Liste des fractions de n/127 en base 5.

Il existe 3 périodes de 42 chiffres pour n/127 en base 5.

Pour toutes les fractions de n/127 en base 5, la période de 1/127 revient alors 42 fois (en orange)

1/127=0,000443003432030333222444001441012414111222...

2/127=0,001441012414111222000443003432030333222444...

3/127=0,002434021401142110223442010423043302334221...

4/127=0,003432030333222444001441012414111222000443...

5/127=0,004430034320303332224440014410124141112220...

6/127=0,010423043302334221002434021401142110223442...

7/127=0,011421102234420104230433023342210024340214...

8/127=0,012414111222000443003432030333222444001441...

9/127=0,013412120204031331231431032324240413113213...

10/127=0,014410124141112220004430034320303332224440...

11/127=0,020403133123143103232424041311321301341212...

12/127=0,021401142110223442010423043302334221002434...

13/127=0,022344201042304330233422100243402140114211...

14/127=0,023342210024340214011421102234420104230433...

15/127=0,024340214011421102234420104230433023342210...

16/127=0,030333222444001441012414111222000443003432...

17/127=0,031331231431032324240413113213013412120204...

18/127=0,032324240413113213013412120204031331231431...

19/127=0,033322244400144101241411122200044300343203...

20/127=0,034320303332224440014410124141112220004430...

21/127=0,040313312314310323242404131132130134121202...

22/127=0,041311321301341212020403133123143103232424...

23/127=0,042304330233422100243402140114211022344201...

24/127=0,043302334221002434021401142110223442010423...

25/127=0,044300343203033322244400144101241411122200...

26/127=0,100243402140114211022344201042304330233422...

27/127=0,101241411122200044300343203033322244400144...

28/127=0,102234420104230433023342210024340214011421...

29/127=0,103232424041311321301341212020403133123143...

30/127=0,104230433023342210024340214011421102234420...

31/127=0,110223442010423043302334221002434021401142...

32/127=0,111222000443003432030333222444001441012414...

33/127=0,112220004430034320303332224440014410124141...

34/127=0,113213013412120204031331231431032324240413...

35/127=0,114211022344201042304330233422100243402140...

36/127=0,120204031331231431032324240413113213013412...

37/127=0,121202040313312314310323242404131132130134...

38/127=0,122200044300343203033322244400144101241411...

39/127=0,123143103232424041311321301341212020403133...

40/127=0,124141112220004430034320303332224440014410...

41/127=0,130134121202040313312314310323242404131132...

42/127=0,131132130134121202040313312314310323242404...

43/127=0,132130134121202040313312314310323242404131...

44/127=0,133123143103232424041311321301341212020403...

45/127=0,134121202040313312314310323242404131132130...

46/127=0,140114211022344201042304330233422100243402...

47/127=0,141112220004430034320303332224440014410124...

48/127=0,142110223442010423043302334221002434021401...

49/127=0,143103232424041311321301341212020403133123...

50/127=0,144101241411122200044300343203033322244400...

51/127=0,200044300343203033322244400144101241411122...

52/127=0,201042304330233422100243402140114211022344...

53/127=0,202040313312314310323242404131132130134121...

54/127=0,203033322244400144101241411122200044300343...

55/127=0,204031331231431032324240413113213013412120...

56/127=0,210024340214011421102234420104230433023342...

57/127=0,211022344201042304330233422100243402140114...

58/127=0,212020403133123143103232424041311321301341...

59/127=0,213013412120204031331231431032324240413113...

60/127=0,214011421102234420104230433023342210024340...

61/127=0,220004430034320303332224440014410124141112...

62/127=0,221002434021401142110223442010423043302334...

63/127=0,222000443003432030333222444001441012414111...

64/127=0,222444001441012414111222000443003432030333...

65/127=0,223442010423043302334221002434021401142110...

66/127=0,224440014410124141112220004430034320303332...

67/127=0,230433023342210024340214011421102234420104...

68/127=0,231431032324240413113213013412120204031331...

69/127=0,232424041311321301341212020403133123143103...

70/127=0,233422100243402140114211022344201042304330...

71/127=0,234420104230433023342210024340214011421102...

72/127=0,240413113213013412120204031331231431032324...

73/127=0,241411122200044300343203033322244400144101...

74/127=0,242404131132130134121202040313312314310323...

75/127=0,243402140114211022344201042304330233422100...

76/127=0,244400144101241411122200044300343203033322...

77/127=0,300343203033322244400144101241411122200044...

78/127=0,301341212020403133123143103232424041311321...

79/127=0,302334221002434021401142110223442010423043...

80/127=0,303332224440014410124141112220004430034320...

81/127=0,304330233422100243402140114211022344201042...

82/127=0,310323242404131132130134121202040313312314...

83/127=0,311321301341212020403133123143103232424041...

84/127=0,312314310323242404131132130134121202040313...

85/127=0,313312314310323242404131132130134121202040...

86/127=0,314310323242404131132130134121202040313312...

87/127=0,320303332224440014410124141112220004430034...

88/127=0,321301341212020403133123143103232424041311...

89/127=0,322244400144101241411122200044300343203033...

90/127=0,323242404131132130134121202040313312314310...

91/127=0,324240413113213013412120204031331231431032...

92/127=0,330233422100243402140114211022344201042304...

93/127=0,331231431032324240413113213013412120204031...

94/127=0,332224440014410124141112220004430034320303...

95/127=0,333222444001441012414111222000443003432030...

96/127=0,334221002434021401142110223442010423043302...

97/127=0,340214011421102234420104230433023342210024...

98/127=0,341212020403133123143103232424041311321301...

99/127=0,342210024340214011421102234420104230433023...

100/127=0,343203033322244400144101241411122200044300...

101/127=0,344201042304330233422100243402140114211022...

102/127=0,400144101241411122200044300343203033322244...

103/127=0,401142110223442010423043302334221002434021...

104/127=0,402140114211022344201042304330233422100243...

105/127=0,403133123143103232424041311321301341212020...

106/127=0,404131132130134121202040313312314310323242...

107/127=0,410124141112220004430034320303332224440014...

108/127=0,411122200044300343203033322244400144101241...

109/127=0,412120204031331231431032324240413113213013...

110/127=0,413113213013412120204031331231431032324240...

111/127=0,414111222000443003432030333222444001441012...

112/127=0,420104230433023342210024340214011421102234...

113/127=0,421102234420104230433023342210024340214011...

114/127=0,422100243402140114211022344201042304330233...

115/127=0,423043302334221002434021401142110223442010...

116/127=0,424041311321301341212020403133123143103232...

117/127=0,430034320303332224440014410124141112220004...

118/127=0,431032324240413113213013412120204031331231...

119/127=0,432030333222444001441012414111222000443003...

120/127=0,433023342210024340214011421102234420104230...

121/127=0,434021401142110223442010423043302334221002...

122/127=0,440014410124141112220004430034320303332224...

123/127=0,441012414111222000443003432030333222444001...

124/127=0,442010423043302334221002434021401142110223...

125/127=0,443003432030333222444001441012414111222000...

126/127=0,444001441012414111222000443003432030333222...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (42) est égal à 126 et donc au premier -1.