Il existe 2 périodes de 65 chiffres pour n/131 en base 7.

Pour toutes les fractions de n/131 en base 7, la période de 1/131 revient alors 65 fois (en orange)

1/131=0,00242204054163155010566152255525310323645201332122313046016043264...

2/131=0,00514411141356343021465334544353620650623402664244626125035116561...

3/131=0,01056615225552531032364520133212231304601604326400242204054163155...

4/131=0,01332122313046016043264002422040541631550105661522555253103236452...

5/131=0,01604326400242204054163155010566152255525310323645201332122313046...

6/131=0,02146533454435362065062340266424462612503511656100514411141356343...

7/131=0,02422040541631550105661522555253103236452013321223130460160432640...

8/131=0,02664244626125035116561005144111413563430214653345443536206506234...

9/131=0,03236452013321223130460160432640024220405416315501056615225552531...

10/131=0,03511656100514411141356343021465334544353620650623402664244626125...

11/131=0,04054163155010566152255525310323645201332122313046016043264002422...

12/131=0,04326400242204054163155010566152255525310323645201332122313046016...

13/131=0,04601604326400242204054163155010566152255525310323645201332122313...

14/131=0,05144111413563430214653345443536206506234026642446261250351165610...

15/131=0,05416315501056615225552531032364520133212231304601604326400242204...

16/131=0,05661522555253103236452013321223130460160432640024220405416315501...

17/131=0,06234026642446261250351165610051441114135634302146533454435362065...

18/131=0,06506234026642446261250351165610051441114135634302146533454435362...

19/131=0,10051441114135634302146533454435362065062340266424462612503511656...

20/131=0,10323645201332122313046016043264002422040541631550105661522555253...

21/131=0,10566152255525310323645201332122313046016043264002422040541631550...

22/131=0,11141356343021465334544353620650623402664244626125035116561005144...

23/131=0,11413563430214653345443536206506234026642446261250351165610051441...

24/131=0,11656100514411141356343021465334544353620650623402664244626125035...

25/131=0,12231304601604326400242204054163155010566152255525310323645201332...

26/131=0,12503511656100514411141356343021465334544353620650623402664244626...

27/131=0,13046016043264002422040541631550105661522555253103236452013321223...

28/131=0,13321223130460160432640024220405416315501056615225552531032364520...

29/131=0,13563430214653345443536206506234026642446261250351165610051441114...

30/131=0,14135634302146533454435362065062340266424462612503511656100514411...

31/131=0,14411141356343021465334544353620650623402664244626125035116561005...

32/131=0,14653345443536206506234026642446261250351165610051441114135634302...

33/131=0,15225552531032364520133212231304601604326400242204054163155010566...

34/131=0,15501056615225552531032364520133212231304601604326400242204054163...

35/131=0,16043264002422040541631550105661522555253103236452013321223130460...

36/131=0,16315501056615225552531032364520133212231304601604326400242204054...

37/131=0,16561005144111413563430214653345443536206506234026642446261250351...

38/131=0,20133212231304601604326400242204054163155010566152255525310323645...

39/131=0,20405416315501056615225552531032364520133212231304601604326400242...

40/131=0,20650623402664244626125035116561005144111413563430214653345443536...

41/131=0,21223130460160432640024220405416315501056615225552531032364520133...

42/131=0,21465334544353620650623402664244626125035116561005144111413563430...

43/131=0,22040541631550105661522555253103236452013321223130460160432640024...

44/131=0,22313046016043264002422040541631550105661522555253103236452013321...

45/131=0,22555253103236452013321223130460160432640024220405416315501056615...

46/131=0,23130460160432640024220405416315501056615225552531032364520133212...

47/131=0,23402664244626125035116561005144111413563430214653345443536206506...

48/131=0,23645201332122313046016043264002422040541631550105661522555253103...

49/131=0,24220405416315501056615225552531032364520133212231304601604326400...

50/131=0,24462612503511656100514411141356343021465334544353620650623402664...

51/131=0,25035116561005144111413563430214653345443536206506234026642446261...

52/131=0,25310323645201332122313046016043264002422040541631550105661522555...

53/131=0,25552531032364520133212231304601604326400242204054163155010566152...

54/131=0,26125035116561005144111413563430214653345443536206506234026642446...

55/131=0,26400242204054163155010566152255525310323645201332122313046016043...

56/131=0,26642446261250351165610051441114135634302146533454435362065062340...

57/131=0,30214653345443536206506234026642446261250351165610051441114135634...

58/131=0,30460160432640024220405416315501056615225552531032364520133212231...

59/131=0,31032364520133212231304601604326400242204054163155010566152255525...

60/131=0,31304601604326400242204054163155010566152255525310323645201332122...

61/131=0,31550105661522555253103236452013321223130460160432640024220405416...

62/131=0,32122313046016043264002422040541631550105661522555253103236452013...

63/131=0,32364520133212231304601604326400242204054163155010566152255525310...

64/131=0,32640024220405416315501056615225552531032364520133212231304601604...

