Il existe 2 périodes de 50 chiffres pour n/101 en base 4.

Pour toutes les fractions de n/101 en base 4, la période de 1/101 revient alors 50 fois (en orange)

1/101=0,00022020313300302230112303331131302003303110322103...

2/101=0,00110101233201211120231213322323210013212221310212...

3/101=0,00132122213102120011010123320121112023121332232321...

4/101=0,00220203133003022301123033311313020033031103221030...

5/101=0,00302230112303331131302003303110322103000220203133...

6/101=0,00330311032210300022020313300302230112303331131302...

7/101=0,01012332012111202312133223232100132122213102120011...

8/101=0,01101012332012111202312133223232100132122213102120...

9/101=0,01123033311313020033031103221030002202031330030223...

10/101=0,01211120231213322323210013212221310212001101012332...

11/101=0,01233201211120231213322323210013212221310212001101...

12/101=0,01321222131021200110101233201211120231213322323210...

13/101=0,02003303110322103000220203133003022301123033311313...

14/101=0,02031330030223011230333113130200330311032210300022...

15/101=0,02120011010123320121112023121332232321001321222131...

16/101=0,02202031330030223011230333113130200330311032210300...

17/101=0,02230112303331131302003303110322103000220203133003...

18/101=0,02312133223232100132122213102120011010123320121112...

19/101=0,03000220203133003022301123033311313020033031103221...

20/101=0,03022301123033311313020033031103221030002202031330...

21/101=0,03110322103000220203133003022301123033311313020033...

22/101=0,03133003022301123033311313020033031103221030002202...

23/101=0,03221030002202031330030223011230333113130200330311...

24/101=0,03303110322103000220203133003022301123033311313020...

25/101=0,03331131302003303110322103000220203133003022301123...

26/101=0,10013212221310212001101012332012111202312133223232...

27/101=0,10101233201211120231213322323210013212221310212001...

28/101=0,10123320121112023121332232321001321222131021200110...

29/101=0,10212001101012332012111202312133223232100132122213...

30/101=0,10300022020313300302230112303331131302003303110322...

31/101=0,10322103000220203133003022301123033311313020033031...

32/101=0,11010123320121112023121332232321001321222131021200...

33/101=0,11032210300022020313300302230112303331131302003303...

34/101=0,11120231213322323210013212221310212001101012332012...

35/101=0,11202312133223232100132122213102120011010123320121...

36/101=0,11230333113130200330311032210300022020313300302230...

37/101=0,11313020033031103221030002202031330030223011230333...

38/101=0,12001101012332012111202312133223232100132122213102...

39/101=0,12023121332232321001321222131021200110101233201211...

40/101=0,12111202312133223232100132122213102120011010123320...

41/101=0,12133223232100132122213102120011010123320121112023...

42/101=0,12221310212001101012332012111202312133223232100132...

43/101=0,12303331131302003303110322103000220203133003022301...

44/101=0,12332012111202312133223232100132122213102120011010...

45/101=0,13020033031103221030002202031330030223011230333113...

46/101=0,13102120011010123320121112023121332232321001321222...

47/101=0,13130200330311032210300022020313300302230112303331...

48/101=0,13212221310212001101012332012111202312133223232100...

49/101=0,13300302230112303331131302003303110322103000220203...

50/101=0,13322323210013212221310212001101012332012111202312...

51/101=0,20011010123320121112023121332232321001321222131021...

52/101=0,20033031103221030002202031330030223011230333113130...

53/101=0,20121112023121332232321001321222131021200110101233...

54/101=0,20203133003022301123033311313020033031103221030002...

55/101=0,20231213322323210013212221310212001101012332012111...

56/101=0,20313300302230112303331131302003303110322103000220...

57/101=0,21001321222131021200110101233201211120231213322323...

58/101=0,21030002202031330030223011230333113130200330311032...

59/101=0,21112023121332232321001321222131021200110101233201...

60/101=0,21200110101233201211120231213322323210013212221310...

61/101=0,21222131021200110101233201211120231213322323210013...

62/101=0,21310212001101012332012111202312133223232100132122...

63/101=0,21332232321001321222131021200110101233201211120231...

64/101=0,22020313300302230112303331131302003303110322103000...

65/101=0,22103000220203133003022301123033311313020033031103...

66/101=0,22131021200110101233201211120231213322323210013212...

67/101=0,22213102120011010123320121112023121332232321001321...

68/101=0,22301123033311313020033031103221030002202031330030...

69/101=0,22323210013212221310212001101012332012111202312133...

70/101=0,23011230333113130200330311032210300022020313300302...

71/101=0,23033311313020033031103221030002202031330030223011...

72/101=0,23121332232321001321222131021200110101233201211120...

73/101=0,23210013212221310212001101012332012111202312133223...

74/101=0,23232100132122213102120011010123320121112023121332...

75/101=0,23320121112023121332232321001321222131021200110101...

76/101=0,30002202031330030223011230333113130200330311032210...

77/101=0,30030223011230333113130200330311032210300022020313...

78/101=0,30112303331131302003303110322103000220203133003022...

79/101=0,30200330311032210300022020313300302230112303331131...

80/101=0,30223011230333113130200330311032210300022020313300...

81/101=0,30311032210300022020313300302230112303331131302003...

82/101=0,30333113130200330311032210300022020313300302230112...

83/101=0,31021200110101233201211120231213322323210013212221...

84/101=0,31103221030002202031330030223011230333113130200330...

85/101=0,31131302003303110322103000220203133003022301123033...

86/101=0,31213322323210013212221310212001101012332012111202...

87/101=0,31302003303110322103000220203133003022301123033311...

88/101=0,31330030223011230333113130200330311032210300022020...

89/101=0,32012111202312133223232100132122213102120011010123...

90/101=0,32100132122213102120011010123320121112023121332232...

91/101=0,32122213102120011010123320121112023121332232321001...

92/101=0,32210300022020313300302230112303331131302003303110...

93/101=0,32232321001321222131021200110101233201211120231213...

94/101=0,32321001321222131021200110101233201211120231213322...

95/101=0,33003022301123033311313020033031103221030002202031...

96/101=0,33031103221030002202031330030223011230333113130200...

97/101=0,33113130200330311032210300022020313300302230112303...

98/101=0,33201211120231213322323210013212221310212001101012...

99/101=0,33223232100132122213102120011010123320121112023121...

100/101=0,33311313020033031103221030002202031330030223011230...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (50) est égal à 100 et donc au premier -1.