Liste des fractions de n/181 en base 4.

Il existe 2 périodes de 90 chiffres pour n/181 en base 4.

Pour toutes les fractions de n/181 en base 4, la période de 1/181 revient alors 90 fois (en orange)

1/181=0,000112220103303101110313022100100332032312130333221113230030232223020311233233001301021203...

2/181=0,000231100213212202221232110200201330131230321333102233120121131112101223133132003202103012...

3/181=0,001003320323121303332211132300302322230203112332330013010212030001122201033031011103130221...

4/181=0,001122201033031011103130221001003320323121303332211132300302322230203112332330013010212030...

5/181=0,001301021203000112220103303101110313022100100332032312130333221113230030232223020311233233...

6/181=0,002013301312303213331022331201211311121012231331320032021030120002311002132122022212321102...

7/181=0,002132122022212321102002013301312303213331022331201211311121012231331320032021030120002311...

8/181=0,002311002132122022212321102002013301312303213331022331201211311121012231331320032021030120...

9/181=0,003023222302031123323300130102120300011222010330310111031302210010033203231213033322111323...

10/181=0,003202103012000231100213212202221232110200201330131230321333102233120121131112101223133132...

11/181=0,003320323121303332211132300302322230203112332330013010212030001122201033031011103130221001...

12/181=0,010033203231213033322111323003023222302031123323300130102120300011222010330310111031302210...

13/181=0,010212030001122201033031011103130221001003320323121303332211132300302322230203112332330013...

14/181=0,010330310111031302210010033203231213033322111323003023222302031123323300130102120300011222...

15/181=0,011103130221001003320323121303332211132300302322230203112332330013010212030001122201033031...

16/181=0,011222010330310111031302210010033203231213033322111323003023222302031123323300130102120300...

17/181=0,012000231100213212202221232110200201330131230321333102233120121131112101223133132003202103...

18/181=0,012113111210122313313200320210301200023110021321220222123211020020133013123032133310223312...

19/181=0,012231331320032021030120002311002132122022212321102002013301312303213331022331201211311121...

20/181=0,013010212030001122201033031011103130221001003320323121303332211132300302322230203112332330...

21/181=0,013123032133310223312012113111210122313313200320210301200023110021321220222123211020020133...

22/181=0,013301312303213331022331201211311121012231331320032021030120002311002132122022212321102002...

23/181=0,020020133013123032133310223312012113111210122313313200320210301200023110021321220222123211...

24/181=0,020133013123032133310223312012113111210122313313200320210301200023110021321220222123211020...

25/181=0,020311233233001301021203000112220103303101110313022100100332032312130333221113230030232223...

26/181=0,021030120002311002132122022212321102002013301312303213331022331201211311121012231331320032...

27/181=0,021203000112220103303101110313022100100332032312130333221113230030232223020311233233001301...

28/181=0,021321220222123211020020133013123032133310223312012113111210122313313200320210301200023110...

29/181=0,022100100332032312130333221113230030232223020311233233001301021203000112220103303101110313...

30/181=0,022212321102002013301312303213331022331201211311121012231331320032021030120002311002132122...

31/181=0,022331201211311121012231331320032021030120002311002132122022212321102002013301312303213331...

32/181=0,023110021321220222123211020020133013123032133310223312012113111210122313313200320210301200...

33/181=0,023222302031123323300130102120300011222010330310111031302210010033203231213033322111323003...

34/181=0,030001122201033031011103130221001003320323121303332211132300302322230203112332330013010212...

35/181=0,030120002311002132122022212321102002013301312303213331022331201211311121012231331320032021...

36/181=0,030232223020311233233001301021203000112220103303101110313022100100332032312130333221113230...

37/181=0,031011103130221001003320323121303332211132300302322230203112332330013010212030001122201033...

38/181=0,031123323300130102120300011222010330310111031302210010033203231213033322111323003023222302...

39/181=0,031302210010033203231213033322111323003023222302031123323300130102120300011222010330310111...

40/181=0,032021030120002311002132122022212321102002013301312303213331022331201211311121012231331320...

41/181=0,032133310223312012113111210122313313200320210301200023110021321220222123211020020133013123...

42/181=0,032312130333221113230030232223020311233233001301021203000112220103303101110313022100100332...

43/181=0,033031011103130221001003320323121303332211132300302322230203112332330013010212030001122201...

