001011001101110110110000110100110010001001001111...

18/97=0,001011111000000101010001110100000111111010101110...

19/97=0,001100100010010011110010110011011101101100001101...

20/97=0,001101001100100010010011110010110011011101101100...

21/97=0,001101110110110000110100110010001001001111001011...

22/97=0,001110100000111111010101110001011111000000101010...

23/97=0,001111001011001101110110110000110100110010001001...

24/97=0,001111110101011100010111110000001010100011101000...

25/97=0,010000011111101010111000101111100000010101000111...

26/97=0,010001001001111001011001101110110110000110100110...

27/97=0,010001110100000111111010101110001011111000000101...

28/97=0,010010011110010110011011101101100001101001100100...

29/97=0,010011001000100100111100101100110111011011000011...

30/97=0,010011110010110011011101101100001101001100100010...

31/97=0,010100011101000001111110101011100010111110000001...

32/97=0,010101000111010000011111101010111000101111100000...

33/97=0,010101110001011111000000101010001110100000111111...

34/97=0,010110011011101101100001101001100100010010011110...

35/97=0,010111000101111100000010101000111010000011111101...

36/97=0,010111110000001010100011101000001111110101011100...

37/97=0,011000011010011001000100100111100101100110111011...

38/97=0,011001000100100111100101100110111011011000011010...

39/97=0,011001101110110110000110100110010001001001111001...

40/97=0,011010011001000100100111100101100110111011011000...

41/97=0,011011000011010011001000100100111100101100110111...

42/97=0,011011101101100001101001100100010010011110010110...

43/97=0,011100010111110000001010100011101000001111110101...

44/97=0,011101000001111110101011100010111110000001010100...

45/97=0,011101101100001101001100100010010011110010110011...

46/97=0,011110010110011011101101100001101001100100010010...

47/97=0,011111000000101010001110100000111111010101110001...

48/97=0,011111101010111000101111100000010101000111010000...

49/97=0,100000010101000111010000011111101010111000101111...

50/97=0,100000111111010101110001011111000000101010001110...

51/97=0,100001101001100100010010011110010110011011101101...

52/97=0,100010010011110010110011011101101100001101001100...

53/97=0,100010111110000001010100011101000001111110101011...

54/97=0,100011101000001111110101011100010111110000001010...

55/97=0,100100010010011110010110011011101101100001101001...

56/97=0,100100111100101100110111011011000011010011001000...

57/97=0,100101100110111011011000011010011001000100100111...

58/97=0,100110010001001001111001011001101110110110000110...

59/97=0,100110111011011000011010011001000100100111100101...

60/97=0,100111100101100110111011011000011010011001000100...

61/97=0,101000001111110101011100010111110000001010100011...

62/97=0,101000111010000011111101010111000101111100000010...

63/97=0,101001100100010010011110010110011011101101100001...

64/97=0,101010001110100000111111010101110001011111000000...

65/97=0,101010111000101111100000010101000111010000011111...

66/97=0,101011100010111110000001010100011101000001111110...

67/97=0,101100001101001100100010010011110010110011011101...

68/97=0,101100110111011011000011010011001000100100111100...

69/97=0,101101100001101001100100010010011110010110011011...

70/97=0,101110001011111000000101010001110100000111111010...

71/97=0,101110110110000110100110010001001001111001011001...

72/97=0,101111100000010101000111010000011111101010111000...

73/97=0,110000001010100011101000001111110101011100010111...

74/97=0,110000110100110010001001001111001011001101110110...

75/97=0,110001011111000000101010001110100000111111010101...

76/97=0,110010001001001111001011001101110110110000110100...

77/97=0,110010110011011101101100001101001100100010010011...

78/97=0,110011011101101100001101001100100010010011110010...

79/97=0,110100000111111010101110001011111000000101010001...

80/97=0,110100110010001001001111001011001101110110110000...

81/97=0,110101011100010111110000001010100011101000001111...

82/97=0,110110000110100110010001001001111001011001101110...

83/97=0,110110110000110100110010001001001111001011001101...

84/97=0,110111011011000011010011001000100100111100101100...

85/97=0,111000000101010001110100000111111010101110001011...

86/97=0,111000101111100000010101000111010000011111101010...

87/97=0,111001011001101110110110000110100110010001001001...

88/97=0,111010000011111101010111000101111100000010101000...

89/97=0,111010101110001011111000000101010001110100000111...

90/97=0,111011011000011010011001000100100111100101100110...

91/97=0,111100000010101000111010000011111101010111000101...

92/97=0,111100101100110111011011000011010011001000100100...

93/97=0,111101010111000101111100000010101000111010000011...

94/97=0,111110000001010100011101000001111110101011100010...

95/97=0,111110101011100010111110000001010100011101000001...

96/97=0,111111010101110001011111000000101010001110100000...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (48) est égal à 96 et donc au premier -1.