Il existe 3 périodes de 60 chiffres pour n/181 en base 6.

Pour toutes les fractions de n/181 en base 6, la période de 1/181 revient alors 60 fois (en orange)

1/181=0,001105433513425034401331405100554450122042130521154224150455...

2/181=0,002215311431254113203103214201553340244124301442352452341354...

3/181=0,003325145345123152004435023302552230410210432403551120532253...

4/181=0,004435023302552230410210432403551120532253003325145345123152...

5/181=0,005544501220421305211542241504550011054335134250344013314051...

6/181=0,011054335134250344013314051005544501220421305211542241504550...

7/181=0,012204213052115422415045500110543351342503440133140510055445...

8/181=0,013314051005544501220421305211542241504550011054335134250344...

9/181=0,014423524523413540022153114312541132031032142015533402441243...

10/181=0,015533402441243014423524523413540022153114312541132031032142...

11/181=0,021043240355112053225300332514534512315200443502330255223041...

12/181=0,022153114312541132031032142015533402441243014423524523413540...

13/181=0,023302552230410210432403551120532253003325145345123152004435...

14/181=0,024412430144235245234135400221531143125411320310321420155334...

15/181=0,025522304102104324035511205322530033251453451231520044350233...

16/181=0,031032142015533402441243014423524523413540022153114312541132...

17/181=0,032142015533402441243014423524523413540022153114312541132031...

18/181=0,033251453451231520044350233025522304102104324035511205322530...

19/181=0,034401331405100554450122042130521154224150455001105433513425...

20/181=0,035511205322530033251453451231520044350233025522304102104324...

21/181=0,041021043240355112053225300332514534512315200443502330255223...

22/181=0,042130521154224150455001105433513425034401331405100554450122...

23/181=0,043240355112053225300332514534512315200443502330255223041021...

24/181=0,044350233025522304102104324035511205322530033251453451231520...

25/181=0,045500110543351342503440133140510055445012204213052115422415...

26/181=0,051005544501220421305211542241504550011054335134250344013314...

27/181=0,052115422415045500110543351342503440133140510055445012204213...

28/181=0,053225300332514534512315200443502330255223041021043240355112...

29/181=0,054335134250344013314051005544501220421305211542241504550011...

30/181=0,055445012204213052115422415045500110543351342503440133140510...

31/181=0,100554450122042130521154224150455001105433513425034401331405...

32/181=0,102104324035511205322530033251453451231520044350233025522304...

33/181=0,103214201553340244124301442352452341354002215311431254113203...

34/181=0,104324035511205322530033251453451231520044350233025522304102...

35/181=0,105433513425034401331405100554450122042130521154224150455001...

36/181=0,110543351342503440133140510055445012204213052115422415045500...

37/181=0,112053225300332514534512315200443502330255223041021043240355...

38/181=0,113203103214201553340244124301442352452341354002215311431254...

39/181=0,114312541132031032142015533402441243014423524523413540022153...

40/181=0,115422415045500110543351342503440133140510055445012204213052...

41/181=0,120532253003325145345123152004435023302552230410210432403551...

42/181=0,122042130521154224150455001105433513425034401331405100554450...

43/181=0,123152004435023302552230410210432403551120532253003325145345...

44/181=0,124301442352452341354002215311431254113203103214201553340244...

45/181=0,125411320310321420155334024412430144235245234135400221531143...

46/181=0,130521154224150455001105433513425034401331405100554450122042...

47/181=0,132031032142015533402441243014423524523413540022153114312541...

48/181=0,133140510055445012204213052115422415045500110543351342503440...

49/181=0,134250344013314051005544501220421305211542241504550011054335...

50/181=0,135400221531143125411320310321420155334024412430144235245234...

51/181=0,140510055445012204213052115422415045500110543351342503440133...

52/181=0,142015533402441243014423524523413540022153114312541132031032...

53/181=0,143125411320310321420155334024412430144235245234135400221531...

54/181=0,144235245234135400221531143125411320310321420155334024412430...

55/181=0,145345123152004435023302552230410210432403551120532253003325...

56/181=0,150455001105433513425034401331405100554450122042130521154224...

57/181=0,152004435023302552230410210432403551120532253003325145345123...

58/181=0,153114312541132031032142015533402441243014423524523413540022...

