Il existe 17 périodes de 8 chiffres pour n/137 en base 10.

Pour toutes les fractions de n/137 en base 10, la période de 1/137 revient alors 8 fois (en orange)

1/137=0,00729927...

2/137=0,01459854...

3/137=0,02189781...

4/137=0,02919708...

5/137=0,03649635...

6/137=0,04379562...

7/137=0,05109489...

8/137=0,05839416...

9/137=0,06569343...

10/137=0,07299270...

11/137=0,08029197...

12/137=0,08759124...

13/137=0,09489051...

14/137=0,10218978...

15/137=0,10948905...

16/137=0,11678832...

17/137=0,12408759...

18/137=0,13138686...

19/137=0,13868613...

20/137=0,14598540...

21/137=0,15328467...

22/137=0,16058394...

23/137=0,16788321...

24/137=0,17518248...

25/137=0,18248175...

26/137=0,18978102...

27/137=0,19708029...

28/137=0,20437956...

29/137=0,21167883...

30/137=0,21897810...

31/137=0,22627737...

32/137=0,23357664...

33/137=0,24087591...

34/137=0,24817518...

35/137=0,25547445...

36/137=0,26277372...

37/137=0,27007299...

38/137=0,27737226...

39/137=0,28467153...

40/137=0,29197080...

41/137=0,29927007...

42/137=0,30656934...

43/137=0,31386861...

44/137=0,32116788...

45/137=0,32846715...

46/137=0,33576642...

47/137=0,34306569...

48/137=0,35036496...

49/137=0,35766423...

50/137=0,36496350...

51/137=0,37226277...

52/137=0,37956204...

53/137=0,38686131...

54/137=0,39416058...

55/137=0,40145985...

56/137=0,40875912...

57/137=0,41605839...

58/137=0,42335766...

59/137=0,43065693...

60/137=0,43795620...

61/137=0,44525547...

62/137=0,45255474...

63/137=0,45985401...

64/137=0,46715328...

65/137=0,47445255...

66/137=0,48175182...

67/137=0,48905109...

68/137=0,49635036...

69/137=0,50364963...

70/137=0,51094890...

71/137=0,51824817...

72/137=0,52554744...

73/137=0,53284671...

74/137=0,54014598...

75/137=0,54744525...

76/137=0,55474452...

77/137=0,56204379...

78/137=0,56934306...

79/137=0,57664233...

80/137=0,58394160...

81/137=0,59124087...

82/137=0,59854014...

83/137=0,60583941...

84/137=0,61313868...

85/137=0,62043795...

86/137=0,62773722...

87/137=0,63503649...

88/137=0,64233576...

89/137=0,64963503...

90/137=0,65693430...

91/137=0,66423357...

92/137=0,67153284...

93/137=0,67883211...

94/137=0,68613138...

95/137=0,69343065...

96/137=0,70072992...

97/137=0,70802919...

98/137=0,71532846...

99/137=0,72262773...

100/137=0,72992700...

101/137=0,73722627...

102/137=0,74452554...

103/137=0,75182481...

104/137=0,75912408...

105/137=0,76642335...

106/137=0,77372262...

107/137=0,78102189...

108/137=0,78832116...

109/137=0,79562043...

110/137=0,80291970...

111/137=0,81021897...

112/137=0,81751824...

113/137=0,82481751...

114/137=0,83211678...

115/137=0,83941605...

116/137=0,84671532...

117/137=0,85401459...

118/137=0,86131386...

119/137=0,86861313...

120/137=0,87591240...

121/137=0,88321167...

122/137=0,89051094...

123/137=0,89781021...

124/137=0,90510948...

125/137=0,91240875...

126/137=0,91970802...

127/137=0,92700729...

128/137=0,93430656...

129/137=0,94160583...

130/137=0,94890510...

131/137=0,95620437...

132/137=0,96350364...

133/137=0,97080291...

134/137=0,97810218...

135/137=0,98540145...

136/137=0,99270072...

On remarque que le produit du nombre de périodes (17) et de leurs longueurs (8) est égal à 136 et donc au premier -1.