Il existe 8 périodes de 14 chiffres pour n/113 en base 4.

Pour toutes les fractions de n/113 en base 4, la période de 1/113 revient alors 14 fois (en orange)

1/113=0,00021003331233...

2/113=0,00102013323132...

3/113=0,00123023321031...

4/113=0,00210033312330...

5/113=0,00231103310223...

6/113=0,00312113302122...

7/113=0,00333123300021...

8/113=0,01020133231320...

9/113=0,01101203223213...

10/113=0,01122213221112...

11/113=0,01203223213011...

12/113=0,01230233210310...

13/113=0,01311303202203...

14/113=0,01332313200102...

15/113=0,02013323132001...

16/113=0,02100333123300...

17/113=0,02122003121133...

18/113=0,02203013113032...

19/113=0,02230023110331...

20/113=0,02311033102230...

21/113=0,02332103100123...

22/113=0,03013113032022...

23/113=0,03100123023321...

24/113=0,03121133021220...

25/113=0,03202203013113...

26/113=0,03223213011012...

27/113=0,03310223002311...

28/113=0,03331233000210...

29/113=0,10012302332103...

30/113=0,10033312330002...

31/113=0,10120322321301...

32/113=0,10201332313200...

33/113=0,10223002311033...

34/113=0,10310012302332...

35/113=0,10331022300231...

36/113=0,11012032232130...

37/113=0,11033102230023...

38/113=0,11120112221322...

39/113=0,11201122213221...

40/113=0,11222132211120...

41/113=0,11303202203013...

42/113=0,11330212200312...

43/113=0,12011222132211...

44/113=0,12032232130110...

45/113=0,12113302122003...

46/113=0,12200312113302...

47/113=0,12221322111201...

48/113=0,12302332103100...

49/113=0,12330002100333...

50/113=0,13011012032232...

51/113=0,13032022030131...

52/113=0,13113032022030...

53/113=0,13200102013323...

54/113=0,13221112011222...

55/113=0,13302122003121...

56/113=0,13323132001020...

57/113=0,20010201332313...

58/113=0,20031211330212...

59/113=0,20112221322111...

60/113=0,20133231320010...

61/113=0,20220301311303...

62/113=0,20301311303202...

63/113=0,20322321301101...

64/113=0,21003331233000...

65/113=0,21031001230233...

66/113=0,21112011222132...

67/113=0,21133021220031...

68/113=0,21220031211330...

69/113=0,21301101203223...

70/113=0,21322111201122...

71/113=0,22003121133021...

72/113=0,22030131130320...

73/113=0,22111201122213...

74/113=0,22132211120112...

75/113=0,22213221112011...

76/113=0,22300231103310...

77/113=0,22321301101203...

78/113=0,23002311033102...

79/113=0,23023321031001...

80/113=0,23110331022300...

81/113=0,23132001020133...

82/113=0,23213011012032...

83/113=0,23300021003331...

84/113=0,23321031001230...

85/113=0,30002100333123...

86/113=0,30023110331022...

87/113=0,30110120322321...

88/113=0,30131130320220...

89/113=0,30212200312113...

90/113=0,30233210310012...

91/113=0,30320220301311...

92/113=0,31001230233210...

93/113=0,31022300231103...

94/113=0,31103310223002...

95/113=0,31130320220301...

96/113=0,31211330212200...

97/113=0,31233000210033...

98/113=0,31320010201332...

99/113=0,32001020133231...

100/113=0,32022030131130...

101/113=0,32103100123023...

102/113=0,32130110120322...

103/113=0,32211120112221...

104/113=0,32232130110120...

105/113=0,32313200102013...

106/113=0,33000210033312...

107/113=0,33021220031211...

108/113=0,33102230023110...

109/113=0,33123300021003...

110/113=0,33210310012302...

111/113=0,33231320010201...

112/113=0,33312330002100...

On remarque que le produit du nombre de périodes (8) et de leurs longueurs (14) est égal à 112 et donc au premier -1.