44/181=0,033203231213033322111323003023222302031123323300130102120300011222010330310111031302210010...

45/181=0,033322111323003023222302031123323300130102120300011222010330310111031302210010033203231213...

46/181=0,100100332032312130333221113230030232223020311233233001301021203000112220103303101110313022...

47/181=0,100213212202221232110200201330131230321333102233120121131112101223133132003202103012000231...

48/181=0,100332032312130333221113230030232223020311233233001301021203000112220103303101110313022100...

49/181=0,101110313022100100332032312130333221113230030232223020311233233001301021203000112220103303...

50/181=0,101223133132003202103012000231100213212202221232110200201330131230321333102233120121131112...

51/181=0,102002013301312303213331022331201211311121012231331320032021030120002311002132122022212321...

52/181=0,102120300011222010330310111031302210010033203231213033322111323003023222302031123323300130...

53/181=0,102233120121131112101223133132003202103012000231100213212202221232110200201330131230321333...

54/181=0,103012000231100213212202221232110200201330131230321333102233120121131112101223133132003202...

55/181=0,103130221001003320323121303332211132300302322230203112332330013010212030001122201033031011...

56/181=0,103303101110313022100100332032312130333221113230030232223020311233233001301021203000112220...

57/181=0,110021321220222123211020020133013123032133310223312012113111210122313313200320210301200023...

58/181=0,110200201330131230321333102233120121131112101223133132003202103012000231100213212202221232...

59/181=0,110313022100100332032312130333221113230030232223020311233233001301021203000112220103303101...

60/181=0,111031302210010033203231213033322111323003023222302031123323300130102120300011222010330310...

61/181=0,111210122313313200320210301200023110021321220222123211020020133013123032133310223312012113...

62/181=0,111323003023222302031123323300130102120300011222010330310111031302210010033203231213033322...

63/181=0,112101223133132003202103012000231100213212202221232110200201330131230321333102233120121131...

64/181=0,112220103303101110313022100100332032312130333221113230030232223020311233233001301021203000...

65/181=0,112332330013010212030001122201033031011103130221001003320323121303332211132300302322230203...

66/181=0,113111210122313313200320210301200023110021321220222123211020020133013123032133310223312012...

67/181=0,113230030232223020311233233001301021203000112220103303101110313022100100332032312130333221...

68/181=0,120002311002132122022212321102002013301312303213331022331201211311121012231331320032021030...

69/181=0,120121131112101223133132003202103012000231100213212202221232110200201330131230321333102233...

70/181=0,120300011222010330310111031302210010033203231213033322111323003023222302031123323300130102...

71/181=0,121012231331320032021030120002311002132122022212321102002013301312303213331022331201211311...

72/181=0,121131112101223133132003202103012000231100213212202221232110200201330131230321333102233120...

73/181=0,121303332211132300302322230203112332330013010212030001122201033031011103130221001003320323...

74/181=0,122022212321102002013301312303213331022331201211311121012231331320032021030120002311002132...

75/181=0,122201033031011103130221001003320323121303332211132300302322230203112332330013010212030001...

76/181=0,122313313200320210301200023110021321220222123211020020133013123032133310223312012113111210...

77/181=0,123032133310223312012113111210122313313200320210301200023110021321220222123211020020133013...

78/181=0,123211020020133013123032133310223312012113111210122313313200320210301200023110021321220222...

79/181=0,123323300130102120300011222010330310111031302210010033203231213033322111323003023222302031...

80/181=0,130102120300011222010330310111031302210010033203231213033322111323003023222302031123323300...

81/181=0,130221001003320323121303332211132300302322230203112332330013010212030001122201033031011103...

82/181=0,130333221113230030232223020311233233001301021203000112220103303101110313022100100332032312...

83/181=0,131112101223133132003202103012000231100213212202221232110200201330131230321333102233120121...

84/181=0,131230321333102233120121131112101223133132003202103012000231100213212202221232110200201330...

85/181=0,132003202103012000231100213212202221232110200201330131230321333102233120121131112101223133...

86/181=0,132122022212321102002013301312303213331022331201211311121012231331320032021030120002311002...

87/181=0,132300302322230203112332330013010212030001122201033031011103130221001003320323121303332211...

88/181=0,133013123032133310223312012113111210122313313200320210301200023110021321220222123211020020...

89/181=0,133132003202103012000231100213212202221232110200201330131230321333102233120121131112101223...

