Il existe 10 périodes de 19 chiffres pour n/191 en base 5.

Pour toutes les fractions de n/191 en base 5, la période de 1/191 revient alors 19 fois (en orange)

1/191=0,0003114003430404324...

2/191=0,0011233012411314203...

3/191=0,0014402021342224032...

4/191=0,0023021030323133411...

5/191=0,0031140034304043240...

6/191=0,0034304043240003114...

7/191=0,0042423102220412443...

8/191=0,0101042111201322322...

9/191=0,0104211120132232201...

10/191=0,0112330124113142030...

11/191=0,0120444133044101404...

12/191=0,0124113142030011233...

13/191=0,0132232201010421112...

14/191=0,0140401204441330441...

15/191=0,0144020213422240320...

16/191=0,0202134222403200144...

17/191=0,0210303231334110023...

18/191=0,0213422240320014402...

19/191=0,0222041244300424231...

20/191=0,0230210303231334110...

21/191=0,0233324312212243434...

22/191=0,0241443321143203313...

23/191=0,0300112330124113142...

24/191=0,0303231334110023021...

25/191=0,0311400343040432400...

26/191=0,0320014402021342224...

27/191=0,0323133411002302103...

28/191=0,0331302414433211432...

29/191=0,0334421423414121311...

30/191=0,0343040432400031140...

31/191=0,0401204441330441014...

32/191=0,0404324000311400343...

33/191=0,0412443004242310222...

34/191=0,0421112013223220101...

35/191=0,0424231022204124430...

36/191=0,0432400031140034304...

37/191=0,0441014040120444133...

38/191=0,0444133044101404012...

39/191=0,1002302103032313341...

40/191=0,1010421112013223220...

41/191=0,1014040120444133044...

42/191=0,1022204124430042423...

43/191=0,1030323133411002302...

44/191=0,1033442142341412131...

45/191=0,1042111201322322010...

46/191=0,1100230210303231334...

47/191=0,1103344214234141213...

48/191=0,1112013223220101042...

49/191=0,1120132232201010421...

50/191=0,1123301241131420300...

51/191=0,1131420300112330124...

52/191=0,1140034304043240003...

53/191=0,1143203313024144332...

54/191=0,1201322322010104211...

55/191=0,1204441330441014040...

56/191=0,1213110334421423414...

57/191=0,1221224343402333243...

58/191=0,1224343402333243122...

59/191=0,1233012411314203001...

60/191=0,1241131420300112330...

61/191=0,1244300424231022204...

62/191=0,1302414433211432033...

63/191=0,1311033442142341412...

64/191=0,1314203001123301241...

65/191=0,1322322010104211120...

66/191=0,1330441014040120444...

67/191=0,1334110023021030323...

68/191=0,1342224032001440202...

69/191=0,1400343040432400031...

70/191=0,1404012044413304410...

71/191=0,1412131103344214234...

72/191=0,1420300112330124113...

73/191=0,1423414121311033442...

74/191=0,1432033130241443321...

75/191=0,1440202134222403200...

76/191=0,1443321143203313024...

77/191=0,2001440202134222403...

78/191=0,2010104211120132232...

79/191=0,2013223220101042111...

80/191=0,2021342224032001440...

81/191=0,2030011233012411314...

82/191=0,2033130241443321143...

83/191=0,2041244300424231022...

84/191=0,2044413304410140401...

85/191=0,2103032313341100230...

86/191=0,2111201322322010104...

87/191=0,2114320331302414433...

88/191=0,2122434340233324312...

89/191=0,2131103344214234141...

90/191=0,2134222403200144020...

91/191=0,2142341412131103344...

92/191=0,2201010421112013223...

93/191=0,2204124430042423102...

94/191=0,2212243434023332431...

95/191=0,2220412443004242310...

96/191=0,2224032001440202134...

97/191=0,2232201010421112013...

98/191=0,2240320014402021342...

99/191=0,2243434023332431221...

100/191=0,2302103032313341100...

101/191=0,2310222041244300424...

102/191=0,2313341100230210303...

103/191=0,2322010104211120132...

104/191=0,2330124113142030011...

105/191=0,2333243122122434340...

106/191=0,2341412131103344214...

107/191=0,2400031140034304043...

108/191=0,2403200144020213422...

109/191=0,2411314203001123301...

110/191=0,2414433211432033130...

111/191=0,2423102220412443004...

112/191=0,2431221224343402333...

113/191=0,2434340233324312212...

114/191=0,2443004242310222041...

115/191=0,3001123301241131420...

116/191=0,3004242310222041244...

117/191=0,3012411314203001123...

118/191=0,3021030323133411002...

119/191=0,3024144332114320331...

120/191=0,3032313341100230210...

121/191=0,3040432400031140034...

122/191=0,3044101404012044413...

123/191=0,3102220412443004242...

124/191=0,3110334421423414121...

125/191=0,3114003430404324000...

126/191=0,3122122434340233324...

127/191=0,3130241443321143203...

128/191=0,3133411002302103032...

129/191=0,3142030011233012411...

130/191=0,3200144020213422240...

131/191=0,3203313024144332114...

132/191=0,3211432033130241443...

133/191=0,3220101042111201322...

134/191=0,3223220101042111201...

135/191=0,3231334110023021030...

136/191=0,3240003114003430404...

137/191=0,3243122122434340233...

138/191=0,3301241131420300112...

139/191=0,3304410140401204441...

140/191=0,3313024144332114320...

141/191=0,3321143203313024144...

142/191=0,3324312212243434023...

143/191=0,3332431221224343402...

144/191=0,3341100230210303231...

145/191=0,3344214234141213110...

146/191=0,3402333243122122434...

147/191=0,3411002302103032313...

148/191=0,3414121311033442142...

149/191=0,3422240320014402021...

150/191=0,3430404324000311400...

151/191=0,3434023332431221224...

152/191=0,3442142341412131103...

153/191=0,4000311400343040432...

154/191=0,4003430404324000311...

155/191=0,4012044413304410140...

156/191=0,4020213422240320014...

157/191=0,4023332431221224343...

158/191=0,4032001440202134222...

159/191=0,4040120444133044101...

160/191=0,4043240003114003430...

161/191=0,4101404012044413304...

162/191=0,4110023021030323133...

163/191=0,4113142030011233012...

164/191=0,4121311033442142341...

165/191=0,4124430042423102220...

166/191=0,4133044101404012044...

167/191=0,4141213110334421423...

168/191=0,4144332114320331302...

169/191=0,4203001123301241131...

170/191=0,4211120132232201010...

171/191=0,4214234141213110334...

172/191=0,4222403200144020213...

173/191=0,4231022204124430042...

174/191=0,4234141213110334421...

175/191=0,4242310222041244300...

176/191=0,4300424231022204124...

177/191=0,4304043240003114003...

178/191=0,4312212243434023332...

179/191=0,4320331302414433211...

180/191=0,4324000311400343040...

181/191=0,4332114320331302414...

182/191=0,4340233324312212243...

183/191=0,4343402333243122122...

184/191=0,4402021342224032001...

185/191=0,4410140401204441330...

186/191=0,4413304410140401204...

187/191=0,4421423414121311033...

188/191=0,4430042423102220412...

189/191=0,4433211432033130241...

190/191=0,4441330441014040120...

On remarque que le produit du nombre de périodes (10) et de leurs longueurs (19) est égal à 190 et donc au premier -1.