Il existe 2 périodes de 53 chiffres pour n/107 en base 4.

Pour toutes les fractions de n/107 en base 4, la période de 1/107 revient alors 53 fois (en orange)

1/107=0,00021210133012211011120201133230313001302311311032331...

2/107=0,00103020332031022022301002333121232003211223222131322...

3/107=0,00130231131103233100021210133012211011120201133230313...

4/107=0,00212101330122110111202011332303130013023113110323310...

5/107=0,00233312123200321122322213132200103020332031022022301...

6/107=0,00321122322213132200103020332031022022301002333121232...

7/107=0,01002333121232003211223222131322001030203320310220223...

8/107=0,01030203320310220223010023331212320032112232221313220...

9/107=0,01112020113323031300130231131103233100021210133012211...

10/107=0,01133230313001302311311032331000212101330122110111202...

11/107=0,01221101112020113323031300130231131103233100021210133...

12/107=0,01302311311032331000212101330122110111202011332303130...

13/107=0,01330122110111202011332303130013023113110323310002121...

14/107=0,02011332303130013023113110323310002121013301221101112...

15/107=0,02033203102202230100233312123200321122322213132200103...

16/107=0,02121013301221101112020113323031300130231131103233100...

17/107=0,02202230100233312123200321122322213132200103020332031...

18/107=0,02230100233312123200321122322213132200103020332031022...

19/107=0,02311311032331000212101330122110111202011332303130013...

20/107=0,02333121232003211223222131322001030203320310220223010...

21/107=0,03020332031022022301002333121232003211223222131322001...

22/107=0,03102202230100233312123200321122322213132200103020332...

23/107=0,03130013023113110323310002121013301221101112020113323...

24/107=0,03211223222131322001030203320310220223010023331212320...

25/107=0,03233100021210133012211011120201133230313001302311311...

26/107=0,03320310220223010023331212320032112232221313220010302...

27/107=0,10002121013301221101112020113323031300130231131103233...

28/107=0,10023331212320032112232221313220010302033203102202230...

29/107=0,10111202011332303130013023113110323310002121013301221...

30/107=0,10133012211011120201133230313001302311311032331000212...

31/107=0,10220223010023331212320032112232221313220010302033203...

32/107=0,10302033203102202230100233312123200321122322213132200...

33/107=0,10323310002121013301221101112020113323031300130231131...

34/107=0,11011120201133230313001302311311032331000212101330122...

35/107=0,11032331000212101330122110111202011332303130013023113...

36/107=0,11120201133230313001302311311032331000212101330122110...

37/107=0,11202011332303130013023113110323310002121013301221101...

38/107=0,11223222131322001030203320310220223010023331212320032...

39/107=0,11311032331000212101330122110111202011332303130013023...

40/107=0,11332303130013023113110323310002121013301221101112020...

41/107=0,12020113323031300130231131103233100021210133012211011...

42/107=0,12101330122110111202011332303130013023113110323310002...

43/107=0,12123200321122322213132200103020332031022022301002333...

44/107=0,12211011120201133230313001302311311032331000212101330...

45/107=0,12232221313220010302033203102202230100233312123200321...

46/107=0,12320032112232221313220010302033203102202230100233312...

47/107=0,13001302311311032331000212101330122110111202011332303...

48/107=0,13023113110323310002121013301221101112020113323031300...

49/107=0,13110323310002121013301221101112020113323031300130231...

50/107=0,13132200103020332031022022301002333121232003211223222...

51/107=0,13220010302033203102202230100233312123200321122322213...

52/107=0,13301221101112020113323031300130231131103233100021210...

53/107=0,13323031300130231131103233100021210133012211011120201...

54/107=0,20010302033203102202230100233312123200321122322213132...

55/107=0,20032112232221313220010302033203102202230100233312123...

56/107=0,20113323031300130231131103233100021210133012211011120...

57/107=0,20201133230313001302311311032331000212101330122110111...

58/107=0,20223010023331212320032112232221313220010302033203102...

59/107=0,20310220223010023331212320032112232221313220010302033...

60/107=0,20332031022022301002333121232003211223222131322001030...

61/107=0,21013301221101112020113323031300130231131103233100021...

62/107=0,21101112020113323031300130231131103233100021210133012...

63/107=0,21122322213132200103020332031022022301002333121232003...

64/107=0,21210133012211011120201133230313001302311311032331000...

65/107=0,21232003211223222131322001030203320310220223010023331...

66/107=0,21313220010302033203102202230100233312123200321122322...

67/107=0,22001030203320310220223010023331212320032112232221313...

68/107=0,22022301002333121232003211223222131322001030203320310...

69/107=0,22110111202011332303130013023113110323310002121013301...

70/107=0,22131322001030203320310220223010023331212320032112232...

71/107=0,22213132200103020332031022022301002333121232003211223...

72/107=0,22301002333121232003211223222131322001030203320310220...

73/107=0,22322213132200103020332031022022301002333121232003211...

74/107=0,23010023331212320032112232221313220010302033203102202...

75/107=0,23031300130231131103233100021210133012211011120201133...

76/107=0,23113110323310002121013301221101112020113323031300130...

77/107=0,23200321122322213132200103020332031022022301002333121...

78/107=0,23222131322001030203320310220223010023331212320032112...

79/107=0,23310002121013301221101112020113323031300130231131103...

80/107=0,23331212320032112232221313220010302033203102202230100...

81/107=0,30013023113110323310002121013301221101112020113323031...

82/107=0,30100233312123200321122322213132200103020332031022022...

83/107=0,30122110111202011332303130013023113110323310002121013...

84/107=0,30203320310220223010023331212320032112232221313220010...

85/107=0,30231131103233100021210133012211011120201133230313001...

86/107=0,30313001302311311032331000212101330122110111202011332...

87/107=0,31000212101330122110111202011332303130013023113110323...

88/107=0,31022022301002333121232003211223222131322001030203320...

89/107=0,31103233100021210133012211011120201133230313001302311...

90/107=0,31131103233100021210133012211011120201133230313001302...

91/107=0,31212320032112232221313220010302033203102202230100233...

92/107=0,31300130231131103233100021210133012211011120201133230...

93/107=0,31322001030203320310220223010023331212320032112232221...

94/107=0,32003211223222131322001030203320310220223010023331212...

95/107=0,32031022022301002333121232003211223222131322001030203...

96/107=0,32112232221313220010302033203102202230100233312123200...

97/107=0,32200103020332031022022301002333121232003211223222131...

98/107=0,32221313220010302033203102202230100233312123200321122...

99/107=0,32303130013023113110323310002121013301221101112020113...

100/107=0,32331000212101330122110111202011332303130013023113110...

101/107=0,33012211011120201133230313001302311311032331000212101...

102/107=0,33100021210133012211011120201133230313001302311311032...

103/107=0,33121232003211223222131322001030203320310220223010023...

104/107=0,33203102202230100233312123200321122322213132200103020...

105/107=0,33230313001302311311032331000212101330122110111202011...

106/107=0,33312123200321122322213132200103020332031022022301002...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (53) est égal à 106 et donc au premier -1.