Il existe 6 périodes de 26 chiffres pour n/157 en base 4.

Pour toutes les fractions de n/157 en base 4, la période de 1/157 revient alors 26 fois (en orange)

1/157=0,00012201123103332113221023...

2/157=0,00031002312213330233102112...

3/157=0,00103210101323323012323201...

4/157=0,00122011231033321132210230...

5/157=0,00200213020203313312031313...

6/157=0,00213020203313312031313002...

7/157=0,00231221333023310211200031...

8/157=0,00310023122133302331021120...

9/157=0,00322230311303301110302203...

10/157=0,01001032101013233230123232...

11/157=0,01013233230123232010010321...

12/157=0,01032101013233230123232010...

13/157=0,01110302203003222303113033...

14/157=0,01123103332113221023000122...

15/157=0,01201311121223213202221211...

16/157=0,01220112310333211322102300...

17/157=0,01232320100103210101323323...

18/157=0,01311121223213202221211012...

19/157=0,01323323012323201001032101...

20/157=0,02002130202033133120313130...

21/157=0,02020331331203131300200213...

22/157=0,02033133120313130020021302...

23/157=0,02112000310023122133302331...

24/157=0,02130202033133120313130020...

25/157=0,02203003222303113033011103...

26/157=0,02221211012013111212232132...

27/157=0,02300012201123103332113221...

28/157=0,02312213330233102112000310...

29/157=0,02331021120003100231221333...

30/157=0,03003222303113033011103022...

31/157=0,03022030032223031130330111...

32/157=0,03100231221333023310211200...

33/157=0,03113033011103022030032223...

34/157=0,03131300200213020203313312...

35/157=0,03210101323323012323201001...

36/157=0,03222303113033011103022030...

37/157=0,03301110302203003222303113...

38/157=0,03313312031313002002130202...

39/157=0,03332113221023000122011231...

40/157=0,10010321010132332301232320...

41/157=0,10023122133302331021120003...

42/157=0,10101323323012323201001032...

43/157=0,10120131112122321320222121...

44/157=0,10132332301232320100103210...

45/157=0,10211200031002312213330233...

46/157=0,10230001220112310333211322...

47/157=0,10302203003222303113033011...

48/157=0,10321010132332301232320100...

49/157=0,10333211322102300012201123...

50/157=0,11012013111212232132022212...

51/157=0,11030220300322230311303301...

52/157=0,11103022030032223031130330...

53/157=0,11121223213202221211012013...

54/157=0,11200031002312213330233102...

55/157=0,11212232132022212110120131...

56/157=0,11231033321132210230001220...

57/157=0,11303301110302203003222303...

58/157=0,11322102300012201123103332...

59/157=0,12000310023122133302331021...

60/157=0,12013111212232132022212110...

61/157=0,12031313002002130202033133...

62/157=0,12110120131112122321320222...

63/157=0,12122321320222121101201311...

64/157=0,12201123103332113221023000...

65/157=0,12213330233102112000310023...

66/157=0,12232132022212110120131112...

67/157=0,12310333211322102300012201...

68/157=0,12323201001032101013233230...

69/157=0,13002002130202033133120313...

70/157=0,13020203313312031313002002...

71/157=0,13033011103022030032223031...

72/157=0,13111212232132022212110120...

73/157=0,13130020021302020331331203...

74/157=0,13202221211012013111212232...

75/157=0,13221023000122011231033321...

76/157=0,13233230123232010010321010...

77/157=0,13312031313002002130202033...

78/157=0,13330233102112000310023122...

79/157=0,20003100231221333023310211...

80/157=0,20021302020331331203131300...

81/157=0,20100103210101323323012323...

82/157=0,20112310333211322102300012...

83/157=0,20131112122321320222121101...

84/157=0,20203313312031313002002130...

85/157=0,20222121101201311121223213...

86/157=0,20300322230311303301110302...

87/157=0,20313130020021302020331331...

88/157=0,20331331203131300200213020...

89/157=0,21010132332301232320100103...

90/157=0,21023000122011231033321132...

91/157=0,21101201311121223213202221...

92/157=0,21120003100231221333023310...

93/157=0,21132210230001220112310333...

94/157=0,21211012013111212232132022...

95/157=0,21223213202221211012013111...

96/157=0,21302020331331203131300200...

97/157=0,21320222121101201311121223...

98/157=0,21333023310211200031002312...

99/157=0,22011231033321132210230001...

100/157=0,22030032223031130330111030...

101/157=0,22102300012201123103332113...

102/157=0,22121101201311121223213202...

103/157=0,22133302331021120003100231...

104/157=0,22212110120131112122321320...

105/157=0,22230311303301110302203003...

106/157=0,22303113033011103022030032...

107/157=0,22321320222121101201311121...

108/157=0,23000122011231033321132210...

109/157=0,23012323201001032101013233...

110/157=0,23031130330111030220300322...

111/157=0,23103332113221023000122011...

112/157=0,23122133302331021120003100...

113/157=0,23201001032101013233230123...

114/157=0,23213202221211012013111212...

115/157=0,23232010010321010132332301...

116/157=0,23310211200031002312213330...

117/157=0,23323012323201001032101013...

118/157=0,30001220112310333211322102...

119/157=0,30020021302020331331203131...

120/157=0,30032223031130330111030220...

121/157=0,30111030220300322230311303...

122/157=0,30123232010010321010132332...

123/157=0,30202033133120313130020021...

124/157=0,30220300322230311303301110...

125/157=0,30233102112000310023122133...

126/157=0,30311303301110302203003222...

127/157=0,30330111030220300322230311...

128/157=0,31002312213330233102112000...

129/157=0,31021120003100231221333023...

130/157=0,31033321132210230001220112...

131/157=0,31112122321320222121101201...

132/157=0,31130330111030220300322230...

133/157=0,31203131300200213020203313...

134/157=0,31221333023310211200031002...

135/157=0,31300200213020203313312031...

136/157=0,31313002002130202033133120...

137/157=0,31331203131300200213020203...

138/157=0,32010010321010132332301232...

139/157=0,32022212110120131112122321...

140/157=0,32101013233230123232010010...

141/157=0,32113221023000122011231033...

142/157=0,32132022212110120131112122...

143/157=0,32210230001220112310333211...

144/157=0,32223031130330111030220300...

145/157=0,32301232320100103210101323...

146/157=0,32320100103210101323323012...

147/157=0,32332301232320100103210101...

148/157=0,33011103022030032223031130...

149/157=0,33023310211200031002312213...

150/157=0,33102112000310023122133302...

151/157=0,33120313130020021302020331...

152/157=0,33133120313130020021302020...

153/157=0,33211322102300012201123103...

154/157=0,33230123232010010321010132...

155/157=0,33302331021120003100231221...

156/157=0,33321132210230001220112310...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (26) est égal à 156 et donc au premier -1.