Il existe 2 périodes de 41 chiffres pour n/83 en base 4.

Pour toutes les fractions de n/83 en base 4, la période de 1/83 revient alors 41 fois (en orange)

1/83=0,00030111211302013231133213110310123300211...

2/83=0,00120223023210033122333032221220313201022...

3/83=0,00211000301112113020132311332131103101233...

4/83=0,00301112113020132311332131103101233002110...

5/83=0,00331223330322212203132010220012022302321...

6/83=0,01022001202230232100331223330322212203132...

7/83=0,01112113020132311332131103101233002110003...

8/83=0,01202230232100331223330322212203132010220...

9/83=0,01233002110003011121130201323113321311031...

10/83=0,01323113321311031012330021100030111211302...

11/83=0,02013231133213110310123300211000301112113...

12/83=0,02110003011121130201323113321311031012330...

13/83=0,02200120223023210033122333032221220313201...

14/83=0,02230232100331223330322212203132010220012...

15/83=0,02321003312233303222122031320102200120223...

16/83=0,03011121130201323113321311031012330021100...

17/83=0,03101233002110003011121130201323113321311...

18/83=0,03132010220012022302321003312233303222122...

19/83=0,03222122031320102200120223023210033122333...

20/83=0,03312233303222122031320102200120223023210...

21/83=0,10003011121130201323113321311031012330021...

22/83=0,10033122333032221220313201022001202230232...

23/83=0,10123300211000301112113020132311332131103...

24/83=0,10220012022302321003312233303222122031320...

25/83=0,10310123300211000301112113020132311332131...

26/83=0,11000301112113020132311332131103101233002...

27/83=0,11031012330021100030111211302013231133213...

28/83=0,11121130201323113321311031012330021100030...

29/83=0,11211302013231133213110310123300211000301...

30/83=0,11302013231133213110310123300211000301112...

31/83=0,11332131103101233002110003011121130201323...

32/83=0,12022302321003312233303222122031320102200...

33/83=0,12113020132311332131103101233002110003011...

34/83=0,12203132010220012022302321003312233303222...

35/83=0,12233303222122031320102200120223023210033...

36/83=0,12330021100030111211302013231133213110310...

37/83=0,13020132311332131103101233002110003011121...

38/83=0,13110310123300211000301112113020132311332...

39/83=0,13201022001202230232100331223330322212203...

40/83=0,13231133213110310123300211000301112113020...

41/83=0,13321311031012330021100030111211302013231...

42/83=0,20012022302321003312233303222122031320102...

43/83=0,20102200120223023210033122333032221220313...

44/83=0,20132311332131103101233002110003011121130...

45/83=0,20223023210033122333032221220313201022001...

46/83=0,20313201022001202230232100331223330322212...

47/83=0,21003312233303222122031320102200120223023...

48/83=0,21100030111211302013231133213110310123300...

49/83=0,21130201323113321311031012330021100030111...

50/83=0,21220313201022001202230232100331223330322...

51/83=0,21311031012330021100030111211302013231133...

52/83=0,22001202230232100331223330322212203132010...

53/83=0,22031320102200120223023210033122333032221...

54/83=0,22122031320102200120223023210033122333032...

55/83=0,22212203132010220012022302321003312233303...

56/83=0,22302321003312233303222122031320102200120...

57/83=0,22333032221220313201022001202230232100331...

58/83=0,23023210033122333032221220313201022001202...

59/83=0,23113321311031012330021100030111211302013...

60/83=0,23210033122333032221220313201022001202230...

61/83=0,23300211000301112113020132311332131103101...

62/83=0,23330322212203132010220012022302321003312...

63/83=0,30021100030111211302013231133213110310123...

64/83=0,30111211302013231133213110310123300211000...

65/83=0,30201323113321311031012330021100030111211...

66/83=0,30232100331223330322212203132010220012022...

67/83=0,30322212203132010220012022302321003312233...

68/83=0,31012330021100030111211302013231133213110...

69/83=0,31103101233002110003011121130201323113321...

70/83=0,31133213110310123300211000301112113020132...

71/83=0,31223330322212203132010220012022302321003...

72/83=0,31320102200120223023210033122333032221220...

73/83=0,32010220012022302321003312233303222122031...

74/83=0,32100331223330322212203132010220012022302...

75/83=0,32131103101233002110003011121130201323113...

76/83=0,32221220313201022001202230232100331223330...

77/83=0,32311332131103101233002110003011121130201...

78/83=0,33002110003011121130201323113321311031012...

79/83=0,33032221220313201022001202230232100331223...

80/83=0,33122333032221220313201022001202230232100...

81/83=0,33213110310123300211000301112113020132311...

82/83=0,33303222122031320102200120223023210033122...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (41) est égal à 82 et donc au premier -1.