Il existe 6 périodes de 11 chiffres pour n/67 en base 9.

Pour toutes les fractions de n/67 en base 9, la période de 1/67 revient alors 11 fois (en orange)

1/67=0,01178285332...

2/67=0,02367581664...

3/67=0,03556877106...

4/67=0,04746273438...

5/67=0,06035568771...

6/67=0,07224865213...

7/67=0,08414261545...

8/67=0,10603556877...

9/67=0,11782853320...

10/67=0,13072248652...

11/67=0,14261545084...

12/67=0,15450841426...

13/67=0,16640236758...

14/67=0,17828533201...

15/67=0,20117828533...

16/67=0,21307224865...

17/67=0,22486521307...

18/67=0,23675816640...

19/67=0,24865213072...

20/67=0,26154508414...

21/67=0,27343804746...

22/67=0,28533201178...

23/67=0,30722486521...

24/67=0,32011782853...

25/67=0,33201178285...

26/67=0,34380474627...

27/67=0,35568771060...

28/67=0,36758166402...

29/67=0,38047462734...

30/67=0,40236758166...

31/67=0,41426154508...

32/67=0,42615450841...

33/67=0,43804746273...

34/67=0,45084142615...

35/67=0,46273438047...

36/67=0,47462734380...

37/67=0,48652130722...

38/67=0,50841426154...

39/67=0,52130722486...

40/67=0,53320117828...

41/67=0,54508414261...

42/67=0,55687710603...

43/67=0,56877106035...

44/67=0,58166402367...

45/67=0,60355687710...

46/67=0,61545084142...

47/67=0,62734380474...

48/67=0,64023675816...

49/67=0,65213072248...

50/67=0,66402367581...

51/67=0,67581664023...

52/67=0,68771060355...

53/67=0,71060355687...

54/67=0,72248652130...

55/67=0,73438047462...

56/67=0,74627343804...

57/67=0,75816640236...

58/67=0,77106035568...

59/67=0,78285332011...

60/67=0,80474627343...

61/67=0,81664023675...

62/67=0,82853320117...

63/67=0,84142615450...

64/67=0,85332011782...

65/67=0,86521307224...

66/67=0,87710603556...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (11) est égal à 66 et donc au premier -1.