Il existe 2 périodes de 74 chiffres pour n/149 en base 4.

Pour toutes les fractions de n/149 en base 4, la période de 1/149 revient alors 74 fois (en orange)

1/149=0,00012313311230033131220303202302223303332102002210330020211303013103111003...

2/149=0,00031233223120132323101213011211113213330210011021320101023212032212222012...

3/149=0,00110213201010232120322122220120003123322312013232310121301121111321333021...

4/149=0,00123133112300331312203032023022233033321020022103300202113030131031110030...

5/149=0,00202113030131031110030001231331123003313122030320230222330333210200221033...

6/149=0,00221033002021130301310311100300012313311230033131220303202302223303332102...

7/149=0,00300012313311230033131220303202302223303332102002210330020211303013103111...

8/149=0,00312332231201323231012130112111132133302100110213201010232120322122220120...

9/149=0,00331312203032023022233033321020022103300202113030131031110030001231331123...

10/149=0,01010232120322122220120003123322312013232310121301121111321333021001102132...

11/149=0,01023212032212222012000312332231201323231012130112111132133302100110213201...

12/149=0,01102132010102321203221222201200031233223120132323101213011211113213330210...

13/149=0,01121111321333021001102132010102321203221222201200031233223120132323101213...

14/149=0,01200031233223120132323101213011211113213330210011021320101023212032212222...

15/149=0,01213011211113213330210011021320101023212032212222012000312332231201323231...

16/149=0,01231331123003313122030320230222330333210200221033002021130301310311100300...

17/149=0,01310311100300012313311230033131220303202302223303332102002210330020211303...

18/149=0,01323231012130112111132133302100110213201010232120322122220120003123322312...

19/149=0,02002210330020211303013103111003000123133112300331312203032023022233033321...

20/149=0,02021130301310311100300012313311230033131220303202302223303332102002210330...

21/149=0,02100110213201010232120322122220120003123322312013232310121301121111321333...

22/149=0,02113030131031110030001231331123003313122030320230222330333210200221033002...

23/149=0,02132010102321203221222201200031233223120132323101213011211113213330210011...

24/149=0,02210330020211303013103111003000123133112300331312203032023022233033321020...

25/149=0,02223303332102002210330020211303013103111003000123133112300331312203032023...

26/149=0,02302223303332102002210330020211303013103111003000123133112300331312203032...

27/149=0,02321203221222201200031233223120132323101213011211113213330210011021320101...

28/149=0,03000123133112300331312203032023022233033321020022103300202113030131031110...

29/149=0,03013103111003000123133112300331312203032023022233033321020022103300202113...

30/149=0,03032023022233033321020022103300202113030131031110030001231331123003313122...

31/149=0,03111003000123133112300331312203032023022233033321020022103300202113030131...

32/149=0,03123322312013232310121301121111321333021001102132010102321203221222201200...

33/149=0,03202302223303332102002210330020211303013103111003000123133112300331312203...

34/149=0,03221222201200031233223120132323101213011211113213330210011021320101023212...

35/149=0,03300202113030131031110030001231331123003313122030320230222330333210200221...

36/149=0,03313122030320230222330333210200221033002021130301310311100300012313311230...

37/149=0,03332102002210330020211303013103111003000123133112300331312203032023022233...

38/149=0,10011021320101023212032212222012000312332231201323231012130112111132133302...

39/149=0,10030001231331123003313122030320230222330333210200221033002021130301310311...

40/149=0,10102321203221222201200031233223120132323101213011211113213330210011021320...

41/149=0,10121301121111321333021001102132010102321203221222201200031233223120132323...

42/149=0,10200221033002021130301310311100300012313311230033131220303202302223303332...

43/149=0,10213201010232120322122220120003123322312013232310121301121111321333021001...

44/149=0,10232120322122220120003123322312013232310121301121111321333021001102132010...

45/149=0,10311100300012313311230033131220303202302223303332102002210330020211303013...

46/149=0,10330020211303013103111003000123133112300331312203032023022233033321020022...

47/149=0,11003000123133112300331312203032023022233033321020022103300202113030131031...

48/149=0,11021320101023212032212222012000312332231201323231012130112111132133302100...

