Il existe 3 périodes de 54 chiffres pour n/163 en base 8.

Pour toutes les fractions de n/163 en base 8, la période de 1/163 revient alors 54 fois (en orange)

1/163=0,003110175511641610506531412774667602266136167271246365...

2/163=0,006220373223503421215263025771557404554274356562514752...

3/163=0,011330570735345231724014440766447207042432546053763337...

4/163=0,014440766447207042432546053763337011330570735345231724...

5/163=0,017551164161050653141277466760226613616727124636500311...

6/163=0,022661361672712463650031101755116416105065314127746676...

7/163=0,025771557404554274356562514752006220373223503421215263...

8/163=0,031101755116416105065314127746676022661361672712463650...

9/163=0,034212152630257715574045542743565625147520062203732235...

10/163=0,037322350342121526302577155740455427435656251475200622...

11/163=0,042432546053763337011330570735345231724014440766447207...

12/163=0,045542743565625147520062203732235034212152630257715574...

13/163=0,050653141277466760226613616727124636500311017551164161...

14/163=0,053763337011330570735345231724014440766447207042432546...

15/163=0,057073534523172401444076644720704243254605376333701133...

16/163=0,062203732235034212152630257715574045542743565625147520...

17/163=0,065314127746676022661361672712463650031101755116416105...

18/163=0,070424325460537633370113305707353452317240144407664472...

19/163=0,073534523172401444076644720704243254605376333701133057...

20/163=0,076644720704243254605376333701133057073534523172401444...

21/163=0,101755116416105065314127746676022661361672712463650031...

22/163=0,105065314127746676022661361672712463650031101755116416...

23/163=0,110175511641610506531412774667602266136167271246365003...

24/163=0,113305707353452317240144407664472070424325460537633370...

25/163=0,116416105065314127746676022661361672712463650031101755...

26/163=0,121526302577155740455427435656251475200622037322350342...

27/163=0,124636500311017551164161050653141277466760226613616727...

28/163=0,127746676022661361672712463650031101755116416105065314...

29/163=0,133057073534523172401444076644720704243254605376333701...

30/163=0,136167271246365003110175511641610506531412774667602266...

31/163=0,141277466760226613616727124636500311017551164161050653...

32/163=0,144407664472070424325460537633370113305707353452317240...

33/163=0,147520062203732235034212152630257715574045542743565625...

34/163=0,152630257715574045542743565625147520062203732235034212...

35/163=0,155740455427435656251475200622037322350342121526302577...

36/163=0,161050653141277466760226613616727124636500311017551164...

37/163=0,164161050653141277466760226613616727124636500311017551...

38/163=0,167271246365003110175511641610506531412774667602266136...

39/163=0,172401444076644720704243254605376333701133057073534523...

40/163=0,175511641610506531412774667602266136167271246365003110...

41/163=0,200622037322350342121526302577155740455427435656251475...

42/163=0,203732235034212152630257715574045542743565625147520062...

43/163=0,207042432546053763337011330570735345231724014440766447...

44/163=0,212152630257715574045542743565625147520062203732235034...

45/163=0,215263025771557404554274356562514752006220373223503421...

46/163=0,220373223503421215263025771557404554274356562514752006...

47/163=0,223503421215263025771557404554274356562514752006220373...

48/163=0,226613616727124636500311017551164161050653141277466760...

49/163=0,231724014440766447207042432546053763337011330570735345...

50/163=0,235034212152630257715574045542743565625147520062203732...

51/163=0,240144407664472070424325460537633370113305707353452317...

52/163=0,243254605376333701133057073534523172401444076644720704...

53/163=0,246365003110175511641610506531412774667602266136167271...

54/163=0,251475200622037322350342121526302577155740455427435656...

55/163=0,254605376333701133057073534523172401444076644720704243...

56/163=0,257715574045542743565625147520062203732235034212152630...

57/163=0,263025771557404554274356562514752006220373223503421215...

58/163=0,266136167271246365003110175511641610506531412774667602...

59/163=0,271246365003110175511641610506531412774667602266136167...

60/163=0,274356562514752006220373223503421215263025771557404554...

61/163=0,277466760226613616727124636500311017551164161050653141...

62/163=0,302577155740455427435656251475200622037322350342121526...

63/163=0,305707353452317240144407664472070424325460537633370113...

64/163=0,311017551164161050653141277466760226613616727124636500...

65/163=0,314127746676022661361672712463650031101755116416105065...

66/163=0,317240144407664472070424325460537633370113305707353452...

67/163=0,322350342121526302577155740455427435656251475200622037...

68/163=0,325460537633370113305707353452317240144407664472070424...

69/163=0,330570735345231724014440766447207042432546053763337011...

70/163=0,333701133057073534523172401444076644720704243254605376...

71/163=0,337011330570735345231724014440766447207042432546053763...

72/163=0,342121526302577155740455427435656251475200622037322350...

73/163=0,345231724014440766447207042432546053763337011330570735...

74/163=0,350342121526302577155740455427435656251475200622037322...

75/163=0,353452317240144407664472070424325460537633370113305707...

76/163=0,356562514752006220373223503421215263025771557404554274...

77/163=0,361672712463650031101755116416105065314127746676022661...

78/163=0,365003110175511641610506531412774667602266136167271246...

79/163=0,370113305707353452317240144407664472070424325460537633...

80/163=0,373223503421215263025771557404554274356562514752006220...

