Il existe 15 périodes de 12 chiffres pour n/181 en base 7.

Pour toutes les fractions de n/181 en base 7, la période de 1/181 revient alors 12 fois (en orange)

1/181=0,001615665051...

2/181=0,003534663132...

3/181=0,005453661213...

4/181=0,010402656264...

5/181=0,012321654345...

6/181=0,014240652426...

7/181=0,016156650510...

8/181=0,021105645561...

9/181=0,023024643642...

10/181=0,024643642023...

11/181=0,026562640104...

12/181=0,031511635155...

13/181=0,033430633236...

14/181=0,035346631320...

15/181=0,040265626401...

16/181=0,042214624452...

17/181=0,044133622533...

18/181=0,046052620614...

19/181=0,051001615665...

20/181=0,052620614046...

21/181=0,054536612130...

22/181=0,056455610211...

23/181=0,061404605262...

24/181=0,063323603343...

25/181=0,065242601424...

26/181=0,100161566505...

27/181=0,102110564556...

28/181=0,104026562640...

29/181=0,105645561021...

30/181=0,110564556102...

31/181=0,112513554153...

32/181=0,114432552234...

33/181=0,116351550315...

34/181=0,121300545366...

35/181=0,123216543450...

36/181=0,125135541531...

37/181=0,130054536612...

38/181=0,132003534663...

39/181=0,133622533044...

40/181=0,135541531125...

41/181=0,140460526206...

42/181=0,142406524260...

43/181=0,144325522341...

44/181=0,146244520422...

45/181=0,151163515503...

46/181=0,153112513554...

47/181=0,155031511635...

48/181=0,156650510016...

49/181=0,161566505100...

50/181=0,163515503151...

51/181=0,165434501232...

52/181=0,200353466313...

53/181=0,202302464364...

54/181=0,204221462445...

55/181=0,206140460526...

56/181=0,211056455610...

57/181=0,213005453661...

58/181=0,214624452042...

59/181=0,216543450123...

60/181=0,221462445204...

61/181=0,223411443255...

62/181=0,225330441336...

63/181=0,230246436420...

64/181=0,232165434501...

65/181=0,234114432552...

66/181=0,236033430633...

67/181=0,240652426014...

68/181=0,242601424065...

69/181=0,244520422146...

70/181=0,246436420230...

71/181=0,251355415311...

72/181=0,253304413362...

73/181=0,255223411443...

74/181=0,260142406524...

75/181=0,262061404605...

76/181=0,264010402656...

77/181=0,265626401040...

78/181=0,300545366121...

79/181=0,302464364202...

80/181=0,304413362253...

81/181=0,306332360334...

82/181=0,311251355415...

83/181=0,313200353466...

84/181=0,315116351550...

85/181=0,320035346631...

86/181=0,321654345012...

87/181=0,323603343063...

88/181=0,325522341144...

89/181=0,330441336225...

90/181=0,332360334306...

91/181=0,334306332360...

92/181=0,336225330441...

93/181=0,341144325522...

94/181=0,343063323603...

95/181=0,345012321654...

96/181=0,346631320035...

97/181=0,351550315116...

98/181=0,353466313200...

99/181=0,355415311251...

100/181=0,360334306332...

101/181=0,362253304413...

102/181=0,364202302464...

103/181=0,366121300545...

104/181=0,401040265626...

105/181=0,402656264010...

106/181=0,404605262061...

107/181=0,406524260142...

108/181=0,411443255223...

109/181=0,413362253304...

110/181=0,415311251355...

111/181=0,420230246436...

112/181=0,422146244520...

113/181=0,424065242601...

114/181=0,426014240652...

115/181=0,430633236033...

116/181=0,432552234114...

117/181=0,434501232165...

118/181=0,436420230246...

119/181=0,441336225330...

120/181=0,443255223411...

121/181=0,445204221462...

122/181=0,450123216543...

123/181=0,452042214624...

124/181=0,453661213005...

125/181=0,455610211056...

126/181=0,460526206140...

127/181=0,462445204221...

128/181=0,464364202302...

129/181=0,466313200353...

130/181=0,501232165434...

131/181=0,503151163515...

132/181=0,505100161566...

133/181=0,510016156650...

134/181=0,511635155031...

135/181=0,513554153112...

136/181=0,515503151163...

137/181=0,520422146244...

138/181=0,522341144325...

139/181=0,524260142406...

140/181=0,526206140460...

141/181=0,531125135541...

142/181=0,533044133622...

143/181=0,534663132003...

144/181=0,536612130054...

145/181=0,541531125135...

146/181=0,543450123216...

147/181=0,545366121300...

148/181=0,550315116351...

149/181=0,552234114432...

150/181=0,554153112513...

151/181=0,556102110564...

152/181=0,561021105645...

153/181=0,562640104026...

154/181=0,564556102110...

155/181=0,566505100161...

156/181=0,601424065242...

157/181=0,603343063323...

158/181=0,605262061404...

159/181=0,610211056455...

160/181=0,612130054536...

161/181=0,614046052620...

162/181=0,615665051001...

163/181=0,620614046052...

164/181=0,622533044133...

165/181=0,624452042214...

166/181=0,626401040265...

167/181=0,631320035346...

168/181=0,633236033430...

169/181=0,635155031511...

170/181=0,640104026562...

171/181=0,642023024643...

172/181=0,643642023024...

173/181=0,645561021105...

174/181=0,650510016156...

175/181=0,652426014240...

176/181=0,654345012321...

177/181=0,656264010402...

178/181=0,661213005453...

179/181=0,663132003534...

180/181=0,665051001615...

On remarque que le produit du nombre de périodes (15) et de leurs longueurs (12) est égal à 180 et donc au premier -1.