Il existe 6 périodes de 16 chiffres pour n/97 en base 8.

Pour toutes les fractions de n/97 en base 8, la période de 1/97 revient alors 16 fois (en orange)

1/97=0,0052164077256137...

2/97=0,0124350176534276...

3/97=0,0176534276012435...

4/97=0,0250720375270574...

5/97=0,0323104474546733...

6/97=0,0375270574025072...

7/97=0,0447454673303231...

8/97=0,0521640772561370...

9/97=0,0574025072037527...

10/97=0,0646211171315666...

11/97=0,0720375270574025...

12/97=0,0772561370052164...

13/97=0,1044745467330323...

14/97=0,1117131566606462...

15/97=0,1171315666064621...

16/97=0,1243501765342760...

17/97=0,1315666064621117...

18/97=0,1370052164077256...

19/97=0,1442236263355415...

20/97=0,1514422362633554...

21/97=0,1566606462111713...

22/97=0,1640772561370052...

23/97=0,1713156660646211...

24/97=0,1765342760124350...

25/97=0,2037527057402507...

26/97=0,2111713156660646...

27/97=0,2164077256137005...

28/97=0,2236263355415144...

29/97=0,2310447454673303...

30/97=0,2362633554151442...

31/97=0,2435017653427601...

32/97=0,2507203752705740...

33/97=0,2561370052164077...

34/97=0,2633554151442236...

35/97=0,2705740250720375...

36/97=0,2760124350176534...

37/97=0,3032310447454673...

38/97=0,3104474546733032...

39/97=0,3156660646211171...

40/97=0,3231044745467330...

41/97=0,3303231044745467...

42/97=0,3355415144223626...

43/97=0,3427601243501765...

44/97=0,3501765342760124...

45/97=0,3554151442236263...

46/97=0,3626335541514422...

47/97=0,3700521640772561...

48/97=0,3752705740250720...

49/97=0,4025072037527057...

50/97=0,4077256137005216...

51/97=0,4151442236263355...

52/97=0,4223626335541514...

53/97=0,4276012435017653...

54/97=0,4350176534276012...

55/97=0,4422362633554151...

56/97=0,4474546733032310...

57/97=0,4546733032310447...

58/97=0,4621117131566606...

59/97=0,4673303231044745...

60/97=0,4745467330323104...

61/97=0,5017653427601243...

62/97=0,5072037527057402...

63/97=0,5144223626335541...

64/97=0,5216407725613700...

65/97=0,5270574025072037...

66/97=0,5342760124350176...

67/97=0,5415144223626335...

68/97=0,5467330323104474...

69/97=0,5541514422362633...

70/97=0,5613700521640772...

71/97=0,5666064621117131...

72/97=0,5740250720375270...

73/97=0,6012435017653427...

74/97=0,6064621117131566...

75/97=0,6137005216407725...

76/97=0,6211171315666064...

77/97=0,6263355415144223...

78/97=0,6335541514422362...

79/97=0,6407725613700521...

80/97=0,6462111713156660...

81/97=0,6534276012435017...

82/97=0,6606462111713156...

83/97=0,6660646211171315...

84/97=0,6733032310447454...

85/97=0,7005216407725613...

86/97=0,7057402507203752...

87/97=0,7131566606462111...

88/97=0,7203752705740250...

89/97=0,7256137005216407...

90/97=0,7330323104474546...

91/97=0,7402507203752705...

92/97=0,7454673303231044...

93/97=0,7527057402507203...

94/97=0,7601243501765342...

95/97=0,7653427601243501...

96/97=0,7725613700521640...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (16) est égal à 96 et donc au premier -1.