90/181=0,133310223312012113111210122313313200320210301200023110021321220222123211020020133013123032...

91/181=0,200023110021321220222123211020020133013123032133310223312012113111210122313313200320210301...

92/181=0,200201330131230321333102233120121131112101223133132003202103012000231100213212202221232110...

93/181=0,200320210301200023110021321220222123211020020133013123032133310223312012113111210122313313...

94/181=0,201033031011103130221001003320323121303332211132300302322230203112332330013010212030001122...

95/181=0,201211311121012231331320032021030120002311002132122022212321102002013301312303213331022331...

96/181=0,201330131230321333102233120121131112101223133132003202103012000231100213212202221232110200...

97/181=0,202103012000231100213212202221232110200201330131230321333102233120121131112101223133132003...

98/181=0,202221232110200201330131230321333102233120121131112101223133132003202103012000231100213212...

99/181=0,203000112220103303101110313022100100332032312130333221113230030232223020311233233001301021...

100/181=0,203112332330013010212030001122201033031011103130221001003320323121303332211132300302322230...

101/181=0,203231213033322111323003023222302031123323300130102120300011222010330310111031302210010033...

102/181=0,210010033203231213033322111323003023222302031123323300130102120300011222010330310111031302...

103/181=0,210122313313200320210301200023110021321220222123211020020133013123032133310223312012113111...

104/181=0,210301200023110021321220222123211020020133013123032133310223312012113111210122313313200320...

105/181=0,211020020133013123032133310223312012113111210122313313200320210301200023110021321220222123...

106/181=0,211132300302322230203112332330013010212030001122201033031011103130221001003320323121303332...

107/181=0,211311121012231331320032021030120002311002132122022212321102002013301312303213331022331201...

108/181=0,212030001122201033031011103130221001003320323121303332211132300302322230203112332330013010...

109/181=0,212202221232110200201330131230321333102233120121131112101223133132003202103012000231100213...

110/181=0,212321102002013301312303213331022331201211311121012231331320032021030120002311002132122022...

111/181=0,213033322111323003023222302031123323300130102120300011222010330310111031302210010033203231...

112/181=0,213212202221232110200201330131230321333102233120121131112101223133132003202103012000231100...

113/181=0,213331022331201211311121012231331320032021030120002311002132122022212321102002013301312303...

114/181=0,220103303101110313022100100332032312130333221113230030232223020311233233001301021203000112...

115/181=0,220222123211020020133013123032133310223312012113111210122313313200320210301200023110021321...

116/181=0,221001003320323121303332211132300302322230203112332330013010212030001122201033031011103130...

117/181=0,221113230030232223020311233233001301021203000112220103303101110313022100100332032312130333...

118/181=0,221232110200201330131230321333102233120121131112101223133132003202103012000231100213212202...

119/181=0,222010330310111031302210010033203231213033322111323003023222302031123323300130102120300011...

120/181=0,222123211020020133013123032133310223312012113111210122313313200320210301200023110021321220...

121/181=0,222302031123323300130102120300011222010330310111031302210010033203231213033322111323003023...

122/181=0,223020311233233001301021203000112220103303101110313022100100332032312130333221113230030232...

123/181=0,223133132003202103012000231100213212202221232110200201330131230321333102233120121131112101...

124/181=0,223312012113111210122313313200320210301200023110021321220222123211020020133013123032133310...

125/181=0,230030232223020311233233001301021203000112220103303101110313022100100332032312130333221113...

126/181=0,230203112332330013010212030001122201033031011103130221001003320323121303332211132300302322...

127/181=0,230321333102233120121131112101223133132003202103012000231100213212202221232110200201330131...

128/181=0,231100213212202221232110200201330131230321333102233120121131112101223133132003202103012000...

129/181=0,231213033322111323003023222302031123323300130102120300011222010330310111031302210010033203...

130/181=0,231331320032021030120002311002132122022212321102002013301312303213331022331201211311121012...

131/181=0,232110200201330131230321333102233120121131112101223133132003202103012000231100213212202221...

132/181=0,232223020311233233001301021203000112220103303101110313022100100332032312130333221113230030...

133/181=0,233001301021203000112220103303101110313022100100332032312130333221113230030232223020311233...

134/181=0,233120121131112101223133132003202103012000231100213212202221232110200201330131230321333102...

135/181=0,233233001301021203000112220103303101110313022100100332032312130333221113230030232223020311...

