Il existe 2 périodes de 95 chiffres pour n/191 en base 3.

Pour toutes les fractions de n/191 en base 3, la période de 1/191 revient alors 95 fois (en orange)

1/191=0,00001021100110201111201020002010020210012111212001010112102022100012002101212220000211220022111...

2/191=0,00002112200221110000102110011020111120102000201002021001211121200101011210202210001200210121222...

3/191=0,00010211001102011112010200020100202100121112120010101121020221000120021012122200002112200221110...

4/191=0,00012002101212220000211220022111000010211001102011112010200020100202100121112120010101121020221...

5/191=0,00020100202100121112120010101121020221000120021012122200002112200221110000102110011020111120102...

6/191=0,00021122002211100001021100110201111201020002010020210012111212001010112102022100012002101212220...

7/191=0,00022220110022001112222120112211202111102120222021220201221011101022121211012020012221022012101...

8/191=0,00101011210202210001200210121222000021122002211100001021100110201111201020002010020210012111212...

9/191=0,00102110011020111120102000201002021001211121200101011210202210001200210121222000021122002211100...

10/191=0,00110201111201020002010020210012111212001010112102022100012002101212220000211220022111000010211...

11/191=0,00111222212011221120211110212022202122020122101110102212121101202001222102201210100022220110022...

12/191=0,00120021012122200002112200221110000102110011020111120102000201002021001211121200101011210202210...

13/191=0,00121112120010101121020221000120021012122200002112200221110000102110011020111120102000201002021...

14/191=0,00122210220121010002222011002200111222212011221120211110212022202122020122101110102212121101202...

15/191=0,00201002021001211121200101011210202210001200210121222000021122002211100001021100110201111201020...

16/191=0,00202100121112120010101121020221000120021012122200002112200221110000102110011020111120102000201...

17/191=0,00210121222000021122002211100001021100110201111201020002010020210012111212001010112102022100012...

18/191=0,00211220022111000010211001102011112010200020100202100121112120010101121020221000120021012122200...

19/191=0,00220011122221201122112021111021202220212202012210111010221212110120200122210220121010002222011...

20/191=0,00221110000102110011020111120102000201002021001211121200101011210202210001200210121222000021122...

21/191=0,00222201100220011122221201122112021111021202220212202012210111010221212110120200122210220121010...

22/191=0,01000222201100220011122221201122112021111021202220212202012210111010221212110120200122210220121...

23/191=0,01002021001211121200101011210202210001200210121222000021122002211100001021100110201111201020002...

24/191=0,01010112102022100012002101212220000211220022111000010211001102011112010200020100202100121112120...

25/191=0,01011210202210001200210121222000021122002211100001021100110201111201020002010020210012111212001...

26/191=0,01020002010020210012111212001010112102022100012002101212220000211220022111000010211001102011112...

27/191=0,01021100110201111201020002010020210012111212001010112102022100012002101212220000211220022111000...

28/191=0,01022121211012020012221022012101000222201100220011122221201122112021111021202220212202012210111...

29/191=0,01100220011122221201122112021111021202220212202012210111010221212110120200122210220121010002222...

30/191=0,01102011112010200020100202100121112120010101121020221000120021012122200002112200221110000102110...

31/191=0,01110102212121101202001222102201210100022220110022001112222120112211202111102120222021220201221...

32/191=0,01111201020002010020210012111212001010112102022100012002101212220000211220022111000010211001102...

33/191=0,01112222120112211202111102120222021220201221011101022121211012020012221022012101000222201100220...

34/191=0,01121020221000120021012122200002112200221110000102110011020111120102000201002021001211121200101...

35/191=0,01122112021111021202220212202012210111010221212110120200122210220121010002222011002200111222212...

36/191=0,01200210121222000021122002211100001021100110201111201020002010020210012111212001010112102022100...

37/191=0,01202001222102201210100022220110022001112222120112211202111102120222021220201221011101022121211...

