Il existe 2 périodes de 89 chiffres pour n/179 en base 3.

Pour toutes les fractions de n/179 en base 3, la période de 1/179 revient alors 89 fois (en orange)

1/179=0,00001100122122111102110112000202100210201110100221210102022110001210212112022220021200201...

2/179=0,00002201022021222211221001001111201121102220201220120211121220010121202001122210120101102...

3/179=0,00011001221221111021101120002021002102011101002212101020221100012102121120222200212002010...

4/179=0,00012102121120222200212002010000110012212211110211011200020210021020111010022121010202211...

5/179=0,00020210021020111010022121010202211000121021211202222002120020100001100122122111102110112...

6/179=0,00022010220212222112210010011112011211022202012201202111212200101212020011222101201011020...

7/179=0,00100111120112110222020122012021112122001012120200112221012010110200002201022021222211221...

8/179=0,00101212020011222101201011020000220102202122221122100100111120112110222020122012021112122...

9/179=0,00110012212211110211011200020210021020111010022121010202211000121021211202222002120020100...

10/179=0,00111120112110222020122012021112122001012120200112221012010110200002201022021222211221001...

11/179=0,00112221012010110200002201022021222211221001001111201121102220201220120211121220010121202...

12/179=0,00121021211202222002120020100001100122122111102110112000202100210201110100221210102022110...

13/179=0,00122122111102110112000202100210201110100221210102022110001210212112022220021200201000011...

14/179=0,00201000011001221221111021101120002021002102011101002212101020221100012102121120222200212...

15/179=0,00202100210201110100221210102022110001210212112022220021200201000011001221221111021101120...

16/179=0,00210201110100221210102022110001210212112022220021200201000011001221221111021101120002021...

17/179=0,00212002010000110012212211110211011200020210021020111010022121010202211000121021211202222...

18/179=0,00220102202122221122100100111120112110222020122012021112122001012120200112221012010110200...

19/179=0,00221210102022110001210212112022220021200201000011001221221111021101120002021002102011101...

20/179=0,01000011001221221111021101120002021002102011101002212101020221100012102121120222200212002...

21/179=0,01001111201121102220201220120211121220010121202001122210120101102000022010220212222112210...

22/179=0,01002212101020221100012102121120222200212002010000110012212211110211011200020210021020111...

23/179=0,01011020000220102202122221122100100111120112110222020122012021112122001012120200112221012...

24/179=0,01012120200112221012010110200002201022021222211221001001111201121102220201220120211121220...

25/179=0,01020221100012102121120222200212002010000110012212211110211011200020210021020111010022121...

26/179=0,01022021222211221001001111201121102220201220120211121220010121202001122210120101102000022...

27/179=0,01100122122111102110112000202100210201110100221210102022110001210212112022220021200201000...

28/179=0,01102000022010220212222112210010011112011211022202012201202111212200101212020011222101201...

29/179=0,01110100221210102022110001210212112022220021200201000011001221221111021101120002021002102...

30/179=0,01111201121102220201220120211121220010121202001122210120101102000022010220212222112210010...

31/179=0,01120002021002102011101002212101020221100012102121120222200212002010000110012212211110211...

32/179=0,01121102220201220120211121220010121202001122210120101102000022010220212222112210010011112...

33/179=0,01122210120101102000022010220212222112210010011112011211022202012201202111212200101212020...

34/179=0,01201011020000220102202122221122100100111120112110222020122012021112122001012120200112221...

35/179=0,01202111212200101212020011222101201011020000220102202122221122100100111120112110222020122...

36/179=0,01210212112022220021200201000011001221221111021101120002021002102011101002212101020221100...

37/179=0,01212020011222101201011020000220102202122221122100100111120112110222020122012021112122001...

38/179=0,01220120211121220010121202001122210120101102000022010220212222112210010011112011211022202...

39/179=0,01221221111021101120002021002102011101002212101020221100012102121120222200212002010000110...

40/179=0,02000022010220212222112210010011112011211022202012201202111212200101212020011222101201011...

41/179=0,02001122210120101102000022010220212222112210010011112011211022202012201202111212200101212...

42/179=0,02010000110012212211110211011200020210021020111010022121010202211000121021211202222002120...

43/179=0,02011101002212101020221100012102121120222200212002010000110012212211110211011200020210021...

