Il existe 3 périodes de 52 chiffres pour n/157 en base 8.

Pour toutes les fractions de n/157 en base 8, la période de 1/157 revient alors 52 fois (en orange)

1/157=0,0032055517713644540150266477457222600641332376275113...

2/157=0,0064133237627511300320555177136445401502664774572226...

3/157=0,0116210757543356040471043676615670202344217373067341...

4/157=0,0150266477457222600641332376275113003205551771364454...

5/157=0,0202344217373067341011621075754335604047104367661567...

6/157=0,0234421737306734101162107575433560404710436766156702...

7/157=0,0266477457222600641332376275113003205551771364454015...

8/157=0,0320555177136445401502664774572226006413323762751130...

9/157=0,0352632717052312141653153474251450607254656361246243...

10/157=0,0404710436766156702023442173730673410116210757543356...

11/157=0,0436766156702023442173730673410116210757543356040471...

12/157=0,0471043676615670202344217373067341011621075754335604...

13/157=0,0523121416531534742514506072546563612462430352632717...

14/157=0,0555177136445401502664774572226006413323762751130032...

15/157=0,0607254656361246243035263271705231214165315347425145...

16/157=0,0641332376275113003205551771364454015026647745722260...

17/157=0,0673410116210757543356040471043676615670202344217373...

18/157=0,0725465636124624303526327170523121416531534742514506...

19/157=0,0757543356040471043676615670202344217373067341011621...

20/157=0,1011621075754335604047104367661567020234421737306734...

21/157=0,1043676615670202344217373067341011621075754335604047...

22/157=0,1075754335604047104367661567020234421737306734101162...

23/157=0,1130032055517713644540150266477457222600641332376275...

24/157=0,1162107575433560404710436766156702023442173730673410...

25/157=0,1214165315347425145060725465636124624303526327170523...

26/157=0,1246243035263271705231214165315347425145060725465636...

27/157=0,1300320555177136445401502664774572226006413323762751...

28/157=0,1332376275113003205551771364454015026647745722260064...

29/157=0,1364454015026647745722260064133237627511300320555177...

30/157=0,1416531534742514506072546563612462430352632717052312...

31/157=0,1450607254656361246243035263271705231214165315347425...

32/157=0,1502664774572226006413323762751130032055517713644540...

33/157=0,1534742514506072546563612462430352632717052312141653...

34/157=0,1567020234421737306734101162107575433560404710436766...

35/157=0,1621075754335604047104367661567020234421737306734101...

36/157=0,1653153474251450607254656361246243035263271705231214...

37/157=0,1705231214165315347425145060725465636124624303526327...

38/157=0,1737306734101162107575433560404710436766156702023442...

39/157=0,1771364454015026647745722260064133237627511300320555...

40/157=0,2023442173730673410116210757543356040471043676615670...

41/157=0,2055517713644540150266477457222600641332376275113003...

42/157=0,2107575433560404710436766156702023442173730673410116...

43/157=0,2141653153474251450607254656361246243035263271705231...

44/157=0,2173730673410116210757543356040471043676615670202344...

45/157=0,2226006413323762751130032055517713644540150266477457...

46/157=0,2260064133237627511300320555177136445401502664774572...

47/157=0,2312141653153474251450607254656361246243035263271705...

48/157=0,2344217373067341011621075754335604047104367661567020...

49/157=0,2376275113003205551771364454015026647745722260064133...

50/157=0,2430352632717052312141653153474251450607254656361246...

51/157=0,2462430352632717052312141653153474251450607254656361...

52/157=0,2514506072546563612462430352632717052312141653153474...

53/157=0,2546563612462430352632717052312141653153474251450607...

54/157=0,2600641332376275113003205551771364454015026647745722...

55/157=0,2632717052312141653153474251450607254656361246243035...

56/157=0,2664774572226006413323762751130032055517713644540150...

57/157=0,2717052312141653153474251450607254656361246243035263...

58/157=0,2751130032055517713644540150266477457222600641332376...

59/157=0,3003205551771364454015026647745722260064133237627511...

60/157=0,3035263271705231214165315347425145060725465636124624...

61/157=0,3067341011621075754335604047104367661567020234421737...

62/157=0,3121416531534742514506072546563612462430352632717052...

63/157=0,3153474251450607254656361246243035263271705231214165...

64/157=0,3205551771364454015026647745722260064133237627511300...

65/157=0,3237627511300320555177136445401502664774572226006413...

66/157=0,3271705231214165315347425145060725465636124624303526...

67/157=0,3323762751130032055517713644540150266477457222600641...

68/157=0,3356040471043676615670202344217373067341011621075754...

69/157=0,3410116210757543356040471043676615670202344217373067...

70/157=0,3442173730673410116210757543356040471043676615670202...

71/157=0,3474251450607254656361246243035263271705231214165315...

72/157=0,3526327170523121416531534742514506072546563612462430...

73/157=0,3560404710436766156702023442173730673410116210757543...

74/157=0,3612462430352632717052312141653153474251450607254656...

75/157=0,3644540150266477457222600641332376275113003205551771...

76/157=0,3676615670202344217373067341011621075754335604047104...

77/157=0,3730673410116210757543356040471043676615670202344217...