81/163=0,376333701133057073534523172401444076644720704243254605...

82/163=0,401444076644720704243254605376333701133057073534523172...

83/163=0,404554274356562514752006220373223503421215263025771557...

84/163=0,407664472070424325460537633370113305707353452317240144...

85/163=0,412774667602266136167271246365003110175511641610506531...

86/163=0,416105065314127746676022661361672712463650031101755116...

87/163=0,421215263025771557404554274356562514752006220373223503...

88/163=0,424325460537633370113305707353452317240144407664472070...

89/163=0,427435656251475200622037322350342121526302577155740455...

90/163=0,432546053763337011330570735345231724014440766447207042...

91/163=0,435656251475200622037322350342121526302577155740455427...

92/163=0,440766447207042432546053763337011330570735345231724014...

93/163=0,444076644720704243254605376333701133057073534523172401...

94/163=0,447207042432546053763337011330570735345231724014440766...

95/163=0,452317240144407664472070424325460537633370113305707353...

96/163=0,455427435656251475200622037322350342121526302577155740...

97/163=0,460537633370113305707353452317240144407664472070424325...

98/163=0,463650031101755116416105065314127746676022661361672712...

99/163=0,466760226613616727124636500311017551164161050653141277...

100/163=0,472070424325460537633370113305707353452317240144407664...

101/163=0,475200622037322350342121526302577155740455427435656251...

102/163=0,500311017551164161050653141277466760226613616727124636...

103/163=0,503421215263025771557404554274356562514752006220373223...

104/163=0,506531412774667602266136167271246365003110175511641610...

105/163=0,511641610506531412774667602266136167271246365003110175...

106/163=0,514752006220373223503421215263025771557404554274356562...

107/163=0,520062203732235034212152630257715574045542743565625147...

108/163=0,523172401444076644720704243254605376333701133057073534...

109/163=0,526302577155740455427435656251475200622037322350342121...

110/163=0,531412774667602266136167271246365003110175511641610506...

111/163=0,534523172401444076644720704243254605376333701133057073...

112/163=0,537633370113305707353452317240144407664472070424325460...

113/163=0,542743565625147520062203732235034212152630257715574045...

114/163=0,546053763337011330570735345231724014440766447207042432...

115/163=0,551164161050653141277466760226613616727124636500311017...

116/163=0,554274356562514752006220373223503421215263025771557404...

117/163=0,557404554274356562514752006220373223503421215263025771...

118/163=0,562514752006220373223503421215263025771557404554274356...

119/163=0,565625147520062203732235034212152630257715574045542743...

120/163=0,570735345231724014440766447207042432546053763337011330...

121/163=0,574045542743565625147520062203732235034212152630257715...

122/163=0,577155740455427435656251475200622037322350342121526302...

123/163=0,602266136167271246365003110175511641610506531412774667...

124/163=0,605376333701133057073534523172401444076644720704243254...

125/163=0,610506531412774667602266136167271246365003110175511641...

126/163=0,613616727124636500311017551164161050653141277466760226...

127/163=0,616727124636500311017551164161050653141277466760226613...

128/163=0,622037322350342121526302577155740455427435656251475200...

129/163=0,625147520062203732235034212152630257715574045542743565...

130/163=0,630257715574045542743565625147520062203732235034212152...

131/163=0,633370113305707353452317240144407664472070424325460537...

132/163=0,636500311017551164161050653141277466760226613616727124...

133/163=0,641610506531412774667602266136167271246365003110175511...

134/163=0,644720704243254605376333701133057073534523172401444076...

135/163=0,650031101755116416105065314127746676022661361672712463...

136/163=0,653141277466760226613616727124636500311017551164161050...

137/163=0,656251475200622037322350342121526302577155740455427435...

138/163=0,661361672712463650031101755116416105065314127746676022...

139/163=0,664472070424325460537633370113305707353452317240144407...

140/163=0,667602266136167271246365003110175511641610506531412774...

141/163=0,672712463650031101755116416105065314127746676022661361...

142/163=0,676022661361672712463650031101755116416105065314127746...

143/163=0,701133057073534523172401444076644720704243254605376333...

144/163=0,704243254605376333701133057073534523172401444076644720...

145/163=0,707353452317240144407664472070424325460537633370113305...

146/163=0,712463650031101755116416105065314127746676022661361672...

147/163=0,715574045542743565625147520062203732235034212152630257...

148/163=0,720704243254605376333701133057073534523172401444076644...

149/163=0,724014440766447207042432546053763337011330570735345231...

150/163=0,727124636500311017551164161050653141277466760226613616...

151/163=0,732235034212152630257715574045542743565625147520062203...

152/163=0,735345231724014440766447207042432546053763337011330570...

153/163=0,740455427435656251475200622037322350342121526302577155...

154/163=0,743565625147520062203732235034212152630257715574045542...

155/163=0,746676022661361672712463650031101755116416105065314127...

156/163=0,752006220373223503421215263025771557404554274356562514...

157/163=0,755116416105065314127746676022661361672712463650031101...

158/163=0,760226613616727124636500311017551164161050653141277466...

159/163=0,763337011330570735345231724014440766447207042432546053...

160/163=0,766447207042432546053763337011330570735345231724014440...

161/163=0,771557404554274356562514752006220373223503421215263025...

162/163=0,774667602266136167271246365003110175511641610506531412...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (54) est égal à 162 et donc au premier -1.