59/181=0,154224150455001105433513425034401331405100554450122042130521...

60/181=0,155334024412430144235245234135400221531143125411320310321420...

61/181=0,200443502330255223041021043240355112053225300332514534512315...

62/181=0,201553340244124301442352452341354002215311431254113203103214...

63/181=0,203103214201553340244124301442352452341354002215311431254113...

64/181=0,204213052115422415045500110543351342503440133140510055445012...

65/181=0,205322530033251453451231520044350233025522304102104324035511...

66/181=0,210432403551120532253003325145345123152004435023302552230410...

67/181=0,211542241504550011054335134250344013314051005544501220421305...

68/181=0,213052115422415045500110543351342503440133140510055445012204...

69/181=0,214201553340244124301442352452341354002215311431254113203103...

70/181=0,215311431254113203103214201553340244124301442352452341354002...

71/181=0,220421305211542241504550011054335134250344013314051005544501...

72/181=0,221531143125411320310321420155334024412430144235245234135400...

73/181=0,223041021043240355112053225300332514534512315200443502330255...

74/181=0,224150455001105433513425034401331405100554450122042130521154...

75/181=0,225300332514534512315200443502330255223041021043240355112053...

76/181=0,230410210432403551120532253003325145345123152004435023302552...

77/181=0,231520044350233025522304102104324035511205322530033251453451...

78/181=0,233025522304102104324035511205322530033251453451231520044350...

79/181=0,234135400221531143125411320310321420155334024412430144235245...

80/181=0,235245234135400221531143125411320310321420155334024412430144...

81/181=0,240355112053225300332514534512315200443502330255223041021043...

82/181=0,241504550011054335134250344013314051005544501220421305211542...

83/181=0,243014423524523413540022153114312541132031032142015533402441...

84/181=0,244124301442352452341354002215311431254113203103214201553340...

85/181=0,245234135400221531143125411320310321420155334024412430144235...

86/181=0,250344013314051005544501220421305211542241504550011054335134...

87/181=0,251453451231520044350233025522304102104324035511205322530033...

88/181=0,253003325145345123152004435023302552230410210432403551120532...

89/181=0,254113203103214201553340244124301442352452341354002215311431...

90/181=0,255223041021043240355112053225300332514534512315200443502330...

91/181=0,300332514534512315200443502330255223041021043240355112053225...

92/181=0,301442352452341354002215311431254113203103214201553340244124...

93/181=0,302552230410210432403551120532253003325145345123152004435023...

94/181=0,304102104324035511205322530033251453451231520044350233025522...

95/181=0,305211542241504550011054335134250344013314051005544501220421...

96/181=0,310321420155334024412430144235245234135400221531143125411320...

97/181=0,311431254113203103214201553340244124301442352452341354002215...

98/181=0,312541132031032142015533402441243014423524523413540022153114...

99/181=0,314051005544501220421305211542241504550011054335134250344013...

100/181=0,315200443502330255223041021043240355112053225300332514534512...

101/181=0,320310321420155334024412430144235245234135400221531143125411...

102/181=0,321420155334024412430144235245234135400221531143125411320310...

103/181=0,322530033251453451231520044350233025522304102104324035511205...

104/181=0,324035511205322530033251453451231520044350233025522304102104...

105/181=0,325145345123152004435023302552230410210432403551120532253003...

106/181=0,330255223041021043240355112053225300332514534512315200443502...

107/181=0,331405100554450122042130521154224150455001105433513425034401...

108/181=0,332514534512315200443502330255223041021043240355112053225300...

109/181=0,334024412430144235245234135400221531143125411320310321420155...

110/181=0,335134250344013314051005544501220421305211542241504550011054...

111/181=0,340244124301442352452341354002215311431254113203103214201553...

112/181=0,341354002215311431254113203103214201553340244124301442352452...

113/181=0,342503440133140510055445012204213052115422415045500110543351...

114/181=0,344013314051005544501220421305211542241504550011054335134250...

115/181=0,345123152004435023302552230410210432403551120532253003325145...

116/181=0,350233025522304102104324035511205322530033251453451231520044...

117/181=0,351342503440133140510055445012204213052115422415045500110543...

118/181=0,352452341354002215311431254113203103214201553340244124301442...

119/181=0,354002215311431254113203103214201553340244124301442352452341...

120/181=0,355112053225300332514534512315200443502330255223041021043240...

