Il existe 2 périodes de 63 chiffres pour n/127 en base 9.

Pour toutes les fractions de n/127 en base 9, la période de 1/127 revient alors 63 fois (en orange)

1/127=0,005658515024857262111752168447328707012428131050825534223614348...

2/127=0,012428131050825534223614348005658515024857262111752168447328707...

3/127=0,018187646075783806335466527454088323037386403162677713672044156...

4/127=0,024857262111752168447328707012428131050825534223614348005658515...

5/127=0,031626777136720441560181876460757838063354665274540883230373864...

6/127=0,037386403162677713672044156018187646075783806335466527454088323...

7/127=0,044156018187646075783806335466527454088323037386403162677713672...

8/127=0,050825534223614348005658515024857262111752168447328707012428131...

9/127=0,056585150248572621117521684473287070124281310508255342236143480...

10/127=0,063354665274540883230373864031626777136720441560181876460757838...

11/127=0,070124281310508255342236143480056585150248572621117521684473287...

12/127=0,075783806335466527454088323037386403162677713672044156018187646...

13/127=0,082553422361434800565851502485726211175216844732870701242813105...

14/127=0,088323037386403162677713672044156018187646075783806335466527454...

15/127=0,105082553422361434800565851502485726211175216844732870701242813...

16/127=0,111752168447328707012428131050825534223614348005658515024857262...

17/127=0,117521684473287070124281310508255342236143480056585150248572621...

18/127=0,124281310508255342236143480056585150248572621117521684473287070...

19/127=0,131050825534223614348005658515024857262111752168447328707012428...

20/127=0,136720441560181876460757838063354665274540883230373864031626777...

21/127=0,143480056585150248572621117521684473287070124281310508255342236...

22/127=0,150248572621117521684473287070124281310508255342236143480056585...

23/127=0,156018187646075783806335466527454088323037386403162677713672044...

24/127=0,162677713672044156018187646075783806335466527454088323037386403...

25/127=0,168447328707012428131050825534223614348005658515024857262111752...

26/127=0,175216844732870701242813105082553422361434800565851502485726211...

27/127=0,181876460757838063354665274540883230373864031626777136720441560...

28/127=0,187646075783806335466527454088323037386403162677713672044156018...

29/127=0,204415601818764607578380633546652745408832303738640316267771367...

30/127=0,211175216844732870701242813105082553422361434800565851502485726...

31/127=0,216844732870701242813105082553422361434800565851502485726211175...

32/127=0,223614348005658515024857262111752168447328707012428131050825534...

33/127=0,230373864031626777136720441560181876460757838063354665274540883...

34/127=0,236143480056585150248572621117521684473287070124281310508255342...

35/127=0,242813105082553422361434800565851502485726211175216844732870701...

36/127=0,248572621117521684473287070124281310508255342236143480056585150...

37/127=0,255342236143480056585150248572621117521684473287070124281310508...

38/127=0,262111752168447328707012428131050825534223614348005658515024857...

39/127=0,267771367204415601818764607578380633546652745408832303738640316...

40/127=0,274540883230373864031626777136720441560181876460757838063354665...

41/127=0,281310508255342236143480056585150248572621117521684473287070124...

42/127=0,287070124281310508255342236143480056585150248572621117521684473...

43/127=0,303738640316267771367204415601818764607578380633546652745408832...

44/127=0,310508255342236143480056585150248572621117521684473287070124281...

45/127=0,316267771367204415601818764607578380633546652745408832303738640...

46/127=0,323037386403162677713672044156018187646075783806335466527454088...

47/127=0,328707012428131050825534223614348005658515024857262111752168447...

48/127=0,335466527454088323037386403162677713672044156018187646075783806...

49/127=0,342236143480056585150248572621117521684473287070124281310508255...

50/127=0,348005658515024857262111752168447328707012428131050825534223614...

51/127=0,354665274540883230373864031626777136720441560181876460757838063...

52/127=0,361434800565851502485726211175216844732870701242813105082553422...

53/127=0,367204415601818764607578380633546652745408832303738640316267771...

54/127=0,373864031626777136720441560181876460757838063354665274540883230...

55/127=0,380633546652745408832303738640316267771367204415601818764607578...

56/127=0,386403162677713672044156018187646075783806335466527454088323037...

57/127=0,403162677713672044156018187646075783806335466527454088323037386...

58/127=0,408832303738640316267771367204415601818764607578380633546652745...

59/127=0,415601818764607578380633546652745408832303738640316267771367204...

60/127=0,422361434800565851502485726211175216844732870701242813105082553...

61/127=0,428131050825534223614348005658515024857262111752168447328707012...

62/127=0,434800565851502485726211175216844732870701242813105082553422361...