38/191=0,01210100022220110022001112222120112211202111102120222021220201221011101022121211012020012221022...

39/191=0,01211121200101011210202210001200210121222000021122002211100001021100110201111201020002010020210...

40/191=0,01212220000211220022111000010211001102011112010200020100202100121112120010101121020221000120021...

41/191=0,01221011101022121211012020012221022012101000222201100220011122221201122112021111021202220212202...

42/191=0,01222102201210100022220110022001112222120112211202111102120222021220201221011101022121211012020...

43/191=0,02000201002021001211121200101011210202210001200210121222000021122002211100001021100110201111201...

44/191=0,02001222102201210100022220110022001112222120112211202111102120222021220201221011101022121211012...

45/191=0,02010020210012111212001010112102022100012002101212220000211220022111000010211001102011112010200...

46/191=0,02011112010200020100202100121112120010101121020221000120021012122200002112200221110000102110011...

47/191=0,02012210111010221212110120200122210220121010002222011002200111222212011221120211110212022202122...

48/191=0,02021001211121200101011210202210001200210121222000021122002211100001021100110201111201020002010...

49/191=0,02022100012002101212220000211220022111000010211001102011112010200020100202100121112120010101121...

50/191=0,02100121112120010101121020221000120021012122200002112200221110000102110011020111120102000201002...

51/191=0,02101212220000211220022111000010211001102011112010200020100202100121112120010101121020221000120...

52/191=0,02110011020111120102000201002021001211121200101011210202210001200210121222000021122002211100001...

53/191=0,02111102120222021220201221011101022121211012020012221022012101000222201100220011122221201122112...

54/191=0,02112200221110000102110011020111120102000201002021001211121200101011210202210001200210121222000...

55/191=0,02120222021220201221011101022121211012020012221022012101000222201100220011122221201122112021111...

56/191=0,02122020122101110102212121101202001222102201210100022220110022001112222120112211202111102120222...

57/191=0,02200111222212011221120211110212022202122020122101110102212121101202001222102201210100022220110...

58/191=0,02201210100022220110022001112222120112211202111102120222021220201221011101022121211012020012221...

59/191=0,02210001200210121222000021122002211100001021100110201111201020002010020210012111212001010112102...

60/191=0,02211100001021100110201111201020002010020210012111212001010112102022100012002101212220000211220...

61/191=0,02212121101202001222102201210100022220110022001112222120112211202111102120222021220201221011101...

62/191=0,02220212202012210111010221212110120200122210220121010002222011002200111222212011221120211110212...

63/191=0,02222011002200111222212011221120211110212022202122020122101110102212121101202001222102201210100...

64/191=0,10000102110011020111120102000201002021001211121200101011210202210001200210121222000021122002211...

65/191=0,10001200210121222000021122002211100001021100110201111201020002010020210012111212001010112102022...

66/191=0,10002222011002200111222212011221120211110212022202122020122101110102212121101202001222102201210...

67/191=0,10011020111120102000201002021001211121200101011210202210001200210121222000021122002211100001021...

68/191=0,10012111212001010112102022100012002101212220000211220022111000010211001102011112010200020100202...

69/191=0,10020210012111212001010112102022100012002101212220000211220022111000010211001102011112010200020...

70/191=0,10022001112222120112211202111102120222021220201221011101022121211012020012221022012101000222201...

71/191=0,10100022220110022001112222120112211202111102120222021220201221011101022121211012020012221022012...

72/191=0,10101121020221000120021012122200002112200221110000102110011020111120102000201002021001211121200...

73/191=0,10102212121101202001222102201210100022220110022001112222120112211202111102120222021220201221011...

74/191=0,10111010221212110120200122210220121010002222011002200111222212011221120211110212022202122020122...

75/191=0,10112102022100012002101212220000211220022111000010211001102011112010200020100202100121112120010...

