Liste des fractions de n/61 en base 3.

Il existe 6 périodes de 10 chiffres pour n/61 en base 3.

Pour toutes les fractions de n/61 en base 3, la période de 1/61 revient alors 10 fois (en orange)

1/61=0,0001022212...

2/61=0,0002122201...

3/61=0,0010222120...

4/61=0,0012022102...

5/61=0,0020122021...

6/61=0,0021222010...

7/61=0,0100021222...

8/61=0,0101121211...

9/61=0,0102221200...

10/61=0,0111021112...

11/61=0,0112121101...

12/61=0,0120221020...

13/61=0,0122021002...

14/61=0,0200120221...

15/61=0,0201220210...

16/61=0,0210020122...

17/61=0,0211120111...

18/61=0,0212220100...

19/61=0,0221020012...

20/61=0,0222120001...

21/61=0,1000212220...

22/61=0,1002012202...

23/61=0,1010112121...

24/61=0,1011212110...

25/61=0,1020012022...

26/61=0,1021112011...

27/61=0,1022212000...

28/61=0,1101011212...

29/61=0,1102111201...

30/61=0,1110211120...

31/61=0,1112011102...

32/61=0,1120111021...

33/61=0,1121211010...

34/61=0,1200010222...

35/61=0,1201110211...

36/61=0,1202210200...

37/61=0,1211010112...

38/61=0,1212110101...

39/61=0,1220210020...

40/61=0,1222010002...

41/61=0,2000102221...

42/61=0,2001202210...

43/61=0,2010002122...

44/61=0,2011102111...

45/61=0,2012202100...

46/61=0,2021002012...

47/61=0,2022102001...

48/61=0,2100201220...

49/61=0,2102001202...

50/61=0,2110101121...

51/61=0,2111201110...

52/61=0,2120001022...

53/61=0,2121101011...

54/61=0,2122201000...

55/61=0,2201000212...

56/61=0,2202100201...

57/61=0,2210200120...

58/61=0,2212000102...

59/61=0,2220100021...

60/61=0,2221200010...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (10) est égal à 60 et donc au premier -1.