44/179=0,02012201202111212200101212020011222101201011020000220102202122221122100100111120112110222...

45/179=0,02021002102011101002212101020221100012102121120222200212002010000110012212211110211011200...

46/179=0,02022110001210212112022220021200201000011001221221111021101120002021002102011101002212101...

47/179=0,02100210201110100221210102022110001210212112022220021200201000011001221221111021101120002...

48/179=0,02102011101002212101020221100012102121120222200212002010000110012212211110211011200020210...

49/179=0,02110112000202100210201110100221210102022110001210212112022220021200201000011001221221111...

50/179=0,02111212200101212020011222101201011020000220102202122221122100100111120112110222020122012...

51/179=0,02120020100001100122122111102110112000202100210201110100221210102022110001210212112022220...

52/179=0,02121120222200212002010000110012212211110211011200020210021020111010022121010202211000121...

53/179=0,02122221122100100111120112110222020122012021112122001012120200112221012010110200002201022...

54/179=0,02201022021222211221001001111201121102220201220120211121220010121202001122210120101102000...

55/179=0,02202122221122100100111120112110222020122012021112122001012120200112221012010110200002201...

56/179=0,02211000121021211202222002120020100001100122122111102110112000202100210201110100221210102...

57/179=0,02212101020221100012102121120222200212002010000110012212211110211011200020210021020111010...

58/179=0,02220201220120211121220010121202001122210120101102000022010220212222112210010011112011211...

59/179=0,02222002120020100001100122122111102110112000202100210201110100221210102022110001210212112...

60/179=0,10000110012212211110211011200020210021020111010022121010202211000121021211202222002120020...

61/179=0,10001210212112022220021200201000011001221221111021101120002021002102011101002212101020221...

62/179=0,10010011112011211022202012201202111212200101212020011222101201011020000220102202122221122...

63/179=0,10011112011211022202012201202111212200101212020011222101201011020000220102202122221122100...

64/179=0,10012212211110211011200020210021020111010022121010202211000121021211202222002120020100001...

65/179=0,10021020111010022121010202211000121021211202222002120020100001100122122111102110112000202...

66/179=0,10022121010202211000121021211202222002120020100001100122122111102110112000202100210201110...

67/179=0,10100221210102022110001210212112022220021200201000011001221221111021101120002021002102011...

68/179=0,10102022110001210212112022220021200201000011001221221111021101120002021002102011101002212...

69/179=0,10110200002201022021222211221001001111201121102220201220120211121220010121202001122210120...

70/179=0,10112000202100210201110100221210102022110001210212112022220021200201000011001221221111021...

71/179=0,10120101102000022010220212222112210010011112011211022202012201202111212200101212020011222...

72/179=0,10121202001122210120101102000022010220212222112210010011112011211022202012201202111212200...

73/179=0,10200002201022021222211221001001111201121102220201220120211121220010121202001122210120101...

74/179=0,10201110100221210102022110001210212112022220021200201000011001221221111021101120002021002...

75/179=0,10202211000121021211202222002120020100001100122122111102110112000202100210201110100221210...

76/179=0,10211011200020210021020111010022121010202211000121021211202222002120020100001100122122111...

77/179=0,10212112022220021200201000011001221221111021101120002021002102011101002212101020221100012...

78/179=0,10220212222112210010011112011211022202012201202111212200101212020011222101201011020000220...

79/179=0,10222020122012021112122001012120200112221012010110200002201022021222211221001001111201121...

80/179=0,11000121021211202222002120020100001100122122111102110112000202100210201110100221210102022...

81/179=0,11001221221111021101120002021002102011101002212101020221100012102121120222200212002010000...

82/179=0,11010022121010202211000121021211202222002120020100001100122122111102110112000202100210201...

83/179=0,11011200020210021020111010022121010202211000121021211202222002120020100001100122122111102...

84/179=0,11020000220102202122221122100100111120112110222020122012021112122001012120200112221012010...

85/179=0,11021101120002021002102011101002212101020221100012102121120222200212002010000110012212211...

86/179=0,11022202012201202111212200101212020011222101201011020000220102202122221122100100111120112...

87/179=0,11101002212101020221100012102121120222200212002010000110012212211110211011200020210021020...

88/179=0,11102110112000202100210201110100221210102022110001210212112022220021200201000011001221221...

