Il existe 2 périodes de 83 chiffres pour n/167 en base 8.

Pour toutes les fractions de n/167 en base 8, la période de 1/167 revient alors 83 fois (en orange)

1/167=0,00304156276052730111451307220061033457412566022312261644014206713702535404462454351...

2/167=0,00610334574125660223122616440142067137025354044624543510030415627605273011145130722...

3/167=0,01114513072200610334574125660223122616440142067137025354044624543510030415627605273...

4/167=0,01420671370253540446245435100304156276052730111451307220061033457412566022312261644...

5/167=0,01725047666326470557716744320365211755465516133763571064075242373315323426774736215...

6/167=0,02231226164401420671370253540446245435100304156276052730111451307220061033457412566...

7/167=0,02535404462454351003041562760527301114513072200610334574125660223122616440142067137...

8/167=0,03041562760527301114513072200610334574125660223122616440142067137025354044624543510...

9/167=0,03345741256602231226164401420671370253540446245435100304156276052730111451307220061...

10/167=0,03652117554655161337635710640752423733153234267747362150172504766632647055771674432...

11/167=0,04156276052730111451307220061033457412566022312261644014206713702535404462454351003...

12/167=0,04462454351003041562760527301114513072200610334574125660223122616440142067137025354...

13/167=0,04766632647055771674432036521175546551613376357106407524237331532342677473621501725...

14/167=0,05273011145130722006103345741256602231226164401420671370253540446245435100304156276...

15/167=0,05577167443203652117554655161337635710640752423733153234267747362150172504766632647...

16/167=0,06103345741256602231226164401420671370253540446245435100304156276052730111451307220...

17/167=0,06407524237331532342677473621501725047666326470557716744320365211755465516133763571...

18/167=0,06713702535404462454351003041562760527301114513072200610334574125660223122616440142...

19/167=0,07220061033457412566022312261644014206713702535404462454351003041562760527301114513...

20/167=0,07524237331532342677473621501725047666326470557716744320365211755465516133763571064...

21/167=0,10030415627605273011145130722006103345741256602231226164401420671370253540446245435...

22/167=0,10334574125660223122616440142067137025354044624543510030415627605273011145130722006...

23/167=0,10640752423733153234267747362150172504766632647055771674432036521175546551613376357...

24/167=0,11145130722006103345741256602231226164401420671370253540446245435100304156276052730...

25/167=0,11451307220061033457412566022312261644014206713702535404462454351003041562760527301...

26/167=0,11755465516133763571064075242373315323426774736215017250476663264705577167443203652...

27/167=0,12261644014206713702535404462454351003041562760527301114513072200610334574125660223...

28/167=0,12566022312261644014206713702535404462454351003041562760527301114513072200610334574...

29/167=0,13072200610334574125660223122616440142067137025354044624543510030415627605273011145...

30/167=0,13376357106407524237331532342677473621501725047666326470557716744320365211755465516...

31/167=0,13702535404462454351003041562760527301114513072200610334574125660223122616440142067...

32/167=0,14206713702535404462454351003041562760527301114513072200610334574125660223122616440...

33/167=0,14513072200610334574125660223122616440142067137025354044624543510030415627605273011...

34/167=0,15017250476663264705577167443203652117554655161337635710640752423733153234267747362...

35/167=0,15323426774736215017250476663264705577167443203652117554655161337635710640752423733...

36/167=0,15627605273011145130722006103345741256602231226164401420671370253540446245435100304...

37/167=0,16133763571064075242373315323426774736215017250476663264705577167443203652117554655...

38/167=0,16440142067137025354044624543510030415627605273011145130722006103345741256602231226...

39/167=0,16744320365211755465516133763571064075242373315323426774736215017250476663264705577...

40/167=0,17250476663264705577167443203652117554655161337635710640752423733153234267747362150...

41/167=0,17554655161337635710640752423733153234267747362150172504766632647055771674432036521...

42/167=0,20061033457412566022312261644014206713702535404462454351003041562760527301114513072...

43/167=0,20365211755465516133763571064075242373315323426774736215017250476663264705577167443...

44/167=0,20671370253540446245435100304156276052730111451307220061033457412566022312261644014...

45/167=0,21175546551613376357106407524237331532342677473621501725047666326470557716744320365...

46/167=0,21501725047666326470557716744320365211755465516133763571064075242373315323426774736...

47/167=0,22006103345741256602231226164401420671370253540446245435100304156276052730111451307...

48/167=0,22312261644014206713702535404462454351003041562760527301114513072200610334574125660...

49/167=0,22616440142067137025354044624543510030415627605273011145130722006103345741256602231...

50/167=0,23122616440142067137025354044624543510030415627605273011145130722006103345741256602...

51/167=0,23426774736215017250476663264705577167443203652117554655161337635710640752423733153...

52/167=0,23733153234267747362150172504766632647055771674432036521175546551613376357106407524...

53/167=0,24237331532342677473621501725047666326470557716744320365211755465516133763571064075...

54/167=0,24543510030415627605273011145130722006103345741256602231226164401420671370253540446...