49/149=0,11100300012313311230033131220303202302223303332102002210330020211303013103...

50/149=0,11113213330210011021320101023212032212222012000312332231201323231012130112...

51/149=0,11132133302100110213201010232120322122220120003123322312013232310121301121...

52/149=0,11211113213330210011021320101023212032212222012000312332231201323231012130...

53/149=0,11230033131220303202302223303332102002210330020211303013103111003000123133...

54/149=0,11303013103111003000123133112300331312203032023022233033321020022103300202...

55/149=0,11321333021001102132010102321203221222201200031233223120132323101213011211...

56/149=0,12000312332231201323231012130112111132133302100110213201010232120322122220...

57/149=0,12013232310121301121111321333021001102132010102321203221222201200031233223...

58/149=0,12032212222012000312332231201323231012130112111132133302100110213201010232...

59/149=0,12111132133302100110213201010232120322122220120003123322312013232310121301...

60/149=0,12130112111132133302100110213201010232120322122220120003123322312013232310...

61/149=0,12203032023022233033321020022103300202113030131031110030001231331123003313...

62/149=0,12222012000312332231201323231012130112111132133302100110213201010232120322...

63/149=0,12300331312203032023022233033321020022103300202113030131031110030001231331...

64/149=0,12313311230033131220303202302223303332102002210330020211303013103111003000...

65/149=0,12332231201323231012130112111132133302100110213201010232120322122220120003...

66/149=0,13011211113213330210011021320101023212032212222012000312332231201323231012...

67/149=0,13030131031110030001231331123003313122030320230222330333210200221033002021...

68/149=0,13103111003000123133112300331312203032023022233033321020022103300202113030...

69/149=0,13122030320230222330333210200221033002021130301310311100300012313311230033...

70/149=0,13201010232120322122220120003123322312013232310121301121111321333021001102...

71/149=0,13213330210011021320101023212032212222012000312332231201323231012130112111...

72/149=0,13232310121301121111321333021001102132010102321203221222201200031233223120...

73/149=0,13311230033131220303202302223303332102002210330020211303013103111003000123...

74/149=0,13330210011021320101023212032212222012000312332231201323231012130112111132...

75/149=0,20003123322312013232310121301121111321333021001102132010102321203221222201...

76/149=0,20022103300202113030131031110030001231331123003313122030320230222330333210...

77/149=0,20101023212032212222012000312332231201323231012130112111132133302100110213...

78/149=0,20120003123322312013232310121301121111321333021001102132010102321203221222...

79/149=0,20132323101213011211113213330210011021320101023212032212222012000312332231...

80/149=0,20211303013103111003000123133112300331312203032023022233033321020022103300...

81/149=0,20230222330333210200221033002021130301310311100300012313311230033131220303...

82/149=0,20303202302223303332102002210330020211303013103111003000123133112300331312...

83/149=0,20322122220120003123322312013232310121301121111321333021001102132010102321...

84/149=0,21001102132010102321203221222201200031233223120132323101213011211113213330...

85/149=0,21020022103300202113030131031110030001231331123003313122030320230222330333...

86/149=0,21033002021130301310311100300012313311230033131220303202302223303332102002...

87/149=0,21111321333021001102132010102321203221222201200031233223120132323101213011...

88/149=0,21130301310311100300012313311230033131220303202302223303332102002210330020...

89/149=0,21203221222201200031233223120132323101213011211113213330210011021320101023...

90/149=0,21222201200031233223120132323101213011211113213330210011021320101023212032...

91/149=0,21301121111321333021001102132010102321203221222201200031233223120132323101...

92/149=0,21320101023212032212222012000312332231201323231012130112111132133302100110...

93/149=0,21333021001102132010102321203221222201200031233223120132323101213011211113...

94/149=0,22012000312332231201323231012130112111132133302100110213201010232120322122...

95/149=0,22030320230222330333210200221033002021130301310311100300012313311230033131...

96/149=0,22103300202113030131031110030001231331123003313122030320230222330333210200...

97/149=0,22122220120003123322312013232310121301121111321333021001102132010102321203...

98/149=0,22201200031233223120132323101213011211113213330210011021320101023212032212...

