Il existe 2 périodes de 48 chiffres pour n/97 en base 3.

Pour toutes les fractions de n/97 en base 3, la période de 1/97 revient alors 48 fois (en orange)

1/97=0,000021111220202212122210222201111002020010100012...

2/97=0,000120000211112202022121222102222011110020200101...

3/97=0,000211112202022121222102222011110020200101000120...

4/97=0,001010001200002111122020221212221022220111100202...

5/97=0,001101120120212101022001221121102102010121200221...

6/97=0,001200002111122020221212221022220111100202001010...

7/97=0,001221121102102010121200221001101120120212101022...

8/97=0,002020010100012000021111220202212122210222201111...

9/97=0,002111122020221212221022220111100202001010001200...

10/97=0,002210011011201202121010220012211211021020101212...

11/97=0,010001200002111122020221212221022220111100202001...

12/97=0,010100012000021111220202212122210222201111002020...

13/97=0,010121200221001101120120212101022001221121102102...

14/97=0,010220012211211021020101212002210011011201202121...

15/97=0,011011201202121010220012211211021020101212002210...

16/97=0,011110020200101000120000211112202022121222102222...

17/97=0,011201202121010220012211211021020101212002210011...

18/97=0,012000021111220202212122210222201111002020010100...

19/97=0,012021210102200122112110210201012120022100110112...

20/97=0,012120022100110112012021210102200122112110210201...

21/97=0,012211211021020101212002210011011201202121010220...

22/97=0,020010100012000021111220202212122210222201111002...

23/97=0,020101212002210011011201202121010220012211211021...

24/97=0,020200101000120000211112202022121222102222011110...

25/97=0,020221212221022220111100202001010001200002111122...

26/97=0,021020101212002210011011201202121010220012211211...

27/97=0,021111220202212122210222201111002020010100012000...

28/97=0,021210102200122112110210201012120022100110112012...

29/97=0,022001221121102102010121200221001101120120212101...

30/97=0,022100110112012021210102200122112110210201012120...

31/97=0,022121222102222011110020200101000120000211112202...

32/97=0,022220111100202001010001200002111122020221212221...

33/97=0,100012000021111220202212122210222201111002020010...

34/97=0,100110112012021210102200122112110210201012120022...

35/97=0,100202001010001200002111122020221212221022220111...

36/97=0,101000120000211112202022121222102222011110020200...

37/97=0,101022001221121102102010121200221001101120120212...

38/97=0,101120120212101022001221121102102010121200221001...

39/97=0,101212002210011011201202121010220012211211021020...

40/97=0,102010121200221001101120120212101022001221121102...

41/97=0,102102010121200221001101120120212101022001221121...

42/97=0,102200122112110210201012120022100110112012021210...

43/97=0,102222011110020200101000120000211112202022121222...

44/97=0,110020200101000120000211112202022121222102222011...

45/97=0,110112012021210102200122112110210201012120022100...

46/97=0,110210201012120022100110112012021210102200122112...

47/97=0,111002020010100012000021111220202212122210222201...

48/97=0,111100202001010001200002111122020221212221022220...

49/97=0,111122020221212221022220111100202001010001200002...

50/97=0,111220202212122210222201111002020010100012000021...

51/97=0,112012021210102200122112110210201012120022100110...

52/97=0,112110210201012120022100110112012021210102200122...

53/97=0,112202022121222102222011110020200101000120000211...

54/97=0,120000211112202022121222102222011110020200101000...

55/97=0,120022100110112012021210102200122112110210201012...

56/97=0,120120212101022001221121102102010121200221001101...

57/97=0,120212101022001221121102102010121200221001101120...

58/97=0,121010220012211211021020101212002210011011201202...

59/97=0,121102102010121200221001101120120212101022001221...

60/97=0,121200221001101120120212101022001221121102102010...

61/97=0,121222102222011110020200101000120000211112202022...

62/97=0,122020221212221022220111100202001010001200002111...

63/97=0,122112110210201012120022100110112012021210102200...

64/97=0,122210222201111002020010100012000021111220202212...

65/97=0,200002111122020221212221022220111100202001010001...

66/97=0,200101000120000211112202022121222102222011110020...

67/97=0,200122112110210201012120022100110112012021210102...

68/97=0,200221001101120120212101022001221121102102010121...

69/97=0,201012120022100110112012021210102200122112110210...

70/97=0,201111002020010100012000021111220202212122210222...

71/97=0,201202121010220012211211021020101212002210011011...

72/97=0,202001010001200002111122020221212221022220111100...

73/97=0,202022121222102222011110020200101000120000211112...

74/97=0,202121010220012211211021020101212002210011011201...

75/97=0,202212122210222201111002020010100012000021111220...

76/97=0,210011011201202121010220012211211021020101212002...

77/97=0,210102200122112110210201012120022100110112012021...

78/97=0,210201012120022100110112012021210102200122112110...

79/97=0,210222201111002020010100012000021111220202212122...

80/97=0,211021020101212002210011011201202121010220012211...

81/97=0,211112202022121222102222011110020200101000120000...

82/97=0,211211021020101212002210011011201202121010220012...

83/97=0,212002210011011201202121010220012211211021020101...

84/97=0,212101022001221121102102010121200221001101120120...

85/97=0,212122210222201111002020010100012000021111220202...

86/97=0,212221022220111100202001010001200002111122020221...

87/97=0,220012211211021020101212002210011011201202121010...

88/97=0,220111100202001010001200002111122020221212221022...

89/97=0,220202212122210222201111002020010100012000021111...

90/97=0,221001101120120212101022001221121102102010121200...

91/97=0,221022220111100202001010001200002111122020221212...

92/97=0,221121102102010121200221001101120120212101022001...

93/97=0,221212221022220111100202001010001200002111122020...

94/97=0,222011110020200101000120000211112202022121222102...

95/97=0,222102222011110020200101000120000211112202022121...

96/97=0,222201111002020010100012000021111220202212122210...

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