Il existe 2 périodes de 30 chiffres pour n/61 en base 4.

Pour toutes les fractions de n/61 en base 4, la période de 1/61 revient alors 30 fois (en orange)

1/61=0,001003021130110332330312203223...

2/61=0,002012102320221331321231013112...

3/61=0,003021130110332330312203223001...

4/61=0,010030211301103323303122032230...

5/61=0,011033233031220322300100302113...

6/61=0,012102320221331321231013112002...

7/61=0,013112002012102320221331321231...

8/61=0,020121023202213313212310131120...

9/61=0,021130110332330312203223001003...

10/61=0,022133132123101311200201210232...

11/61=0,023202213313212310131120020121...

12/61=0,030211301103323303122032230010...

13/61=0,031220322300100302113011033233...

14/61=0,032230010030211301103323303122...

15/61=0,033233031220322300100302113011...

16/61=0,100302113011033233031220322300...

17/61=0,101311200201210232022133132123...

18/61=0,102320221331321231013112002012...

19/61=0,103323303122032230010030211301...

20/61=0,110332330312203223001003021130...

21/61=0,112002012102320221331321231013...

22/61=0,113011033233031220322300100302...

23/61=0,120020121023202213313212310131...

24/61=0,121023202213313212310131120020...

25/61=0,122032230010030211301103323303...

26/61=0,123101311200201210232022133132...

27/61=0,130110332330312203223001003021...

28/61=0,131120020121023202213313212310...

29/61=0,132123101311200201210232022133...

30/61=0,133132123101311200201210232022...

31/61=0,200201210232022133132123101311...

32/61=0,201210232022133132123101311200...

33/61=0,202213313212310131120020121023...

34/61=0,203223001003021130110332330312...

35/61=0,210232022133132123101311200201...

36/61=0,211301103323303122032230010030...

37/61=0,212310131120020121023202213313...

38/61=0,213313212310131120020121023202...

39/61=0,220322300100302113011033233031...

40/61=0,221331321231013112002012102320...

41/61=0,223001003021130110332330312203...

42/61=0,230010030211301103323303122032...

43/61=0,231013112002012102320221331321...

44/61=0,232022133132123101311200201210...

45/61=0,233031220322300100302113011033...

46/61=0,300100302113011033233031220322...

47/61=0,301103323303122032230010030211...

48/61=0,302113011033233031220322300100...

49/61=0,303122032230010030211301103323...

50/61=0,310131120020121023202213313212...

51/61=0,311200201210232022133132123101...

52/61=0,312203223001003021130110332330...

53/61=0,313212310131120020121023202213...

54/61=0,320221331321231013112002012102...

55/61=0,321231013112002012102320221331...

56/61=0,322300100302113011033233031220...

57/61=0,323303122032230010030211301103...

58/61=0,330312203223001003021130110332...

59/61=0,331321231013112002012102320221...

60/61=0,332330312203223001003021130110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (30) est égal à 60 et donc au premier -1.