65/131=0,33212231304601604326400242204054163155010566152255525310323645201...

66/131=0,33454435362065062340266424462612503511656100514411141356343021465...

67/131=0,34026642446261250351165610051441114135634302146533454435362065062...

68/131=0,34302146533454435362065062340266424462612503511656100514411141356...

69/131=0,34544353620650623402664244626125035116561005144111413563430214653...

70/131=0,35116561005144111413563430214653345443536206506234026642446261250...

71/131=0,35362065062340266424462612503511656100514411141356343021465334544...

72/131=0,35634302146533454435362065062340266424462612503511656100514411141...

73/131=0,36206506234026642446261250351165610051441114135634302146533454435...

74/131=0,36452013321223130460160432640024220405416315501056615225552531032...

75/131=0,40024220405416315501056615225552531032364520133212231304601604326...

76/131=0,40266424462612503511656100514411141356343021465334544353620650623...

77/131=0,40541631550105661522555253103236452013321223130460160432640024220...

78/131=0,41114135634302146533454435362065062340266424462612503511656100514...

79/131=0,41356343021465334544353620650623402664244626125035116561005144111...

80/131=0,41631550105661522555253103236452013321223130460160432640024220405...

81/131=0,42204054163155010566152255525310323645201332122313046016043264002...

82/131=0,42446261250351165610051441114135634302146533454435362065062340266...

83/131=0,43021465334544353620650623402664244626125035116561005144111413563...

84/131=0,43264002422040541631550105661522555253103236452013321223130460160...

85/131=0,43536206506234026642446261250351165610051441114135634302146533454...

86/131=0,44111413563430214653345443536206506234026642446261250351165610051...

87/131=0,44353620650623402664244626125035116561005144111413563430214653345...

88/131=0,44626125035116561005144111413563430214653345443536206506234026642...

89/131=0,45201332122313046016043264002422040541631550105661522555253103236...

90/131=0,45443536206506234026642446261250351165610051441114135634302146533...

91/131=0,46016043264002422040541631550105661522555253103236452013321223130...

92/131=0,46261250351165610051441114135634302146533454435362065062340266424...

93/131=0,46533454435362065062340266424462612503511656100514411141356343021...

94/131=0,50105661522555253103236452013321223130460160432640024220405416315...

95/131=0,50351165610051441114135634302146533454435362065062340266424462612...

96/131=0,50623402664244626125035116561005144111413563430214653345443536206...

97/131=0,51165610051441114135634302146533454435362065062340266424462612503...

98/131=0,51441114135634302146533454435362065062340266424462612503511656100...

99/131=0,52013321223130460160432640024220405416315501056615225552531032364...

100/131=0,52255525310323645201332122313046016043264002422040541631550105661...

101/131=0,52531032364520133212231304601604326400242204054163155010566152255...

102/131=0,53103236452013321223130460160432640024220405416315501056615225552...

103/131=0,53345443536206506234026642446261250351165610051441114135634302146...

104/131=0,53620650623402664244626125035116561005144111413563430214653345443...

105/131=0,54163155010566152255525310323645201332122313046016043264002422040...

106/131=0,54435362065062340266424462612503511656100514411141356343021465334...

107/131=0,55010566152255525310323645201332122313046016043264002422040541631...

108/131=0,55253103236452013321223130460160432640024220405416315501056615225...

109/131=0,55525310323645201332122313046016043264002422040541631550105661522...

110/131=0,56100514411141356343021465334544353620650623402664244626125035116...

111/131=0,56343021465334544353620650623402664244626125035116561005144111413...

112/131=0,56615225552531032364520133212231304601604326400242204054163155010...

113/131=0,60160432640024220405416315501056615225552531032364520133212231304...

114/131=0,60432640024220405416315501056615225552531032364520133212231304601...

115/131=0,61005144111413563430214653345443536206506234026642446261250351165...

116/131=0,61250351165610051441114135634302146533454435362065062340266424462...

117/131=0,61522555253103236452013321223130460160432640024220405416315501056...

118/131=0,62065062340266424462612503511656100514411141356343021465334544353...

119/131=0,62340266424462612503511656100514411141356343021465334544353620650...

120/131=0,62612503511656100514411141356343021465334544353620650623402664244...

121/131=0,63155010566152255525310323645201332122313046016043264002422040541...

122/131=0,63430214653345443536206506234026642446261250351165610051441114135...

123/131=0,64002422040541631550105661522555253103236452013321223130460160432...

124/131=0,64244626125035116561005144111413563430214653345443536206506234026...

125/131=0,64520133212231304601604326400242204054163155010566152255525310323...

126/131=0,65062340266424462612503511656100514411141356343021465334544353620...

127/131=0,65334544353620650623402664244626125035116561005144111413563430214...

128/131=0,65610051441114135634302146533454435362065062340266424462612503511...

129/131=0,66152255525310323645201332122313046016043264002422040541631550105...

130/131=0,66424462612503511656100514411141356343021465334544353620650623402...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (65) est égal à 130 et donc au premier -1.