Il existe 2 périodes de 83 chiffres pour n/167 en base 6.

Pour toutes les fractions de n/167 en base 6, la période de 1/167 revient alors 83 fois (en orange)

1/167=0,00114321325243332014203003514044242144400510130153502212105220023304305453110403241...

2/167=0,00233043054531104032410011432132524333201420300351404424214440051013015350221210522...

3/167=0,00351404424214440051013015350221210522002330430545311040324100114321325243332014203...

4/167=0,00510130153502212105220023304305453110403241001143213252433320142030035140442421444...

5/167=0,01024451523145544123423031222354135255204151131341115504542540205334345033553225125...

6/167=0,01143213252433320142030035140442421444005101301535022121052200233043054531104032410...

7/167=0,01301535022121052200233043054531104032410011432132524333201420300351404424214440051...

8/167=0,01420300351404424214440051013015350221210522002330430545311040324100114321325243332...

9/167=0,01535022121052200233043054531104032410011432132524333201420300351404424214440051013...

10/167=0,02053343450335532251250102445152314554412342303122235413525520415113134111550454254...

11/167=0,02212105220023304305453110403241001143213252433320142030035140442421444005101301535...

12/167=0,02330430545311040324100114321325243332014203003514044242144400510130153502212105220...

13/167=0,02445152314554412342303122235413525520415113134111550454254020533434503355322512501...

14/167=0,03003514044242144400510130153502212105220023304305453110403241001143213252433320142...

15/167=0,03122235413525520415113134111550454254020533434503355322512501024451523145544123423...

16/167=0,03241001143213252433320142030035140442421444005101301535022121052200233043054531104...

17/167=0,03355322512501024451523145544123423031222354135255204151131341115504542540205334345...

18/167=0,03514044242144400510130153502212105220023304305453110403241001143213252433320142030...

19/167=0,04032410011432132524333201420300351404424214440051013015350221210522002330430545311...

20/167=0,04151131341115504542540205334345033553225125010244515231455441234230312223541352552...

21/167=0,04305453110403241001143213252433320142030035140442421444005101301535022121052200233...

22/167=0,04424214440051013015350221210522002330430545311040324100114321325243332014203003514...

23/167=0,04542540205334345033553225125010244515231455441234230312223541352552041511313411155...

24/167=0,05101301535022121052200233043054531104032410011432132524333201420300351404424214440...

25/167=0,05220023304305453110403241001143213252433320142030035140442421444005101301535022121...

26/167=0,05334345033553225125010244515231455441234230312223541352552041511313411155045425402...

27/167=0,05453110403241001143213252433320142030035140442421444005101301535022121052200233043...

28/167=0,10011432132524333201420300351404424214440051013015350221210522002330430545311040324...

29/167=0,10130153502212105220023304305453110403241001143213252433320142030035140442421444005...

30/167=0,10244515231455441234230312223541352552041511313411155045425402053343450335532251250...

31/167=0,10403241001143213252433320142030035140442421444005101301535022121052200233043054531...

32/167=0,10522002330430545311040324100114321325243332014203003514044242144400510130153502212...

33/167=0,11040324100114321325243332014203003514044242144400510130153502212105220023304305453...

34/167=0,11155045425402053343450335532251250102445152314554412342303122235413525520415113134...

35/167=0,11313411155045425402053343450335532251250102445152314554412342303122235413525520415...

36/167=0,11432132524333201420300351404424214440051013015350221210522002330430545311040324100...

37/167=0,11550454254020533434503355322512501024451523145544123423031222354135255204151131341...

38/167=0,12105220023304305453110403241001143213252433320142030035140442421444005101301535022...

39/167=0,12223541352552041511313411155045425402053343450335532251250102445152314554412342303...

40/167=0,12342303122235413525520415113134111550454254020533434503355322512501024451523145544...

41/167=0,12501024451523145544123423031222354135255204151131341115504542540205334345033553225...

42/167=0,13015350221210522002330430545311040324100114321325243332014203003514044242144400510...

43/167=0,13134111550454254020533434503355322512501024451523145544123423031222354135255204151...

44/167=0,13252433320142030035140442421444005101301535022121052200233043054531104032410011432...

45/167=0,13411155045425402053343450335532251250102445152314554412342303122235413525520415113...

46/167=0,13525520415113134111550454254020533434503355322512501024451523145544123423031222354...

47/167=0,14044242144400510130153502212105220023304305453110403241001143213252433320142030035...

48/167=0,14203003514044242144400510130153502212105220023304305453110403241001143213252433320...

49/167=0,14321325243332014203003514044242144400510130153502212105220023304305453110403241001...

50/167=0,14440051013015350221210522002330430545311040324100114321325243332014203003514044242...

51/167=0,14554412342303122235413525520415113134111550454254020533434503355322512501024451523...

52/167=0,15113134111550454254020533434503355322512501024451523145544123423031222354135255204...

53/167=0,15231455441234230312223541352552041511313411155045425402053343450335532251250102445...

54/167=0,15350221210522002330430545311040324100114321325243332014203003514044242144400510130...

