Il existe 2 périodes de 33 chiffres pour n/67 en base 6.

Pour toutes les fractions de n/67 en base 6, la période de 1/67 revient alors 33 fois (en orange)

1/67=0,003120205212332542154531514113045...

2/67=0,010240414425105524353503432230134...

3/67=0,013401024041442510552435350343223...

4/67=0,020521233254215453151411304500312...

5/67=0,024041442510552435350343223013401...

6/67=0,031202052123325421545315141130450...

7/67=0,034322301340102404144251055243535...

8/67=0,041442510552435350343223013401024...

9/67=0,045003120205212332542154531514113...

10/67=0,052123325421545315141130450031202...

11/67=0,055243535034322301340102404144251...

12/67=0,102404144251055243535034322301340...

13/67=0,105524353503432230134010240414425...

14/67=0,113045003120205212332542154531514...

15/67=0,120205212332542154531514113045003...

16/67=0,123325421545315141130450031202052...

17/67=0,130450031202052123325421545315141...

18/67=0,134010240414425105524353503432230...

19/67=0,141130450031202052123325421545315...

20/67=0,144251055243535034322301340102404...

21/67=0,151411304500312020521233254215453...

22/67=0,154531514113045003120205212332542...

23/67=0,202052123325421545315141130450031...

24/67=0,205212332542154531514113045003120...

25/67=0,212332542154531514113045003120205...

26/67=0,215453151411304500312020521233254...

27/67=0,223013401024041442510552435350343...

28/67=0,230134010240414425105524353503432...

29/67=0,233254215453151411304500312020521...

30/67=0,240414425105524353503432230134010...

31/67=0,243535034322301340102404144251055...

32/67=0,251055243535034322301340102404144...

33/67=0,254215453151411304500312020521233...

34/67=0,301340102404144251055243535034322...

35/67=0,304500312020521233254215453151411...

36/67=0,312020521233254215453151411304500...

37/67=0,315141130450031202052123325421545...

38/67=0,322301340102404144251055243535034...

39/67=0,325421545315141130450031202052123...

40/67=0,332542154531514113045003120205212...

41/67=0,340102404144251055243535034322301...

42/67=0,343223013401024041442510552435350...

43/67=0,350343223013401024041442510552435...

44/67=0,353503432230134010240414425105524...

45/67=0,401024041442510552435350343223013...

46/67=0,404144251055243535034322301340102...

47/67=0,411304500312020521233254215453151...

48/67=0,414425105524353503432230134010240...

49/67=0,421545315141130450031202052123325...

50/67=0,425105524353503432230134010240414...

51/67=0,432230134010240414425105524353503...

52/67=0,435350343223013401024041442510552...

53/67=0,442510552435350343223013401024041...

54/67=0,450031202052123325421545315141130...

55/67=0,453151411304500312020521233254215...

56/67=0,500312020521233254215453151411304...

57/67=0,503432230134010240414425105524353...

58/67=0,510552435350343223013401024041442...

59/67=0,514113045003120205212332542154531...

60/67=0,521233254215453151411304500312020...

61/67=0,524353503432230134010240414425105...

62/67=0,531514113045003120205212332542154...

63/67=0,535034322301340102404144251055243...

64/67=0,542154531514113045003120205212332...

65/67=0,545315141130450031202052123325421...

66/67=0,552435350343223013401024041442510...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (33) est égal à 66 et donc au premier -1.