89/179=0,11110211011200020210021020111010022121010202211000121021211202222002120020100001100122122...

90/179=0,11112011211022202012201202111212200101212020011222101201011020000220102202122221122100100...

91/179=0,11120112110222020122012021112122001012120200112221012010110200002201022021222211221001001...

92/179=0,11121220010121202001122210120101102000022010220212222112210010011112011211022202012201202...

93/179=0,11200020210021020111010022121010202211000121021211202222002120020100001100122122111102110...

94/179=0,11201121102220201220120211121220010121202001122210120101102000022010220212222112210010011...

95/179=0,11202222002120020100001100122122111102110112000202100210201110100221210102022110001210212...

96/179=0,11211022202012201202111212200101212020011222101201011020000220102202122221122100100111120...

97/179=0,11212200101212020011222101201011020000220102202122221122100100111120112110222020122012021...

98/179=0,11221001001111201121102220201220120211121220010121202001122210120101102000022010220212222...

99/179=0,11222101201011020000220102202122221122100100111120112110222020122012021112122001012120200...

100/179=0,12000202100210201110100221210102022110001210212112022220021200201000011001221221111021101...

101/179=0,12002010000110012212211110211011200020210021020111010022121010202211000121021211202222002...

102/179=0,12010110200002201022021222211221001001111201121102220201220120211121220010121202001122210...

103/179=0,12011211022202012201202111212200101212020011222101201011020000220102202122221122100100111...

104/179=0,12020011222101201011020000220102202122221122100100111120112110222020122012021112122001012...

105/179=0,12021112122001012120200112221012010110200002201022021222211221001001111201121102220201220...

106/179=0,12022220021200201000011001221221111021101120002021002102011101002212101020221100012102121...

107/179=0,12101020221100012102121120222200212002010000110012212211110211011200020210021020111010022...

108/179=0,12102121120222200212002010000110012212211110211011200020210021020111010022121010202211000...

109/179=0,12110222020122012021112122001012120200112221012010110200002201022021222211221001001111201...

110/179=0,12112022220021200201000011001221221111021101120002021002102011101002212101020221100012102...

111/179=0,12120200112221012010110200002201022021222211221001001111201121102220201220120211121220010...

112/179=0,12122001012120200112221012010110200002201022021222211221001001111201121102220201220120211...

113/179=0,12200101212020011222101201011020000220102202122221122100100111120112110222020122012021112...

114/179=0,12201202111212200101212020011222101201011020000220102202122221122100100111120112110222020...

115/179=0,12210010011112011211022202012201202111212200101212020011222101201011020000220102202122221...

116/179=0,12211110211011200020210021020111010022121010202211000121021211202222002120020100001100122...

117/179=0,12212211110211011200020210021020111010022121010202211000121021211202222002120020100001100...

118/179=0,12221012010110200002201022021222211221001001111201121102220201220120211121220010121202001...

119/179=0,12222112210010011112011211022202012201202111212200101212020011222101201011020000220102202...

120/179=0,20000220102202122221122100100111120112110222020122012021112122001012120200112221012010110...

121/179=0,20002021002102011101002212101020221100012102121120222200212002010000110012212211110211011...

122/179=0,20010121202001122210120101102000022010220212222112210010011112011211022202012201202111212...

123/179=0,20011222101201011020000220102202122221122100100111120112110222020122012021112122001012120...

124/179=0,20020100001100122122111102110112000202100210201110100221210102022110001210212112022220021...

125/179=0,20021200201000011001221221111021101120002021002102011101002212101020221100012102121120222...

126/179=0,20100001100122122111102110112000202100210201110100221210102022110001210212112022220021200...

127/179=0,20101102000022010220212222112210010011112011211022202012201202111212200101212020011222101...

128/179=0,20102202122221122100100111120112110222020122012021112122001012120200112221012010110200002...

129/179=0,20111010022121010202211000121021211202222002120020100001100122122111102110112000202100210...

130/179=0,20112110222020122012021112122001012120200112221012010110200002201022021222211221001001111...

131/179=0,20120211121220010121202001122210120101102000022010220212222112210010011112011211022202012...

132/179=0,20122012021112122001012120200112221012010110200002201022021222211221001001111201121102220...

133/179=0,20200112221012010110200002201022021222211221001001111201121102220201220120211121220010121...