76/191=0,10120200122210220121010002222011002200111222212011221120211110212022202122020122101110102212121...

77/191=0,10121222000021122002211100001021100110201111201020002010020210012111212001010112102022100012002...

78/191=0,10200020100202100121112120010101121020221000120021012122200002112200221110000102110011020111120...

79/191=0,10201111201020002010020210012111212001010112102022100012002101212220000211220022111000010211001...

80/191=0,10202210001200210121222000021122002211100001021100110201111201020002010020210012111212001010112...

81/191=0,10211001102011112010200020100202100121112120010101121020221000120021012122200002112200221110000...

82/191=0,10212022202122020122101110102212121101202001222102201210100022220110022001112222120112211202111...

83/191=0,10220121010002222011002200111222212011221120211110212022202122020122101110102212121101202001222...

84/191=0,10221212110120200122210220121010002222011002200111222212011221120211110212022202122020122101110...

85/191=0,11000010211001102011112010200020100202100121112120010101121020221000120021012122200002112200221...

86/191=0,11001102011112010200020100202100121112120010101121020221000120021012122200002112200221110000102...

87/191=0,11002200111222212011221120211110212022202122020122101110102212121101202001222102201210100022220...

88/191=0,11010221212110120200122210220121010002222011002200111222212011221120211110212022202122020122101...

89/191=0,11012020012221022012101000222201100220011122221201122112021111021202220212202012210111010221212...

90/191=0,11020111120102000201002021001211121200101011210202210001200210121222000021122002211100001021100...

91/191=0,11021202220212202012210111010221212110120200122210220121010002222011002200111222212011221120211...

92/191=0,11100001021100110201111201020002010020210012111212001010112102022100012002101212220000211220022...

93/191=0,11101022121211012020012221022012101000222201100220011122221201122112021111021202220212202012210...

94/191=0,11102120222021220201221011101022121211012020012221022012101000222201100220011122221201122112021...

95/191=0,11110212022202122020122101110102212121101202001222102201210100022220110022001112222120112211202...

96/191=0,11112010200020100202100121112120010101121020221000120021012122200002112200221110000102110011020...

97/191=0,11120102000201002021001211121200101011210202210001200210121222000021122002211100001021100110201...

98/191=0,11121200101011210202210001200210121222000021122002211100001021100110201111201020002010020210012...

99/191=0,11122221201122112021111021202220212202012210111010221212110120200122210220121010002222011002200...

100/191=0,11201020002010020210012111212001010112102022100012002101212220000211220022111000010211001102011...

101/191=0,11202111102120222021220201221011101022121211012020012221022012101000222201100220011122221201122...

102/191=0,11210202210001200210121222000021122002211100001021100110201111201020002010020210012111212001010...

103/191=0,11212001010112102022100012002101212220000211220022111000010211001102011112010200020100202100121...

104/191=0,11220022111000010211001102011112010200020100202100121112120010101121020221000120021012122200002...

105/191=0,11221120211110212022202122020122101110102212121101202001222102201210100022220110022001112222120...

106/191=0,11222212011221120211110212022202122020122101110102212121101202001222102201210100022220110022001...

107/191=0,12001010112102022100012002101212220000211220022111000010211001102011112010200020100202100121112...

108/191=0,12002101212220000211220022111000010211001102011112010200020100202100121112120010101121020221000...

109/191=0,12010200020100202100121112120010101121020221000120021012122200002112200221110000102110011020111...

110/191=0,12011221120211110212022202122020122101110102212121101202001222102201210100022220110022001112222...

111/191=0,12020012221022012101000222201100220011122221201122112021111021202220212202012210111010221212110...

112/191=0,12021111021202220212202012210111010221212110120200122210220121010002222011002200111222212011221...

113/191=0,12022202122020122101110102212121101202001222102201210100022220110022001112222120112211202111102...

114/191=0,12101000222201100220011122221201122112021111021202220212202012210111010221212110120200122210220...