136/181=0,300011222010330310111031302210010033203231213033322111323003023222302031123323300130102120...

137/181=0,300130102120300011222010330310111031302210010033203231213033322111323003023222302031123323...

138/181=0,300302322230203112332330013010212030001122201033031011103130221001003320323121303332211132...

139/181=0,301021203000112220103303101110313022100100332032312130333221113230030232223020311233233001...

140/181=0,301200023110021321220222123211020020133013123032133310223312012113111210122313313200320210...

141/181=0,301312303213331022331201211311121012231331320032021030120002311002132122022212321102002013...

142/181=0,302031123323300130102120300011222010330310111031302210010033203231213033322111323003023222...

143/181=0,302210010033203231213033322111323003023222302031123323300130102120300011222010330310111031...

144/181=0,302322230203112332330013010212030001122201033031011103130221001003320323121303332211132300...

145/181=0,303101110313022100100332032312130333221113230030232223020311233233001301021203000112220103...

146/181=0,303213331022331201211311121012231331320032021030120002311002132122022212321102002013301312...

147/181=0,303332211132300302322230203112332330013010212030001122201033031011103130221001003320323121...

148/181=0,310111031302210010033203231213033322111323003023222302031123323300130102120300011222010330...

149/181=0,310223312012113111210122313313200320210301200023110021321220222123211020020133013123032133...

150/181=0,311002132122022212321102002013301312303213331022331201211311121012231331320032021030120002...

151/181=0,311121012231331320032021030120002311002132122022212321102002013301312303213331022331201211...

152/181=0,311233233001301021203000112220103303101110313022100100332032312130333221113230030232223020...

153/181=0,312012113111210122313313200320210301200023110021321220222123211020020133013123032133310223...

154/181=0,312130333221113230030232223020311233233001301021203000112220103303101110313022100100332032...

155/181=0,312303213331022331201211311121012231331320032021030120002311002132122022212321102002013301...

156/181=0,313022100100332032312130333221113230030232223020311233233001301021203000112220103303101110...

157/181=0,313200320210301200023110021321220222123211020020133013123032133310223312012113111210122313...

158/181=0,313313200320210301200023110021321220222123211020020133013123032133310223312012113111210122...

159/181=0,320032021030120002311002132122022212321102002013301312303213331022331201211311121012231331...

160/181=0,320210301200023110021321220222123211020020133013123032133310223312012113111210122313313200...

161/181=0,320323121303332211132300302322230203112332330013010212030001122201033031011103130221001003...

162/181=0,321102002013301312303213331022331201211311121012231331320032021030120002311002132122022212...

163/181=0,321220222123211020020133013123032133310223312012113111210122313313200320210301200023110021...

164/181=0,321333102233120121131112101223133132003202103012000231100213212202221232110200201330131230...

165/181=0,322111323003023222302031123323300130102120300011222010330310111031302210010033203231213033...

166/181=0,322230203112332330013010212030001122201033031011103130221001003320323121303332211132300302...

167/181=0,323003023222302031123323300130102120300011222010330310111031302210010033203231213033322111...

168/181=0,323121303332211132300302322230203112332330013010212030001122201033031011103130221001003320...

169/181=0,323300130102120300011222010330310111031302210010033203231213033322111323003023222302031123...

170/181=0,330013010212030001122201033031011103130221001003320323121303332211132300302322230203112332...

171/181=0,330131230321333102233120121131112101223133132003202103012000231100213212202221232110200201...

172/181=0,330310111031302210010033203231213033322111323003023222302031123323300130102120300011222010...

173/181=0,331022331201211311121012231331320032021030120002311002132122022212321102002013301312303213...

174/181=0,331201211311121012231331320032021030120002311002132122022212321102002013301312303213331022...

175/181=0,331320032021030120002311002132122022212321102002013301312303213331022331201211311121012231...

176/181=0,332032312130333221113230030232223020311233233001301021203000112220103303101110313022100100...

177/181=0,332211132300302322230203112332330013010212030001122201033031011103130221001003320323121303...

178/181=0,332330013010212030001122201033031011103130221001003320323121303332211132300302322230203112...

179/181=0,333102233120121131112101223133132003202103012000231100213212202221232110200201330131230321...

180/181=0,333221113230030232223020311233233001301021203000112220103303101110313022100100332032312130...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (90) est égal à 180 et donc au premier -1.