Il existe 12 périodes de 15 chiffres pour n/181 en base 5.

Pour toutes les fractions de n/181 en base 5, la période de 1/181 revient alors 15 fois (en orange)

1/181=0,000321130333104...

2/181=0,001142311221213...

3/181=0,002013442104322...

4/181=0,002340122442431...

5/181=0,003211303331040...

6/181=0,004032434214144...

7/181=0,004404120102303...

8/181=0,010230300440412...

9/181=0,011101431324021...

10/181=0,011423112212130...

11/181=0,012244243100234...

12/181=0,013120423433343...

13/181=0,013442104322002...

14/181=0,014313240210111...

15/181=0,020134421043220...

16/181=0,021011101431324...

17/181=0,021332232314433...

18/181=0,022203413203042...

19/181=0,023030044041201...

20/181=0,023401224424310...

21/181=0,024222410312414...

22/181=0,030044041201023...

23/181=0,030420222034132...

24/181=0,031241402422241...

25/181=0,032113033310400...

26/181=0,032434214144004...

27/181=0,033310400032113...

28/181=0,034132030420222...

29/181=0,040003211303331...

30/181=0,040324342141440...

31/181=0,041201023030044...

32/181=0,042022203413203...

33/181=0,042343334301312...

34/181=0,043220020134421...

35/181=0,044041201023030...

36/181=0,044412331411134...

37/181=0,100234012244243...

38/181=0,101110143132402...

39/181=0,101431324021011...

40/181=0,102303004404120...

41/181=0,103124140242224...

42/181=0,104000321130333...

43/181=0,104322002013442...

44/181=0,110143132402101...

45/181=0,111014313240210...

46/181=0,111340444123314...

47/181=0,112212130011423...

48/181=0,113033310400032...

49/181=0,113404441233141...

50/181=0,114231122121300...

51/181=0,120102303004404...

52/181=0,120423433343013...

53/181=0,121300114231122...

54/181=0,122121300114231...

55/181=0,122442431002340...

56/181=0,123314111340444...

57/181=0,124140242224103...

58/181=0,130011423112212...

59/181=0,130333104000321...

60/181=0,131204234333430...

61/181=0,132030420222034...

62/181=0,132402101110143...

63/181=0,133223231443302...

64/181=0,134044412331411...

65/181=0,134421043220020...

66/181=0,140242224103124...

67/181=0,141113404441233...

68/181=0,141440040324342...

69/181=0,142311221213001...

70/181=0,143132402101110...

71/181=0,144004032434214...

72/181=0,144330213322323...

73/181=0,200201344210432...

74/181=0,201023030044041...

75/181=0,201344210432200...

76/181=0,202220341320304...

77/181=0,203042022203413...

78/181=0,203413203042022...

79/181=0,204234333430131...

80/181=0,210111014313240...

81/181=0,210432200201344...

82/181=0,211303331040003...

83/181=0,212130011423112...

84/181=0,213001142311221...

85/181=0,213322323144330...

86/181=0,214144004032434...

87/181=0,220020134421043...

88/181=0,220341320304202...

89/181=0,221213001142311...

90/181=0,222034132030420...

91/181=0,222410312414024...

92/181=0,223231443302133...

93/181=0,224103124140242...

94/181=0,224424310023401...

95/181=0,230300440412010...

96/181=0,231122121300114...

97/181=0,231443302133223...

98/181=0,232314433021332...

99/181=0,233141113404441...

100/181=0,234012244243100...

101/181=0,234333430131204...

102/181=0,240210111014313...

103/181=0,241031241402422...

104/181=0,241402422241031...

105/181=0,242224103124140...

106/181=0,243100234012244...

107/181=0,243421414400403...

108/181=0,244243100234012...

109/181=0,300114231122121...

110/181=0,300440412010230...

111/181=0,301312042343334...

112/181=0,302133223231443...

113/181=0,303004404120102...

114/181=0,303331040003211...

115/181=0,304202220341320...

116/181=0,310023401224424...

117/181=0,310400032113033...

118/181=0,311221213001142...

119/181=0,312042343334301...

120/181=0,312414024222410...

121/181=0,313240210111014...

122/181=0,314111340444123...

123/181=0,314433021332232...

124/181=0,320304202220341...

125/181=0,321130333104000...

126/181=0,322002013442104...

127/181=0,322323144330213...

128/181=0,323144330213322...

129/181=0,324021011101431...

130/181=0,324342141440040...

131/181=0,330213322323144...

132/181=0,331040003211303...

133/181=0,331411134044412...

134/181=0,332232314433021...

135/181=0,333104000321130...

136/181=0,333430131204234...

137/181=0,334301312042343...

138/181=0,340122442431002...

139/181=0,340444123314111...

140/181=0,341320304202220...

141/181=0,342141440040324...

142/181=0,343013120423433...

143/181=0,343334301312042...

144/181=0,344210432200201...

145/181=0,400032113033310...

146/181=0,400403243421414...

147/181=0,401224424310023...

148/181=0,402101110143132...

149/181=0,402422241031241...

150/181=0,403243421414400...

151/181=0,404120102303004...

152/181=0,404441233141113...

153/181=0,410312414024222...

154/181=0,411134044412331...

155/181=0,412010230300440...

156/181=0,412331411134044...

157/181=0,413203042022203...

158/181=0,414024222410312...

159/181=0,414400403243421...

160/181=0,420222034132030...

161/181=0,421043220020134...

162/181=0,421414400403243...

163/181=0,422241031241402...

164/181=0,423112212130011...

165/181=0,423433343013120...

166/181=0,424310023401224...

167/181=0,430131204234333...

168/181=0,431002340122442...

169/181=0,431324021011101...

170/181=0,432200201344210...

171/181=0,433021332232314...

172/181=0,433343013120423...

173/181=0,434214144004032...

174/181=0,440040324342141...

175/181=0,440412010230300...

176/181=0,441233141113404...

177/181=0,442104322002013...

178/181=0,442431002340122...

179/181=0,443302133223231...

180/181=0,444123314111340...

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