55/167=0,25047666326470557716744320365211755465516133763571064075242373315323426774736215017...

56/167=0,25354044624543510030415627605273011145130722006103345741256602231226164401420671370...

57/167=0,25660223122616440142067137025354044624543510030415627605273011145130722006103345741...

58/167=0,26164401420671370253540446245435100304156276052730111451307220061033457412566022312...

59/167=0,26470557716744320365211755465516133763571064075242373315323426774736215017250476663...

60/167=0,26774736215017250476663264705577167443203652117554655161337635710640752423733153234...

61/167=0,27301114513072200610334574125660223122616440142067137025354044624543510030415627605...

62/167=0,27605273011145130722006103345741256602231226164401420671370253540446245435100304156...

63/167=0,30111451307220061033457412566022312261644014206713702535404462454351003041562760527...

64/167=0,30415627605273011145130722006103345741256602231226164401420671370253540446245435100...

65/167=0,30722006103345741256602231226164401420671370253540446245435100304156276052730111451...

66/167=0,31226164401420671370253540446245435100304156276052730111451307220061033457412566022...

67/167=0,31532342677473621501725047666326470557716744320365211755465516133763571064075242373...

68/167=0,32036521175546551613376357106407524237331532342677473621501725047666326470557716744...

69/167=0,32342677473621501725047666326470557716744320365211755465516133763571064075242373315...

70/167=0,32647055771674432036521175546551613376357106407524237331532342677473621501725047666...

71/167=0,33153234267747362150172504766632647055771674432036521175546551613376357106407524237...

72/167=0,33457412566022312261644014206713702535404462454351003041562760527301114513072200610...

73/167=0,33763571064075242373315323426774736215017250476663264705577167443203652117554655161...

74/167=0,34267747362150172504766632647055771674432036521175546551613376357106407524237331532...

75/167=0,34574125660223122616440142067137025354044624543510030415627605273011145130722006103...

76/167=0,35100304156276052730111451307220061033457412566022312261644014206713702535404462454...

77/167=0,35404462454351003041562760527301114513072200610334574125660223122616440142067137025...

78/167=0,35710640752423733153234267747362150172504766632647055771674432036521175546551613376...

79/167=0,36215017250476663264705577167443203652117554655161337635710640752423733153234267747...

80/167=0,36521175546551613376357106407524237331532342677473621501725047666326470557716744320...

81/167=0,37025354044624543510030415627605273011145130722006103345741256602231226164401420671...

82/167=0,37331532342677473621501725047666326470557716744320365211755465516133763571064075242...

83/167=0,37635710640752423733153234267747362150172504766632647055771674432036521175546551613...

84/167=0,40142067137025354044624543510030415627605273011145130722006103345741256602231226164...

85/167=0,40446245435100304156276052730111451307220061033457412566022312261644014206713702535...

86/167=0,40752423733153234267747362150172504766632647055771674432036521175546551613376357106...

87/167=0,41256602231226164401420671370253540446245435100304156276052730111451307220061033457...

88/167=0,41562760527301114513072200610334574125660223122616440142067137025354044624543510030...

89/167=0,42067137025354044624543510030415627605273011145130722006103345741256602231226164401...

90/167=0,42373315323426774736215017250476663264705577167443203652117554655161337635710640752...

91/167=0,42677473621501725047666326470557716744320365211755465516133763571064075242373315323...

92/167=0,43203652117554655161337635710640752423733153234267747362150172504766632647055771674...

93/167=0,43510030415627605273011145130722006103345741256602231226164401420671370253540446245...

94/167=0,44014206713702535404462454351003041562760527301114513072200610334574125660223122616...

95/167=0,44320365211755465516133763571064075242373315323426774736215017250476663264705577167...

96/167=0,44624543510030415627605273011145130722006103345741256602231226164401420671370253540...

97/167=0,45130722006103345741256602231226164401420671370253540446245435100304156276052730111...

98/167=0,45435100304156276052730111451307220061033457412566022312261644014206713702535404462...

99/167=0,45741256602231226164401420671370253540446245435100304156276052730111451307220061033...

100/167=0,46245435100304156276052730111451307220061033457412566022312261644014206713702535404...

101/167=0,46551613376357106407524237331532342677473621501725047666326470557716744320365211755...

102/167=0,47055771674432036521175546551613376357106407524237331532342677473621501725047666326...

103/167=0,47362150172504766632647055771674432036521175546551613376357106407524237331532342677...

104/167=0,47666326470557716744320365211755465516133763571064075242373315323426774736215017250...

105/167=0,50172504766632647055771674432036521175546551613376357106407524237331532342677473621...

106/167=0,50476663264705577167443203652117554655161337635710640752423733153234267747362150172...

107/167=0,51003041562760527301114513072200610334574125660223122616440142067137025354044624543...

108/167=0,51307220061033457412566022312261644014206713702535404462454351003041562760527301114...

109/167=0,51613376357106407524237331532342677473621501725047666326470557716744320365211755465...

110/167=0,52117554655161337635710640752423733153234267747362150172504766632647055771674432036...