134/179=0,20201220120211121220010121202001122210120101102000022010220212222112210010011112011211022...

135/179=0,20210021020111010022121010202211000121021211202222002120020100001100122122111102110112000...

136/179=0,20211121220010121202001122210120101102000022010220212222112210010011112011211022202012201...

137/179=0,20212222112210010011112011211022202012201202111212200101212020011222101201011020000220102...

138/179=0,20221100012102121120222200212002010000110012212211110211011200020210021020111010022121010...

139/179=0,20222200212002010000110012212211110211011200020210021020111010022121010202211000121021211...

140/179=0,21001001111201121102220201220120211121220010121202001122210120101102000022010220212222112...

141/179=0,21002102011101002212101020221100012102121120222200212002010000110012212211110211011200020...

142/179=0,21010202211000121021211202222002120020100001100122122111102110112000202100210201110100221...

143/179=0,21012010110200002201022021222211221001001111201121102220201220120211121220010121202001122...

144/179=0,21020111010022121010202211000121021211202222002120020100001100122122111102110112000202100...

145/179=0,21021211202222002120020100001100122122111102110112000202100210201110100221210102022110001...

146/179=0,21100012102121120222200212002010000110012212211110211011200020210021020111010022121010202...

147/179=0,21101120002021002102011101002212101020221100012102121120222200212002010000110012212211110...

148/179=0,21102220201220120211121220010121202001122210120101102000022010220212222112210010011112011...

149/179=0,21111021101120002021002102011101002212101020221100012102121120222200212002010000110012212...

150/179=0,21112122001012120200112221012010110200002201022021222211221001001111201121102220201220120...

151/179=0,21120222200212002010000110012212211110211011200020210021020111010022121010202211000121021...

152/179=0,21122100100111120112110222020122012021112122001012120200112221012010110200002201022021222...

153/179=0,21200201000011001221221111021101120002021002102011101002212101020221100012102121120222200...

154/179=0,21202001122210120101102000022010220212222112210010011112011211022202012201202111212200101...

155/179=0,21210102022110001210212112022220021200201000011001221221111021101120002021002102011101002...

156/179=0,21211202222002120020100001100122122111102110112000202100210201110100221210102022110001210...

157/179=0,21220010121202001122210120101102000022010220212222112210010011112011211022202012201202111...

158/179=0,21221111021101120002021002102011101002212101020221100012102121120222200212002010000110012...

159/179=0,21222211221001001111201121102220201220120211121220010121202001122210120101102000022010220...

160/179=0,22001012120200112221012010110200002201022021222211221001001111201121102220201220120211121...

161/179=0,22002120020100001100122122111102110112000202100210201110100221210102022110001210212112022...

162/179=0,22010220212222112210010011112011211022202012201202111212200101212020011222101201011020000...

163/179=0,22012021112122001012120200112221012010110200002201022021222211221001001111201121102220201...

164/179=0,22020122012021112122001012120200112221012010110200002201022021222211221001001111201121102...

165/179=0,22021222211221001001111201121102220201220120211121220010121202001122210120101102000022010...

166/179=0,22100100111120112110222020122012021112122001012120200112221012010110200002201022021222211...

167/179=0,22101201011020000220102202122221122100100111120112110222020122012021112122001012120200112...

168/179=0,22110001210212112022220021200201000011001221221111021101120002021002102011101002212101020...

169/179=0,22111102110112000202100210201110100221210102022110001210212112022220021200201000011001221...

170/179=0,22112210010011112011211022202012201202111212200101212020011222101201011020000220102202122...

171/179=0,22121010202211000121021211202222002120020100001100122122111102110112000202100210201110100...

172/179=0,22122111102110112000202100210201110100221210102022110001210212112022220021200201000011001...

173/179=0,22200212002010000110012212211110211011200020210021020111010022121010202211000121021211202...

174/179=0,22202012201202111212200101212020011222101201011020000220102202122221122100100111120112110...

175/179=0,22210120101102000022010220212222112210010011112011211022202012201202111212200101212020011...

176/179=0,22211221001001111201121102220201220120211121220010121202001122210120101102000022010220212...

177/179=0,22220021200201000011001221221111021101120002021002102011101002212101020221100012102121120...

178/179=0,22221122100100111120112110222020122012021112122001012120200112221012010110200002201022021...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (89) est égal à 178 et donc au premier -1.