99/149=0,22220120003123322312013232310121301121111321333021001102132010102321203221...

100/149=0,22233033321020022103300202113030131031110030001231331123003313122030320230...

101/149=0,22312013232310121301121111321333021001102132010102321203221222201200031233...

102/149=0,22330333210200221033002021130301310311100300012313311230033131220303202302...

103/149=0,23003313122030320230222330333210200221033002021130301310311100300012313311...

104/149=0,23022233033321020022103300202113030131031110030001231331123003313122030320...

105/149=0,23101213011211113213330210011021320101023212032212222012000312332231201323...

106/149=0,23120132323101213011211113213330210011021320101023212032212222012000312332...

107/149=0,23133112300331312203032023022233033321020022103300202113030131031110030001...

108/149=0,23212032212222012000312332231201323231012130112111132133302100110213201010...

109/149=0,23231012130112111132133302100110213201010232120322122220120003123322312013...

110/149=0,23303332102002210330020211303013103111003000123133112300331312203032023022...

111/149=0,23322312013232310121301121111321333021001102132010102321203221222201200031...

112/149=0,30001231331123003313122030320230222330333210200221033002021130301310311100...

113/149=0,30020211303013103111003000123133112300331312203032023022233033321020022103...

114/149=0,30033131220303202302223303332102002210330020211303013103111003000123133112...

115/149=0,30112111132133302100110213201010232120322122220120003123322312013232310121...

116/149=0,30131031110030001231331123003313122030320230222330333210200221033002021130...

117/149=0,30210011021320101023212032212222012000312332231201323231012130112111132133...

118/149=0,30222330333210200221033002021130301310311100300012313311230033131220303202...

119/149=0,30301310311100300012313311230033131220303202302223303332102002210330020211...

120/149=0,30320230222330333210200221033002021130301310311100300012313311230033131220...

121/149=0,30333210200221033002021130301310311100300012313311230033131220303202302223...

122/149=0,31012130112111132133302100110213201010232120322122220120003123322312013232...

123/149=0,31031110030001231331123003313122030320230222330333210200221033002021130301...

124/149=0,31110030001231331123003313122030320230222330333210200221033002021130301310...

125/149=0,31123003313122030320230222330333210200221033002021130301310311100300012313...

126/149=0,31201323231012130112111132133302100110213201010232120322122220120003123322...

127/149=0,31220303202302223303332102002210330020211303013103111003000123133112300331...

128/149=0,31233223120132323101213011211113213330210011021320101023212032212222012000...

129/149=0,31312203032023022233033321020022103300202113030131031110030001231331123003...

130/149=0,31331123003313122030320230222330333210200221033002021130301310311100300012...

131/149=0,32010102321203221222201200031233223120132323101213011211113213330210011021...

132/149=0,32023022233033321020022103300202113030131031110030001231331123003313122030...

133/149=0,32102002210330020211303013103111003000123133112300331312203032023022233033...

134/149=0,32120322122220120003123322312013232310121301121111321333021001102132010102...

135/149=0,32133302100110213201010232120322122220120003123322312013232310121301121111...

136/149=0,32212222012000312332231201323231012130112111132133302100110213201010232120...

137/149=0,32231201323231012130112111132133302100110213201010232120322122220120003123...

138/149=0,32310121301121111321333021001102132010102321203221222201200031233223120132...

139/149=0,32323101213011211113213330210011021320101023212032212222012000312332231201...

140/149=0,33002021130301310311100300012313311230033131220303202302223303332102002210...

141/149=0,33021001102132010102321203221222201200031233223120132323101213011211113213...

142/149=0,33033321020022103300202113030131031110030001231331123003313122030320230222...

143/149=0,33112300331312203032023022233033321020022103300202113030131031110030001231...

144/149=0,33131220303202302223303332102002210330020211303013103111003000123133112300...

145/149=0,33210200221033002021130301310311100300012313311230033131220303202302223303...

146/149=0,33223120132323101213011211113213330210011021320101023212032212222012000312...

147/149=0,33302100110213201010232120322122220120003123322312013232310121301121111321...

148/149=0,33321020022103300202113030131031110030001231331123003313122030320230222330...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (74) est égal à 148 et donc au premier -1.