Il existe 2 périodes de 69 chiffres pour n/139 en base 5.

Pour toutes les fractions de n/139 en base 5, la période de 1/139 revient alors 69 fois (en orange)

1/139=0,000422201112141340130213211311404124241010144212234110241432400324431...

2/139=0,001344402224333230310431423123313304032020343430023221033420301204412...

3/139=0,002322103342030120441200134440222433323031043142312331330403202034343...

4/139=0,003244310004222011121413401302132113114041242410101442122341102414324...

5/139=0,004222011121413401302132113114041242410101442122341102414324003244310...

6/139=0,010144212234110241432400324431000422201112141340130213211311404124241...

7/139=0,011121413401302132113114041242410101442122341102414324003244310004222...

8/139=0,012044120013444022243332303104314231233133040320203434300232210334203...

9/139=0,013021321131140412424101014421223411024143240032443100042220111214134...

10/139=0,013444022243332303104314231233133040320203434300232210334203012044120...

11/139=0,014421223411024143240032443100042220111214134013021321131140412424101...

12/139=0,020343430023221033420301204412001344402224333230310431423123313304032...

13/139=0,021321131140412424101014421223411024143240032443100042220111214134013...

14/139=0,022243332303104314231233133040320203434300232210334203012044120013444...

15/139=0,023221033420301204412001344402224333230310431423123313304032020343430...

16/139=0,024143240032443100042220111214134013021321131140412424101014421223411...

17/139=0,030120441200134440222433323031043142312331330403202034343002322103342...

18/139=0,031043142312331330403202034343002322103342030120441200134440222433323...

19/139=0,032020343430023221033420301204412001344402224333230310431423123313304...

20/139=0,032443100042220111214134013021321131140412424101014421223411024143240...

21/139=0,033420301204412001344402224333230310431423123313304032020343430023221...

22/139=0,034343002322103342030120441200134440222433323031043142312331330403202...

23/139=0,040320203434300232210334203012044120013444022243332303104314231233133...

24/139=0,041242410101442122341102414324003244310004222011121413401302132113114...

25/139=0,042220111214134013021321131140412424101014421223411024143240032443100...

26/139=0,043142312331330403202034343002322103342030120441200134440222433323031...

27/139=0,044120013444022243332303104314231233133040320203434300232210334203012...

28/139=0,100042220111214134013021321131140412424101014421223411024143240032443...

29/139=0,101014421223411024143240032443100042220111214134013021321131140412424...

30/139=0,101442122341102414324003244310004222011121413401302132113114041242410...

31/139=0,102414324003244310004222011121413401302132113114041242410101442122341...

32/139=0,103342030120441200134440222433323031043142312331330403202034343002322...

33/139=0,104314231233133040320203434300232210334203012044120013444022243332303...

34/139=0,110241432400324431000422201112141340130213211311404124241010144212234...

35/139=0,111214134013021321131140412424101014421223411024143240032443100042220...

36/139=0,112141340130213211311404124241010144212234110241432400324431000422201...

37/139=0,113114041242410101442122341102414324003244310004222011121413401302132...

38/139=0,114041242410101442122341102414324003244310004222011121413401302132113...

39/139=0,120013444022243332303104314231233133040320203434300232210334203012044...

40/139=0,120441200134440222433323031043142312331330403202034343002322103342030...

41/139=0,121413401302132113114041242410101442122341102414324003244310004222011...

42/139=0,122341102414324003244310004222011121413401302132113114041242410101442...

43/139=0,123313304032020343430023221033420301204412001344402224333230310431423...

44/139=0,124241010144212234110241432400324431000422201112141340130213211311404...

45/139=0,130213211311404124241010144212234110241432400324431000422201112141340...

46/139=0,131140412424101014421223411024143240032443100042220111214134013021321...

47/139=0,132113114041242410101442122341102414324003244310004222011121413401302...

48/139=0,133040320203434300232210334203012044120013444022243332303104314231233...

49/139=0,134013021321131140412424101014421223411024143240032443100042220111214...

50/139=0,134440222433323031043142312331330403202034343002322103342030120441200...

51/139=0,140412424101014421223411024143240032443100042220111214134013021321131...

52/139=0,141340130213211311404124241010144212234110241432400324431000422201112...

53/139=0,142312331330403202034343002322103342030120441200134440222433323031043...

54/139=0,143240032443100042220111214134013021321131140412424101014421223411024...

55/139=0,144212234110241432400324431000422201112141340130213211311404124241010...

56/139=0,200134440222433323031043142312331330403202034343002322103342030120441...

57/139=0,201112141340130213211311404124241010144212234110241432400324431000422...

58/139=0,202034343002322103342030120441200134440222433323031043142312331330403...

59/139=0,203012044120013444022243332303104314231233133040320203434300232210334...

60/139=0,203434300232210334203012044120013444022243332303104314231233133040320...

61/139=0,204412001344402224333230310431423123313304032020343430023221033420301...

62/139=0,210334203012044120013444022243332303104314231233133040320203434300232...

63/139=0,211311404124241010144212234110241432400324431000422201112141340130213...

64/139=0,212234110241432400324431000422201112141340130213211311404124241010144...

65/139=0,213211311404124241010144212234110241432400324431000422201112141340130...

66/139=0,214134013021321131140412424101014421223411024143240032443100042220111...

67/139=0,220111214134013021321131140412424101014421223411024143240032443100042...

68/139=0,221033420301204412001344402224333230310431423123313304032020343430023...

