Il existe 2 périodes de 53 chiffres pour n/107 en base 3.

Pour toutes les fractions de n/107 en base 3, la période de 1/107 revient alors 53 fois (en orange)

1/107=0,00002021022120122102002202221111010021120101121011001...

2/107=0,00011112122011021211012112212222020120010210012022002...

3/107=0,00020210221201221020022022211110100211201011210110010...

4/107=0,00100002021022120122102002202221111010021120101121011...

5/107=0,00102100120220020001111212201102121101211221222202012...

6/107=0,00111121220110212110121122122220201200102100120220020...

7/107=0,00120220020001111212201102121101211221222202012001021...

8/107=0,00200011112122011021211012112212222020120010210012022...

9/107=0,00202102212012210200220222111101002112010112101100100...

10/107=0,00211201011210110010000202102212012210200220222111101...

11/107=0,00220222111101002112010112101100100002021022120122102...

12/107=0,01000020210221201221020022022211110100211201011210110...

13/107=0,01002112010112101100100002021022120122102002202221111...

14/107=0,01011210110010000202102212012210200220222111101002112...

15/107=0,01021001202200200011112122011021211012112212222020120...

16/107=0,01100100002021022120122102002202221111010021120101121...

17/107=0,01102121101211221222202012001021001202200200011112122...

18/107=0,01111212201102121101211221222202012001021001202200200...

19/107=0,01121011001000020210221201221020022022211110100211201...

20/107=0,01200102100120220020001111212201102121101211221222202...

21/107=0,01202200200011112122011021211012112212222020120010210...

22/107=0,01211221222202012001021001202200200011112122011021211...

23/107=0,01221020022022211110100211201011210110010000202102212...

24/107=0,02000111121220110212110121122122220201200102100120220...

25/107=0,02002202221111010021120101121011001000020210221201221...

26/107=0,02012001021001202200200011112122011021211012112212222...

27/107=0,02021022120122102002202221111010021120101121011001000...

28/107=0,02100120220020001111212201102121101211221222202012001...

29/107=0,02102212012210200220222111101002112010112101100100002...

30/107=0,02112010112101100100002021022120122102002202221111010...

31/107=0,02121101211221222202012001021001202200200011112122011...

32/107=0,02200200011112122011021211012112212222020120010210012...

33/107=0,02202221111010021120101121011001000020210221201221020...

34/107=0,02212012210200220222111101002112010112101100100002021...

35/107=0,02221111010021120101121011001000020210221201221020022...

36/107=0,10000202102212012210200220222111101002112010112101100...

37/107=0,10010000202102212012210200220222111101002112010112101...

38/107=0,10012022002000111121220110212110121122122220201200102...

39/107=0,10021120101121011001000020210221201221020022022211110...

40/107=0,10100211201011210110010000202102212012210200220222111...

41/107=0,10110010000202102212012210200220222111101002112010112...

42/107=0,10112101100100002021022120122102002202221111010021120...

43/107=0,10121122122220201200102100120220020001111212201102121...

44/107=0,10200220222111101002112010112101100100002021022120122...

45/107=0,10210012022002000111121220110212110121122122220201200...

46/107=0,10212110121122122220201200102100120220020001111212201...

47/107=0,10221201221020022022211110100211201011210110010000202...

48/107=0,11001000020210221201221020022022211110100211201011210...

49/107=0,11010021120101121011001000020210221201221020022022211...

50/107=0,11012112212222020120010210012022002000111121220110212...

51/107=0,11021211012112212222020120010210012022002000111121220...

52/107=0,11101002112010112101100100002021022120122102002202221...

53/107=0,11110100211201011210110010000202102212012210200220222...

54/107=0,11112122011021211012112212222020120010210012022002000...

55/107=0,11121220110212110121122122220201200102100120220020001...

56/107=0,11201011210110010000202102212012210200220222111101002...

57/107=0,11210110010000202102212012210200220222111101002112010...

58/107=0,11212201102121101211221222202012001021001202200200011...

59/107=0,11221222202012001021001202200200011112122011021211012...

60/107=0,12001021001202200200011112122011021211012112212222020...

61/107=0,12010112101100100002021022120122102002202221111010021...

62/107=0,12012210200220222111101002112010112101100100002021022...

63/107=0,12022002000111121220110212110121122122220201200102100...

64/107=0,12101100100002021022120122102002202221111010021120101...

65/107=0,12110121122122220201200102100120220020001111212201102...

66/107=0,12112212222020120010210012022002000111121220110212110...

67/107=0,12122011021211012112212222020120010210012022002000111...

68/107=0,12201102121101211221222202012001021001202200200011112...

69/107=0,12210200220222111101002112010112101100100002021022120...

70/107=0,12212222020120010210012022002000111121220110212110121...

71/107=0,12222020120010210012022002000111121220110212110121122...

72/107=0,20001111212201102121101211221222202012001021001202200...

73/107=0,20010210012022002000111121220110212110121122122220201...

74/107=0,20020001111212201102121101211221222202012001021001202...

75/107=0,20022022211110100211201011210110010000202102212012210...

76/107=0,20101121011001000020210221201221020022022211110100211...

77/107=0,20110212110121122122220201200102100120220020001111212...

78/107=0,20120010210012022002000111121220110212110121122122220...

79/107=0,20122102002202221111010021120101121011001000020210221...

80/107=0,20201200102100120220020001111212201102121101211221222...

81/107=0,20210221201221020022022211110100211201011210110010000...

82/107=0,20220020001111212201102121101211221222202012001021001...

83/107=0,20222111101002112010112101100100002021022120122102002...

84/107=0,21001202200200011112122011021211012112212222020120010...

85/107=0,21011001000020210221201221020022022211110100211201011...

86/107=0,21020022022211110100211201011210110010000202102212012...

87/107=0,21022120122102002202221111010021120101121011001000020...

88/107=0,21101211221222202012001021001202200200011112122011021...

89/107=0,21111010021120101121011001000020210221201221020022022...

90/107=0,21120101121011001000020210221201221020022022211110100...

91/107=0,21122122220201200102100120220020001111212201102121101...

92/107=0,21201221020022022211110100211201011210110010000202102...

93/107=0,21211012112212222020120010210012022002000111121220110...

94/107=0,21220110212110121122122220201200102100120220020001111...

95/107=0,21222202012001021001202200200011112122011021211012112...

96/107=0,22002000111121220110212110121122122220201200102100120...

97/107=0,22011021211012112212222020120010210012022002000111121...

98/107=0,22020120010210012022002000111121220110212110121122122...

99/107=0,22022211110100211201011210110010000202102212012210200...

100/107=0,22102002202221111010021120101121011001000020210221201...

101/107=0,22111101002112010112101100100002021022120122102002202...

102/107=0,22120122102002202221111010021120101121011001000020210...

103/107=0,22122220201200102100120220020001111212201102121101211...

104/107=0,22202012001021001202200200011112122011021211012112212...

105/107=0,22211110100211201011210110010000202102212012210200220...

106/107=0,22220201200102100120220020001111212201102121101211221...

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