78/157=0,3762751130032055517713644540150266477457222600641332...

79/157=0,4015026647745722260064133237627511300320555177136445...

80/157=0,4047104367661567020234421737306734101162107575433560...

81/157=0,4101162107575433560404710436766156702023442173730673...

82/157=0,4133237627511300320555177136445401502664774572226006...

83/157=0,4165315347425145060725465636124624303526327170523121...

84/157=0,4217373067341011621075754335604047104367661567020234...

85/157=0,4251450607254656361246243035263271705231214165315347...

86/157=0,4303526327170523121416531534742514506072546563612462...

87/157=0,4335604047104367661567020234421737306734101162107575...

88/157=0,4367661567020234421737306734101162107575433560404710...

89/157=0,4421737306734101162107575433560404710436766156702023...

90/157=0,4454015026647745722260064133237627511300320555177136...

91/157=0,4506072546563612462430352632717052312141653153474251...

92/157=0,4540150266477457222600641332376275113003205551771364...

93/157=0,4572226006413323762751130032055517713644540150266477...

94/157=0,4624303526327170523121416531534742514506072546563612...

95/157=0,4656361246243035263271705231214165315347425145060725...

96/157=0,4710436766156702023442173730673410116210757543356040...

97/157=0,4742514506072546563612462430352632717052312141653153...

98/157=0,4774572226006413323762751130032055517713644540150266...

99/157=0,5026647745722260064133237627511300320555177136445401...

100/157=0,5060725465636124624303526327170523121416531534742514...

101/157=0,5113003205551771364454015026647745722260064133237627...

102/157=0,5145060725465636124624303526327170523121416531534742...

103/157=0,5177136445401502664774572226006413323762751130032055...

104/157=0,5231214165315347425145060725465636124624303526327170...

105/157=0,5263271705231214165315347425145060725465636124624303...

106/157=0,5315347425145060725465636124624303526327170523121416...

107/157=0,5347425145060725465636124624303526327170523121416531...

108/157=0,5401502664774572226006413323762751130032055517713644...

109/157=0,5433560404710436766156702023442173730673410116210757...

110/157=0,5465636124624303526327170523121416531534742514506072...

111/157=0,5517713644540150266477457222600641332376275113003205...

112/157=0,5551771364454015026647745722260064133237627511300320...

113/157=0,5604047104367661567020234421737306734101162107575433...

114/157=0,5636124624303526327170523121416531534742514506072546...

115/157=0,5670202344217373067341011621075754335604047104367661...

116/157=0,5722260064133237627511300320555177136445401502664774...

117/157=0,5754335604047104367661567020234421737306734101162107...

118/157=0,6006413323762751130032055517713644540150266477457222...

119/157=0,6040471043676615670202344217373067341011621075754335...

120/157=0,6072546563612462430352632717052312141653153474251450...

121/157=0,6124624303526327170523121416531534742514506072546563...

122/157=0,6156702023442173730673410116210757543356040471043676...

123/157=0,6210757543356040471043676615670202344217373067341011...

124/157=0,6243035263271705231214165315347425145060725465636124...

125/157=0,6275113003205551771364454015026647745722260064133237...

126/157=0,6327170523121416531534742514506072546563612462430352...

127/157=0,6361246243035263271705231214165315347425145060725465...

128/157=0,6413323762751130032055517713644540150266477457222600...

129/157=0,6445401502664774572226006413323762751130032055517713...

130/157=0,6477457222600641332376275113003205551771364454015026...

131/157=0,6531534742514506072546563612462430352632717052312141...

132/157=0,6563612462430352632717052312141653153474251450607254...

133/157=0,6615670202344217373067341011621075754335604047104367...

134/157=0,6647745722260064133237627511300320555177136445401502...

135/157=0,6702023442173730673410116210757543356040471043676615...

136/157=0,6734101162107575433560404710436766156702023442173730...

137/157=0,6766156702023442173730673410116210757543356040471043...

138/157=0,7020234421737306734101162107575433560404710436766156...

139/157=0,7052312141653153474251450607254656361246243035263271...

140/157=0,7104367661567020234421737306734101162107575433560404...

141/157=0,7136445401502664774572226006413323762751130032055517...

142/157=0,7170523121416531534742514506072546563612462430352632...

143/157=0,7222600641332376275113003205551771364454015026647745...

144/157=0,7254656361246243035263271705231214165315347425145060...

145/157=0,7306734101162107575433560404710436766156702023442173...

146/157=0,7341011621075754335604047104367661567020234421737306...

147/157=0,7373067341011621075754335604047104367661567020234421...

148/157=0,7425145060725465636124624303526327170523121416531534...

149/157=0,7457222600641332376275113003205551771364454015026647...

150/157=0,7511300320555177136445401502664774572226006413323762...

151/157=0,7543356040471043676615670202344217373067341011621075...

152/157=0,7575433560404710436766156702023442173730673410116210...

153/157=0,7627511300320555177136445401502664774572226006413323...

154/157=0,7661567020234421737306734101162107575433560404710436...

155/157=0,7713644540150266477457222600641332376275113003205551...

156/157=0,7745722260064133237627511300320555177136445401502664...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (52) est égal à 156 et donc au premier -1.