55/167=0,15504542540205334345033553225125010244515231455441234230312223541352552041511313411...

56/167=0,20023304305453110403241001143213252433320142030035140442421444005101301535022121052...

57/167=0,20142030035140442421444005101301535022121052200233043054531104032410011432132524333...

58/167=0,20300351404424214440051013015350221210522002330430545311040324100114321325243332014...

59/167=0,20415113134111550454254020533434503355322512501024451523145544123423031222354135255...

60/167=0,20533434503355322512501024451523145544123423031222354135255204151131341115504542540...

61/167=0,21052200233043054531104032410011432132524333201420300351404424214440051013015350221...

62/167=0,21210522002330430545311040324100114321325243332014203003514044242144400510130153502...

63/167=0,21325243332014203003514044242144400510130153502212105220023304305453110403241001143...

64/167=0,21444005101301535022121052200233043054531104032410011432132524333201420300351404424...

65/167=0,22002330430545311040324100114321325243332014203003514044242144400510130153502212105...

66/167=0,22121052200233043054531104032410011432132524333201420300351404424214440051013015350...

67/167=0,22235413525520415113134111550454254020533434503355322512501024451523145544123423031...

68/167=0,22354135255204151131341115504542540205334345033553225125010244515231455441234230312...

69/167=0,22512501024451523145544123423031222354135255204151131341115504542540205334345033553...

70/167=0,23031222354135255204151131341115504542540205334345033553225125010244515231455441234...

71/167=0,23145544123423031222354135255204151131341115504542540205334345033553225125010244515...

72/167=0,23304305453110403241001143213252433320142030035140442421444005101301535022121052200...

73/167=0,23423031222354135255204151131341115504542540205334345033553225125010244515231455441...

74/167=0,23541352552041511313411155045425402053343450335532251250102445152314554412342303122...

75/167=0,24100114321325243332014203003514044242144400510130153502212105220023304305453110403...

76/167=0,24214440051013015350221210522002330430545311040324100114321325243332014203003514044...

77/167=0,24333201420300351404424214440051013015350221210522002330430545311040324100114321325...

78/167=0,24451523145544123423031222354135255204151131341115504542540205334345033553225125010...

79/167=0,25010244515231455441234230312223541352552041511313411155045425402053343450335532251...

80/167=0,25125010244515231455441234230312223541352552041511313411155045425402053343450335532...

81/167=0,25243332014203003514044242144400510130153502212105220023304305453110403241001143213...

82/167=0,25402053343450335532251250102445152314554412342303122235413525520415113134111550454...

83/167=0,25520415113134111550454254020533434503355322512501024451523145544123423031222354135...

84/167=0,30035140442421444005101301535022121052200233043054531104032410011432132524333201420...

85/167=0,30153502212105220023304305453110403241001143213252433320142030035140442421444005101...

86/167=0,30312223541352552041511313411155045425402053343450335532251250102445152314554412342...

87/167=0,30430545311040324100114321325243332014203003514044242144400510130153502212105220023...

88/167=0,30545311040324100114321325243332014203003514044242144400510130153502212105220023304...

89/167=0,31104032410011432132524333201420300351404424214440051013015350221210522002330430545...

90/167=0,31222354135255204151131341115504542540205334345033553225125010244515231455441234230...

91/167=0,31341115504542540205334345033553225125010244515231455441234230312223541352552041511...

92/167=0,31455441234230312223541352552041511313411155045425402053343450335532251250102445152...

93/167=0,32014203003514044242144400510130153502212105220023304305453110403241001143213252433...

94/167=0,32132524333201420300351404424214440051013015350221210522002330430545311040324100114...

95/167=0,32251250102445152314554412342303122235413525520415113134111550454254020533434503355...

96/167=0,32410011432132524333201420300351404424214440051013015350221210522002330430545311040...

97/167=0,32524333201420300351404424214440051013015350221210522002330430545311040324100114321...

98/167=0,33043054531104032410011432132524333201420300351404424214440051013015350221210522002...

99/167=0,33201420300351404424214440051013015350221210522002330430545311040324100114321325243...

100/167=0,33320142030035140442421444005101301535022121052200233043054531104032410011432132524...

101/167=0,33434503355322512501024451523145544123423031222354135255204151131341115504542540205...

102/167=0,33553225125010244515231455441234230312223541352552041511313411155045425402053343450...

103/167=0,34111550454254020533434503355322512501024451523145544123423031222354135255204151131...

104/167=0,34230312223541352552041511313411155045425402053343450335532251250102445152314554412...

105/167=0,34345033553225125010244515231455441234230312223541352552041511313411155045425402053...

106/167=0,34503355322512501024451523145544123423031222354135255204151131341115504542540205334...

107/167=0,35022121052200233043054531104032410011432132524333201420300351404424214440051013015...

108/167=0,35140442421444005101301535022121052200233043054531104032410011432132524333201420300...

109/167=0,35255204151131341115504542540205334345033553225125010244515231455441234230312223541...

110/167=0,35413525520415113134111550454254020533434503355322512501024451523145544123423031222...

