Il existe 3 périodes de 20 chiffres pour n/61 en base 8.

Pour toutes les fractions de n/61 en base 8, la période de 1/61 revient alors 20 fois (en orange)

1/61=0,01031134247674664353...

2/61=0,02062270517571550726...

3/61=0,03113424767466435301...

4/61=0,04144561237363321654...

5/61=0,05175715507260206227...

6/61=0,06227051757155072602...

7/61=0,07260206227051757155...

8/61=0,10311342476746643530...

9/61=0,11342476746643530103...

10/61=0,12373633216540414456...

11/61=0,13424767466435301031...

12/61=0,14456123736332165404...

13/61=0,15507260206227051757...

14/61=0,16540414456123736332...

15/61=0,17571550726020622705...

16/61=0,20622705175715507260...

17/61=0,21654041445612373633...

18/61=0,22705175715507260206...

19/61=0,23736332165404144561...

20/61=0,24767466435301031134...

21/61=0,26020622705175715507...

22/61=0,27051757155072602062...

23/61=0,30103113424767466435...

24/61=0,31134247674664353010...

25/61=0,32165404144561237363...

26/61=0,33216540414456123736...

27/61=0,34247674664353010311...

28/61=0,35301031134247674664...

29/61=0,36332165404144561237...

30/61=0,37363321654041445612...

31/61=0,40414456123736332165...

32/61=0,41445612373633216540...

33/61=0,42476746643530103113...

34/61=0,43530103113424767466...

35/61=0,44561237363321654041...

36/61=0,45612373633216540414...

37/61=0,46643530103113424767...

38/61=0,47674664353010311342...

39/61=0,50726020622705175715...

40/61=0,51757155072602062270...

41/61=0,53010311342476746643...

42/61=0,54041445612373633216...

43/61=0,55072602062270517571...

44/61=0,56123736332165404144...

45/61=0,57155072602062270517...

46/61=0,60206227051757155072...

47/61=0,61237363321654041445...

48/61=0,62270517571550726020...

49/61=0,63321654041445612373...

50/61=0,64353010311342476746...

51/61=0,65404144561237363321...

52/61=0,66435301031134247674...

53/61=0,67466435301031134247...

54/61=0,70517571550726020622...

55/61=0,71550726020622705175...

56/61=0,72602062270517571550...

57/61=0,73633216540414456123...

58/61=0,74664353010311342476...

59/61=0,75715507260206227051...

60/61=0,76746643530103113424...

On remarque que le produit du nombre de périodes (3) et de leurs longueurs (20) est égal à 60 et donc au premier -1.