Une période unique fait résonner toutes les fractions de n/157 en base 5.  

Le microscope numérique permet alors d'en observer le graphe. 

1/157=0,000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312...

2/157=0,001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124...

3/157=0,002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441...

4/157=0,003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303...

5/157=0,003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120...

6/157=0,004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432...

7/157=0,010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244...

8/157=0,011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111...

9/157=0,012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423...

10/157=0,012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240...

11/157=0,013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102...

12/157=0,014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414...

13/157=0,020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231...

14/157=0,021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043...

15/157=0,021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410...

16/157=0,022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222...

17/157=0,023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034...

18/157=0,024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401...

19/157=0,030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213...

20/157=0,030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030...

21/157=0,031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342...

22/157=0,032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204...

23/157=0,033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021...

24/157=0,034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333...

25/157=0,034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200...

26/157=0,040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012...

27/157=0,041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324...

28/157=0,042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141...

29/157=0,043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003...

30/157=0,043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320...

31/157=0,044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132...

32/157=0,100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444...

33/157=0,101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311...

34/157=0,102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123...

35/157=0,102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440...

36/157=0,103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302...

37/157=0,104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114...

38/157=0,110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431...

39/157=0,111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243...

40/157=0,111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110...

41/157=0,112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422...

42/157=0,113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234...

43/157=0,114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101...

44/157=0,120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413...

45/157=0,120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230...

46/157=0,121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042...

47/157=0,122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404...

48/157=0,123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221...

49/157=0,124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033...

50/157=0,124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400...

51/157=0,130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212...

52/157=0,131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024...

53/157=0,132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341...

54/157=0,132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203...

55/157=0,133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020...

56/157=0,134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332...

57/157=0,140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144...

58/157=0,141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011...

59/157=0,141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323...

60/157=0,142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140...

61/157=0,143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002...

62/157=0,144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314...

63/157=0,200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131...

64/157=0,200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443...

65/157=0,201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310...

66/157=0,202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122...

67/157=0,203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434...

68/157=0,204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301...

69/157=0,204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113...

70/157=0,210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430...

71/157=0,211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242...

72/157=0,212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104...

73/157=0,213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421...

74/157=0,213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233...

75/157=0,214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100...

76/157=0,220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412...

77/157=0,221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224...

78/157=0,222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041...

79/157=0,222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403...

80/157=0,223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220...

81/157=0,224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032...

82/157=0,230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344...

83/157=0,231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211...

84/157=0,231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023...

85/157=0,232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340...

86/157=0,233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202...

87/157=0,234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014...

88/157=0,240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331...

89/157=0,240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143...

90/157=0,241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010...

91/157=0,242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322...

92/157=0,243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134...

93/157=0,244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001...

94/157=0,244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313...

95/157=0,300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130...

96/157=0,301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442...

97/157=0,302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304...

98/157=0,303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121...

99/157=0,303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433...

100/157=0,304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300...

101/157=0,310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112...

102/157=0,311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424...

103/157=0,312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241...

104/157=0,312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103...

105/157=0,313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420...

106/157=0,314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232...

107/157=0,320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044...

108/157=0,320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411...

109/157=0,321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223...

110/157=0,322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040...

111/157=0,323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402...

112/157=0,324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214...

113/157=0,324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031...

114/157=0,330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343...

115/157=0,331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210...

116/157=0,332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022...

117/157=0,333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334...

118/157=0,333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201...

119/157=0,334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013...

120/157=0,340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330...

121/157=0,341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142...

122/157=0,342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004...

123/157=0,342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321...

124/157=0,343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133...

125/157=0,344230120403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000...

126/157=0,400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312...

127/157=0,401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124...

128/157=0,401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441...

129/157=0,402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303...

130/157=0,403222422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120...

131/157=0,404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432...

132/157=0,410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244...

133/157=0,410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111...

134/157=0,411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423...

135/157=0,412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240...

136/157=0,413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102...

137/157=0,414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414...

138/157=0,414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231...

139/157=0,420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043...

140/157=0,421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410...

141/157=0,422112310201333433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222...

142/157=0,423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213424311101114104212130300304302103312400124401024131200034...

143/157=0,423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401...

144/157=0,424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021432404122202233213...

145/157=0,430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030...

146/157=0,431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342...

147/157=0,432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204...

148/157=0,432404122202233213424311101114104212130300304302103312400124401024131200034423012040322242211231020133343330340232314144140142341132044320043420313244410021...

149/157=0,433303402323141441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333...

150/157=0,434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200...

151/157=0,440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012...

152/157=0,441002143240412220223321342431110111410421213030030430210331240012440102413120003442301204032224221123102013334333034023231414414014234113204432004342031324...

153/157=0,441401423411320443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141...

154/157=0,442301204032224221123102013334333034023231414414014234113204432004342031324441002143240412220223321342431110111410421213030030430210331240012440102413120003...

155/157=0,443200434203132444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320...

156/157=0,444100214324041222022332134243111011141042121303003043021033124001244010241312000344230120403222422112310201333433303402323141441401423411320443200434203132...