63/127=0,441560181876460757838063354665274540883230373864031626777136720...

64/127=0,447328707012428131050825534223614348005658515024857262111752168...

65/127=0,454088323037386403162677713672044156018187646075783806335466527...

66/127=0,460757838063354665274540883230373864031626777136720441560181876...

67/127=0,466527454088323037386403162677713672044156018187646075783806335...

68/127=0,473287070124281310508255342236143480056585150248572621117521684...

69/127=0,480056585150248572621117521684473287070124281310508255342236143...

70/127=0,485726211175216844732870701242813105082553422361434800565851502...

71/127=0,502485726211175216844732870701242813105082553422361434800565851...

72/127=0,508255342236143480056585150248572621117521684473287070124281310...

73/127=0,515024857262111752168447328707012428131050825534223614348005658...

74/127=0,521684473287070124281310508255342236143480056585150248572621117...

75/127=0,527454088323037386403162677713672044156018187646075783806335466...

76/127=0,534223614348005658515024857262111752168447328707012428131050825...

77/127=0,540883230373864031626777136720441560181876460757838063354665274...

78/127=0,546652745408832303738640316267771367204415601818764607578380633...

79/127=0,553422361434800565851502485726211175216844732870701242813105082...

80/127=0,560181876460757838063354665274540883230373864031626777136720441...

81/127=0,565851502485726211175216844732870701242813105082553422361434800...

82/127=0,572621117521684473287070124281310508255342236143480056585150248...

83/127=0,578380633546652745408832303738640316267771367204415601818764607...

84/127=0,585150248572621117521684473287070124281310508255342236143480056...

85/127=0,601818764607578380633546652745408832303738640316267771367204415...

86/127=0,607578380633546652745408832303738640316267771367204415601818764...

87/127=0,614348005658515024857262111752168447328707012428131050825534223...

88/127=0,621117521684473287070124281310508255342236143480056585150248572...

89/127=0,626777136720441560181876460757838063354665274540883230373864031...

90/127=0,633546652745408832303738640316267771367204415601818764607578380...

91/127=0,640316267771367204415601818764607578380633546652745408832303738...

92/127=0,646075783806335466527454088323037386403162677713672044156018187...

93/127=0,652745408832303738640316267771367204415601818764607578380633546...

94/127=0,658515024857262111752168447328707012428131050825534223614348005...

95/127=0,665274540883230373864031626777136720441560181876460757838063354...

96/127=0,672044156018187646075783806335466527454088323037386403162677713...

97/127=0,677713672044156018187646075783806335466527454088323037386403162...

98/127=0,684473287070124281310508255342236143480056585150248572621117521...

99/127=0,701242813105082553422361434800565851502485726211175216844732870...

100/127=0,707012428131050825534223614348005658515024857262111752168447328...

101/127=0,713672044156018187646075783806335466527454088323037386403162677...

102/127=0,720441560181876460757838063354665274540883230373864031626777136...

103/127=0,726211175216844732870701242813105082553422361434800565851502485...

104/127=0,732870701242813105082553422361434800565851502485726211175216844...

105/127=0,738640316267771367204415601818764607578380633546652745408832303...

106/127=0,745408832303738640316267771367204415601818764607578380633546652...

107/127=0,752168447328707012428131050825534223614348005658515024857262111...

108/127=0,757838063354665274540883230373864031626777136720441560181876460...

109/127=0,764607578380633546652745408832303738640316267771367204415601818...

110/127=0,771367204415601818764607578380633546652745408832303738640316267...

111/127=0,777136720441560181876460757838063354665274540883230373864031626...

112/127=0,783806335466527454088323037386403162677713672044156018187646075...

113/127=0,800565851502485726211175216844732870701242813105082553422361434...

114/127=0,806335466527454088323037386403162677713672044156018187646075783...

115/127=0,813105082553422361434800565851502485726211175216844732870701242...

116/127=0,818764607578380633546652745408832303738640316267771367204415601...

117/127=0,825534223614348005658515024857262111752168447328707012428131050...

118/127=0,832303738640316267771367204415601818764607578380633546652745408...

119/127=0,838063354665274540883230373864031626777136720441560181876460757...

120/127=0,844732870701242813105082553422361434800565851502485726211175216...

121/127=0,851502485726211175216844732870701242813105082553422361434800565...

122/127=0,857262111752168447328707012428131050825534223614348005658515024...

123/127=0,864031626777136720441560181876460757838063354665274540883230373...

124/127=0,870701242813105082553422361434800565851502485726211175216844732...

125/127=0,876460757838063354665274540883230373864031626777136720441560181...

126/127=0,883230373864031626777136720441560181876460757838063354665274540...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (63) est égal à 126 et donc au premier -1.