Il existe 3 périodes de 22 chiffres pour n/67 en base 8.

Pour toutes les fractions de n/67 en base 8, la période de 1/67 revient alors 22 fois (en orange)

1/67=0,0075104615277026731625...

2/67=0,0172211432576055663452...

3/67=0,0267316250075104615277...

4/67=0,0364423065374133547124...

5/67=0,0461527702673162500751...

6/67=0,0556634520172211432576...

7/67=0,0653741335471240364423...

8/67=0,0751046152770267316250...

9/67=0,1046152770267316250075...

10/67=0,1143257605566345201722...

11/67=0,1240364423065374133547...

12/67=0,1335471240364423065374...

13/67=0,1432576055663452017221...

14/67=0,1527702673162500751046...

15/67=0,1625007510461527702673...

16/67=0,1722114325760556634520...

17/67=0,2017221143257605566345...

18/67=0,2114325760556634520172...

19/67=0,2211432576055663452017...

20/67=0,2306537413354712403644...

21/67=0,2403644230653741335471...

22/67=0,2500751046152770267316...

23/67=0,2576055663452017221143...

24/67=0,2673162500751046152770...

25/67=0,2770267316250075104615...

26/67=0,3065374133547124036442...

27/67=0,3162500751046152770267...

28/67=0,3257605566345201722114...

29/67=0,3354712403644230653741...

30/67=0,3452017221143257605566...

31/67=0,3547124036442306537413...

32/67=0,3644230653741335471240...

33/67=0,3741335471240364423065...

34/67=0,4036442306537413354712...

35/67=0,4133547124036442306537...

36/67=0,4230653741335471240364...

37/67=0,4325760556634520172211...

38/67=0,4423065374133547124036...

39/67=0,4520172211432576055663...

40/67=0,4615277026731625007510...

41/67=0,4712403644230653741335...

42/67=0,5007510461527702673162...

43/67=0,5104615277026731625007...

44/67=0,5201722114325760556634...

45/67=0,5277026731625007510461...

46/67=0,5374133547124036442306...

47/67=0,5471240364423065374133...

48/67=0,5566345201722114325760...

49/67=0,5663452017221143257605...

50/67=0,5760556634520172211432...

51/67=0,6055663452017221143257...

52/67=0,6152770267316250075104...

53/67=0,6250075104615277026731...

54/67=0,6345201722114325760556...

55/67=0,6442306537413354712403...

56/67=0,6537413354712403644230...

57/67=0,6634520172211432576055...

58/67=0,6731625007510461527702...

59/67=0,7026731625007510461527...

60/67=0,7124036442306537413354...

61/67=0,7221143257605566345201...

62/67=0,7316250075104615277026...

63/67=0,7413354712403644230653...

64/67=0,7510461527702673162500...

65/67=0,7605566345201722114325...

66/67=0,7702673162500751046152...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (22) est égal à 66 et donc au premier -1.