115/191=0,12102022100012002101212220000211220022111000010211001102011112010200020100202100121112120010101...

116/191=0,12110120200122210220121010002222011002200111222212011221120211110212022202122020122101110102212...

117/191=0,12111212001010112102022100012002101212220000211220022111000010211001102011112010200020100202100...

118/191=0,12120010101121020221000120021012122200002112200221110000102110011020111120102000201002021001211...

119/191=0,12121101202001222102201210100022220110022001112222120112211202111102120222021220201221011101022...

120/191=0,12122200002112200221110000102110011020111120102000201002021001211121200101011210202210001200210...

121/191=0,12200221110000102110011020111120102000201002021001211121200101011210202210001200210121222000021...

122/191=0,12202012210111010221212110120200122210220121010002222011002200111222212011221120211110212022202...

123/191=0,12210111010221212110120200122210220121010002222011002200111222212011221120211110212022202122020...

124/191=0,12211202111102120222021220201221011101022121211012020012221022012101000222201100220011122221201...

125/191=0,12220000211220022111000010211001102011112010200020100202100121112120010101121020221000120021012...

126/191=0,12221022012101000222201100220011122221201122112021111021202220212202012210111010221212110120200...

127/191=0,12222120112211202111102120222021220201221011101022121211012020012221022012101000222201100220011...

128/191=0,20000211220022111000010211001102011112010200020100202100121112120010101121020221000120021012122...

129/191=0,20002010020210012111212001010112102022100012002101212220000211220022111000010211001102011112010...

130/191=0,20010101121020221000120021012122200002112200221110000102110011020111120102000201002021001211121...

131/191=0,20011122221201122112021111021202220212202012210111010221212110120200122210220121010002222011002...

132/191=0,20012221022012101000222201100220011122221201122112021111021202220212202012210111010221212110120...

133/191=0,20021012122200002112200221110000102110011020111120102000201002021001211121200101011210202210001...

134/191=0,20022111000010211001102011112010200020100202100121112120010101121020221000120021012122200002112...

135/191=0,20100202100121112120010101121020221000120021012122200002112200221110000102110011020111120102000...

136/191=0,20102000201002021001211121200101011210202210001200210121222000021122002211100001021100110201111...

137/191=0,20110022001112222120112211202111102120222021220201221011101022121211012020012221022012101000222...

138/191=0,20111120102000201002021001211121200101011210202210001200210121222000021122002211100001021100110...

139/191=0,20112211202111102120222021220201221011101022121211012020012221022012101000222201100220011122221...

140/191=0,20121010002222011002200111222212011221120211110212022202122020122101110102212121101202001222102...

141/191=0,20122101110102212121101202001222102201210100022220110022001112222120112211202111102120222021220...

142/191=0,20200122210220121010002222011002200111222212011221120211110212022202122020122101110102212121101...

143/191=0,20201221011101022121211012020012221022012101000222201100220011122221201122112021111021202220212...

144/191=0,20210012111212001010112102022100012002101212220000211220022111000010211001102011112010200020100...

145/191=0,20211110212022202122020122101110102212121101202001222102201210100022220110022001112222120112211...

146/191=0,20212202012210111010221212110120200122210220121010002222011002200111222212011221120211110212022...

147/191=0,20221000120021012122200002112200221110000102110011020111120102000201002021001211121200101011210...

148/191=0,20222021220201221011101022121211012020012221022012101000222201100220011122221201122112021111021...

149/191=0,21000120021012122200002112200221110000102110011020111120102000201002021001211121200101011210202...

150/191=0,21001211121200101011210202210001200210121222000021122002211100001021100110201111201020002010020...

151/191=0,21010002222011002200111222212011221120211110212022202122020122101110102212121101202001222102201...

152/191=0,21011101022121211012020012221022012101000222201100220011122221201122112021111021202220212202012...