69/139=0,222011121413401302132113114041242410101442122341102414324003244310004...

70/139=0,222433323031043142312331330403202034343002322103342030120441200134440...

71/139=0,223411024143240032443100042220111214134013021321131140412424101014421...

72/139=0,224333230310431423123313304032020343430023221033420301204412001344402...

73/139=0,230310431423123313304032020343430023221033420301204412001344402224333...

74/139=0,231233133040320203434300232210334203012044120013444022243332303104314...

75/139=0,232210334203012044120013444022243332303104314231233133040320203434300...

76/139=0,233133040320203434300232210334203012044120013444022243332303104314231...

77/139=0,234110241432400324431000422201112141340130213211311404124241010144212...

78/139=0,240032443100042220111214134013021321131140412424101014421223411024143...

79/139=0,241010144212234110241432400324431000422201112141340130213211311404124...

80/139=0,241432400324431000422201112141340130213211311404124241010144212234110...

81/139=0,242410101442122341102414324003244310004222011121413401302132113114041...

82/139=0,243332303104314231233133040320203434300232210334203012044120013444022...

83/139=0,244310004222011121413401302132113114041242410101442122341102414324003...

84/139=0,300232210334203012044120013444022243332303104314231233133040320203434...

85/139=0,301204412001344402224333230310431423123313304032020343430023221033420...

86/139=0,302132113114041242410101442122341102414324003244310004222011121413401...

87/139=0,303104314231233133040320203434300232210334203012044120013444022243332...

88/139=0,304032020343430023221033420301204412001344402224333230310431423123313...

89/139=0,310004222011121413401302132113114041242410101442122341102414324003244...

90/139=0,310431423123313304032020343430023221033420301204412001344402224333230...

91/139=0,311404124241010144212234110241432400324431000422201112141340130213211...

92/139=0,312331330403202034343002322103342030120441200134440222433323031043142...

93/139=0,313304032020343430023221033420301204412001344402224333230310431423123...

94/139=0,314231233133040320203434300232210334203012044120013444022243332303104...

95/139=0,320203434300232210334203012044120013444022243332303104314231233133040...

96/139=0,321131140412424101014421223411024143240032443100042220111214134013021...

97/139=0,322103342030120441200134440222433323031043142312331330403202034343002...

98/139=0,323031043142312331330403202034343002322103342030120441200134440222433...

99/139=0,324003244310004222011121413401302132113114041242410101442122341102414...

100/139=0,324431000422201112141340130213211311404124241010144212234110241432400...

101/139=0,330403202034343002322103342030120441200134440222433323031043142312331...

102/139=0,331330403202034343002322103342030120441200134440222433323031043142312...

103/139=0,332303104314231233133040320203434300232210334203012044120013444022243...

104/139=0,333230310431423123313304032020343430023221033420301204412001344402224...

105/139=0,334203012044120013444022243332303104314231233133040320203434300232210...

106/139=0,340130213211311404124241010144212234110241432400324431000422201112141...

107/139=0,341102414324003244310004222011121413401302132113114041242410101442122...

108/139=0,342030120441200134440222433323031043142312331330403202034343002322103...

109/139=0,343002322103342030120441200134440222433323031043142312331330403202034...

110/139=0,343430023221033420301204412001344402224333230310431423123313304032020...

111/139=0,344402224333230310431423123313304032020343430023221033420301204412001...

112/139=0,400324431000422201112141340130213211311404124241010144212234110241432...

113/139=0,401302132113114041242410101442122341102414324003244310004222011121413...

114/139=0,402224333230310431423123313304032020343430023221033420301204412001344...

115/139=0,403202034343002322103342030120441200134440222433323031043142312331330...

116/139=0,404124241010144212234110241432400324431000422201112141340130213211311...

117/139=0,410101442122341102414324003244310004222011121413401302132113114041242...

118/139=0,411024143240032443100042220111214134013021321131140412424101014421223...

119/139=0,412001344402224333230310431423123313304032020343430023221033420301204...

120/139=0,412424101014421223411024143240032443100042220111214134013021321131140...

121/139=0,413401302132113114041242410101442122341102414324003244310004222011121...

122/139=0,414324003244310004222011121413401302132113114041242410101442122341102...

123/139=0,420301204412001344402224333230310431423123313304032020343430023221033...

124/139=0,421223411024143240032443100042220111214134013021321131140412424101014...

125/139=0,422201112141340130213211311404124241010144212234110241432400324431000...

126/139=0,423123313304032020343430023221033420301204412001344402224333230310431...

127/139=0,424101014421223411024143240032443100042220111214134013021321131140412...

128/139=0,430023221033420301204412001344402224333230310431423123313304032020343...

129/139=0,431000422201112141340130213211311404124241010144212234110241432400324...

130/139=0,431423123313304032020343430023221033420301204412001344402224333230310...

131/139=0,432400324431000422201112141340130213211311404124241010144212234110241...

132/139=0,433323031043142312331330403202034343002322103342030120441200134440222...

133/139=0,434300232210334203012044120013444022243332303104314231233133040320203...

134/139=0,440222433323031043142312331330403202034343002322103342030120441200134...

135/139=0,441200134440222433323031043142312331330403202034343002322103342030120...

136/139=0,442122341102414324003244310004222011121413401302132113114041242410101...

137/139=0,443100042220111214134013021321131140412424101014421223411024143240032...

138/139=0,444022243332303104314231233133040320203434300232210334203012044120013...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (69) est égal à 138 et donc au premier -1.