121/181=0,400221531143125411320310321420155334024412430144235245234135...

122/181=0,401331405100554450122042130521154224150455001105433513425034...

123/181=0,402441243014423524523413540022153114312541132031032142015533...

124/181=0,403551120532253003325145345123152004435023302552230410210432...

125/181=0,405100554450122042130521154224150455001105433513425034401331...

126/181=0,410210432403551120532253003325145345123152004435023302552230...

127/181=0,411320310321420155334024412430144235245234135400221531143125...

128/181=0,412430144235245234135400221531143125411320310321420155334024...

129/181=0,413540022153114312541132031032142015533402441243014423524523...

130/181=0,415045500110543351342503440133140510055445012204213052115422...

131/181=0,420155334024412430144235245234135400221531143125411320310321...

132/181=0,421305211542241504550011054335134250344013314051005544501220...

133/181=0,422415045500110543351342503440133140510055445012204213052115...

134/181=0,423524523413540022153114312541132031032142015533402441243014...

135/181=0,425034401331405100554450122042130521154224150455001105433513...

136/181=0,430144235245234135400221531143125411320310321420155334024412...

137/181=0,431254113203103214201553340244124301442352452341354002215311...

138/181=0,432403551120532253003325145345123152004435023302552230410210...

139/181=0,433513425034401331405100554450122042130521154224150455001105...

140/181=0,435023302552230410210432403551120532253003325145345123152004...

141/181=0,440133140510055445012204213052115422415045500110543351342503...

142/181=0,441243014423524523413540022153114312541132031032142015533402...

143/181=0,442352452341354002215311431254113203103214201553340244124301...

144/181=0,443502330255223041021043240355112053225300332514534512315200...

145/181=0,445012204213052115422415045500110543351342503440133140510055...

146/181=0,450122042130521154224150455001105433513425034401331405100554...

147/181=0,451231520044350233025522304102104324035511205322530033251453...

148/181=0,452341354002215311431254113203103214201553340244124301442352...

149/181=0,453451231520044350233025522304102104324035511205322530033251...

150/181=0,455001105433513425034401331405100554450122042130521154224150...

151/181=0,500110543351342503440133140510055445012204213052115422415045...

152/181=0,501220421305211542241504550011054335134250344013314051005544...

153/181=0,502330255223041021043240355112053225300332514534512315200443...

154/181=0,503440133140510055445012204213052115422415045500110543351342...

155/181=0,504550011054335134250344013314051005544501220421305211542241...

156/181=0,510055445012204213052115422415045500110543351342503440133140...

157/181=0,511205322530033251453451231520044350233025522304102104324035...

158/181=0,512315200443502330255223041021043240355112053225300332514534...

159/181=0,513425034401331405100554450122042130521154224150455001105433...

160/181=0,514534512315200443502330255223041021043240355112053225300332...

161/181=0,520044350233025522304102104324035511205322530033251453451231...

162/181=0,521154224150455001105433513425034401331405100554450122042130...

163/181=0,522304102104324035511205322530033251453451231520044350233025...

164/181=0,523413540022153114312541132031032142015533402441243014423524...

165/181=0,524523413540022153114312541132031032142015533402441243014423...

166/181=0,530033251453451231520044350233025522304102104324035511205322...

167/181=0,531143125411320310321420155334024412430144235245234135400221...

168/181=0,532253003325145345123152004435023302552230410210432403551120...

169/181=0,533402441243014423524523413540022153114312541132031032142015...

170/181=0,534512315200443502330255223041021043240355112053225300332514...

171/181=0,540022153114312541132031032142015533402441243014423524523413...

172/181=0,541132031032142015533402441243014423524523413540022153114312...

173/181=0,542241504550011054335134250344013314051005544501220421305211...

174/181=0,543351342503440133140510055445012204213052115422415045500110...

175/181=0,544501220421305211542241504550011054335134250344013314051005...

176/181=0,550011054335134250344013314051005544501220421305211542241504...

177/181=0,551120532253003325145345123152004435023302552230410210432403...

178/181=0,552230410210432403551120532253003325145345123152004435023302...

179/181=0,553340244124301442352452341354002215311431254113203103214201...

180/181=0,554450122042130521154224150455001105433513425034401331405100...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (60) est égal à 180 et donc au premier -1.