153/191=0,21012122200002112200221110000102110011020111120102000201002021001211121200101011210202210001200...

154/191=0,21020221000120021012122200002112200221110000102110011020111120102000201002021001211121200101011...

155/191=0,21022012101000222201100220011122221201122112021111021202220212202012210111010221212110120200122...

156/191=0,21100110201111201020002010020210012111212001010112102022100012002101212220000211220022111000010...

157/191=0,21101202001222102201210100022220110022001112222120112211202111102120222021220201221011101022121...

158/191=0,21110000102110011020111120102000201002021001211121200101011210202210001200210121222000021122002...

159/191=0,21111021202220212202012210111010221212110120200122210220121010002222011002200111222212011221120...

160/191=0,21112120010101121020221000120021012122200002112200221110000102110011020111120102000201002021001...

161/191=0,21120211110212022202122020122101110102212121101202001222102201210100022220110022001112222120112...

162/191=0,21122002211100001021100110201111201020002010020210012111212001010112102022100012002101212220000...

163/191=0,21200101011210202210001200210121222000021122002211100001021100110201111201020002010020210012111...

164/191=0,21201122112021111021202220212202012210111010221212110120200122210220121010002222011002200111222...

165/191=0,21202220212202012210111010221212110120200122210220121010002222011002200111222212011221120211110...

166/191=0,21211012020012221022012101000222201100220011122221201122112021111021202220212202012210111010221...

167/191=0,21212110120200122210220121010002222011002200111222212011221120211110212022202122020122101110102...

168/191=0,21220201221011101022121211012020012221022012101000222201100220011122221201122112021111021202220...

169/191=0,21222000021122002211100001021100110201111201020002010020210012111212001010112102022100012002101...

170/191=0,22000021122002211100001021100110201111201020002010020210012111212001010112102022100012002101212...

171/191=0,22001112222120112211202111102120222021220201221011101022121211012020012221022012101000222201100...

172/191=0,22002211100001021100110201111201020002010020210012111212001010112102022100012002101212220000211...

173/191=0,22011002200111222212011221120211110212022202122020122101110102212121101202001222102201210100022...

174/191=0,22012101000222201100220011122221201122112021111021202220212202012210111010221212110120200122210...

175/191=0,22020122101110102212121101202001222102201210100022220110022001112222120112211202111102120222021...

176/191=0,22021220201221011101022121211012020012221022012101000222201100220011122221201122112021111021202...

177/191=0,22100012002101212220000211220022111000010211001102011112010200020100202100121112120010101121020...

178/191=0,22101110102212121101202001222102201210100022220110022001112222120112211202111102120222021220201...

179/191=0,22102201210100022220110022001112222120112211202111102120222021220201221011101022121211012020012...

180/191=0,22111000010211001102011112010200020100202100121112120010101121020221000120021012122200002112200...

181/191=0,22112021111021202220212202012210111010221212110120200122210220121010002222011002200111222212011...

182/191=0,22120112211202111102120222021220201221011101022121211012020012221022012101000222201100220011122...

183/191=0,22121211012020012221022012101000222201100220011122221201122112021111021202220212202012210111010...

184/191=0,22200002112200221110000102110011020111120102000201002021001211121200101011210202210001200210121...

185/191=0,22201100220011122221201122112021111021202220212202012210111010221212110120200122210220121010002...

186/191=0,22202122020122101110102212121101202001222102201210100022220110022001112222120112211202111102120...

187/191=0,22210220121010002222011002200111222212011221120211110212022202122020122101110102212121101202001...

188/191=0,22212011221120211110212022202122020122101110102212121101202001222102201210100022220110022001112...

189/191=0,22220110022001112222120112211202111102120222021220201221011101022121211012020012221022012101000...

190/191=0,22221201122112021111021202220212202012210111010221212110120200122210220121010002222011002200111...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (95) est égal à 190 et donc au premier -1.