111/167=0,52423733153234267747362150172504766632647055771674432036521175546551613376357106407...

112/167=0,52730111451307220061033457412566022312261644014206713702535404462454351003041562760...

113/167=0,53234267747362150172504766632647055771674432036521175546551613376357106407524237331...

114/167=0,53540446245435100304156276052730111451307220061033457412566022312261644014206713702...

115/167=0,54044624543510030415627605273011145130722006103345741256602231226164401420671370253...

116/167=0,54351003041562760527301114513072200610334574125660223122616440142067137025354044624...

117/167=0,54655161337635710640752423733153234267747362150172504766632647055771674432036521175...

118/167=0,55161337635710640752423733153234267747362150172504766632647055771674432036521175546...

119/167=0,55465516133763571064075242373315323426774736215017250476663264705577167443203652117...

120/167=0,55771674432036521175546551613376357106407524237331532342677473621501725047666326470...

121/167=0,56276052730111451307220061033457412566022312261644014206713702535404462454351003041...

122/167=0,56602231226164401420671370253540446245435100304156276052730111451307220061033457412...

123/167=0,57106407524237331532342677473621501725047666326470557716744320365211755465516133763...

124/167=0,57412566022312261644014206713702535404462454351003041562760527301114513072200610334...

125/167=0,57716744320365211755465516133763571064075242373315323426774736215017250476663264705...

126/167=0,60223122616440142067137025354044624543510030415627605273011145130722006103345741256...

127/167=0,60527301114513072200610334574125660223122616440142067137025354044624543510030415627...

128/167=0,61033457412566022312261644014206713702535404462454351003041562760527301114513072200...

129/167=0,61337635710640752423733153234267747362150172504766632647055771674432036521175546551...

130/167=0,61644014206713702535404462454351003041562760527301114513072200610334574125660223122...

131/167=0,62150172504766632647055771674432036521175546551613376357106407524237331532342677473...

132/167=0,62454351003041562760527301114513072200610334574125660223122616440142067137025354044...

133/167=0,62760527301114513072200610334574125660223122616440142067137025354044624543510030415...

134/167=0,63264705577167443203652117554655161337635710640752423733153234267747362150172504766...

135/167=0,63571064075242373315323426774736215017250476663264705577167443203652117554655161337...

136/167=0,64075242373315323426774736215017250476663264705577167443203652117554655161337635710...

137/167=0,64401420671370253540446245435100304156276052730111451307220061033457412566022312261...

138/167=0,64705577167443203652117554655161337635710640752423733153234267747362150172504766632...

139/167=0,65211755465516133763571064075242373315323426774736215017250476663264705577167443203...

140/167=0,65516133763571064075242373315323426774736215017250476663264705577167443203652117554...

141/167=0,66022312261644014206713702535404462454351003041562760527301114513072200610334574125...

142/167=0,66326470557716744320365211755465516133763571064075242373315323426774736215017250476...

143/167=0,66632647055771674432036521175546551613376357106407524237331532342677473621501725047...

144/167=0,67137025354044624543510030415627605273011145130722006103345741256602231226164401420...

145/167=0,67443203652117554655161337635710640752423733153234267747362150172504766632647055771...

146/167=0,67747362150172504766632647055771674432036521175546551613376357106407524237331532342...

147/167=0,70253540446245435100304156276052730111451307220061033457412566022312261644014206713...

148/167=0,70557716744320365211755465516133763571064075242373315323426774736215017250476663264...

149/167=0,71064075242373315323426774736215017250476663264705577167443203652117554655161337635...

150/167=0,71370253540446245435100304156276052730111451307220061033457412566022312261644014206...

151/167=0,71674432036521175546551613376357106407524237331532342677473621501725047666326470557...

152/167=0,72200610334574125660223122616440142067137025354044624543510030415627605273011145130...

153/167=0,72504766632647055771674432036521175546551613376357106407524237331532342677473621501...

154/167=0,73011145130722006103345741256602231226164401420671370253540446245435100304156276052...

155/167=0,73315323426774736215017250476663264705577167443203652117554655161337635710640752423...

156/167=0,73621501725047666326470557716744320365211755465516133763571064075242373315323426774...

157/167=0,74125660223122616440142067137025354044624543510030415627605273011145130722006103345...

158/167=0,74432036521175546551613376357106407524237331532342677473621501725047666326470557716...

159/167=0,74736215017250476663264705577167443203652117554655161337635710640752423733153234267...

160/167=0,75242373315323426774736215017250476663264705577167443203652117554655161337635710640...

161/167=0,75546551613376357106407524237331532342677473621501725047666326470557716744320365211...

162/167=0,76052730111451307220061033457412566022312261644014206713702535404462454351003041562...

163/167=0,76357106407524237331532342677473621501725047666326470557716744320365211755465516133...

164/167=0,76663264705577167443203652117554655161337635710640752423733153234267747362150172504...

165/167=0,77167443203652117554655161337635710640752423733153234267747362150172504766632647055...

166/167=0,77473621501725047666326470557716744320365211755465516133763571064075242373315323426...

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