111/167=0,35532251250102445152314554412342303122235413525520415113134111550454254020533434503...

112/167=0,40051013015350221210522002330430545311040324100114321325243332014203003514044242144...

113/167=0,40205334345033553225125010244515231455441234230312223541352552041511313411155045425...

114/167=0,40324100114321325243332014203003514044242144400510130153502212105220023304305453110...

115/167=0,40442421444005101301535022121052200233043054531104032410011432132524333201420300351...

116/167=0,41001143213252433320142030035140442421444005101301535022121052200233043054531104032...

117/167=0,41115504542540205334345033553225125010244515231455441234230312223541352552041511313...

118/167=0,41234230312223541352552041511313411155045425402053343450335532251250102445152314554...

119/167=0,41352552041511313411155045425402053343450335532251250102445152314554412342303122235...

120/167=0,41511313411155045425402053343450335532251250102445152314554412342303122235413525520...

121/167=0,42030035140442421444005101301535022121052200233043054531104032410011432132524333201...

122/167=0,42144400510130153502212105220023304305453110403241001143213252433320142030035140442...

123/167=0,42303122235413525520415113134111550454254020533434503355322512501024451523145544123...

124/167=0,42421444005101301535022121052200233043054531104032410011432132524333201420300351404...

125/167=0,42540205334345033553225125010244515231455441234230312223541352552041511313411155045...

126/167=0,43054531104032410011432132524333201420300351404424214440051013015350221210522002330...

127/167=0,43213252433320142030035140442421444005101301535022121052200233043054531104032410011...

128/167=0,43332014203003514044242144400510130153502212105220023304305453110403241001143213252...

129/167=0,43450335532251250102445152314554412342303122235413525520415113134111550454254020533...

130/167=0,44005101301535022121052200233043054531104032410011432132524333201420300351404424214...

131/167=0,44123423031222354135255204151131341115504542540205334345033553225125010244515231455...

132/167=0,44242144400510130153502212105220023304305453110403241001143213252433320142030035140...

133/167=0,44400510130153502212105220023304305453110403241001143213252433320142030035140442421...

134/167=0,44515231455441234230312223541352552041511313411155045425402053343450335532251250102...

135/167=0,45033553225125010244515231455441234230312223541352552041511313411155045425402053343...

136/167=0,45152314554412342303122235413525520415113134111550454254020533434503355322512501024...

137/167=0,45311040324100114321325243332014203003514044242144400510130153502212105220023304305...

138/167=0,45425402053343450335532251250102445152314554412342303122235413525520415113134111550...

139/167=0,45544123423031222354135255204151131341115504542540205334345033553225125010244515231...

140/167=0,50102445152314554412342303122235413525520415113134111550454254020533434503355322512...

141/167=0,50221210522002330430545311040324100114321325243332014203003514044242144400510130153...

142/167=0,50335532251250102445152314554412342303122235413525520415113134111550454254020533434...

143/167=0,50454254020533434503355322512501024451523145544123423031222354135255204151131341115...

144/167=0,51013015350221210522002330430545311040324100114321325243332014203003514044242144400...

145/167=0,51131341115504542540205334345033553225125010244515231455441234230312223541352552041...

146/167=0,51250102445152314554412342303122235413525520415113134111550454254020533434503355322...

147/167=0,51404424214440051013015350221210522002330430545311040324100114321325243332014203003...

148/167=0,51523145544123423031222354135255204151131341115504542540205334345033553225125010244...

149/167=0,52041511313411155045425402053343450335532251250102445152314554412342303122235413525...

150/167=0,52200233043054531104032410011432132524333201420300351404424214440051013015350221210...

151/167=0,52314554412342303122235413525520415113134111550454254020533434503355322512501024451...

152/167=0,52433320142030035140442421444005101301535022121052200233043054531104032410011432132...

153/167=0,52552041511313411155045425402053343450335532251250102445152314554412342303122235413...

154/167=0,53110403241001143213252433320142030035140442421444005101301535022121052200233043054...

155/167=0,53225125010244515231455441234230312223541352552041511313411155045425402053343450335...

156/167=0,53343450335532251250102445152314554412342303122235413525520415113134111550454254020...

157/167=0,53502212105220023304305453110403241001143213252433320142030035140442421444005101301...

158/167=0,54020533434503355322512501024451523145544123423031222354135255204151131341115504542...

159/167=0,54135255204151131341115504542540205334345033553225125010244515231455441234230312223...

160/167=0,54254020533434503355322512501024451523145544123423031222354135255204151131341115504...

161/167=0,54412342303122235413525520415113134111550454254020533434503355322512501024451523145...

162/167=0,54531104032410011432132524333201420300351404424214440051013015350221210522002330430...

163/167=0,55045425402053343450335532251250102445152314554412342303122235413525520415113134111...

164/167=0,55204151131341115504542540205334345033553225125010244515231455441234230312223541352...

165/167=0,55322512501024451523145544123423031222354135255204151131341115504542540205334345033...

166/167=0,55441234230312223541352552041511313411155045425402053343450335532251250102445152314...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (83) est égal à 166 et donc au premier -1.