Il existe 4 périodes de 37 chiffres pour n/149 en base 5.

Pour toutes les fractions de n/149 en base 5, la période de 1/149 revient alors 37 fois (en orange)

1/149=0,0004044131023202411232434030432211101...

2/149=0,0013143312101410323020423111414422202...

3/149=0,0022242443130113234303412142402133303...

4/149=0,0031342124203321201041401223334344404...

5/149=0,0040441310232024112324340304322111010...

6/149=0,0100040441310232024112324340304322111...

7/149=0,0104140122333434440400313421242033212...

8/149=0,0113234303412142402133303002224244313...

9/149=0,0122333434440400313421242033212010414...

10/149=0,0131433121014103230204231114144222020...

11/149=0,0141032302042311141442220200131433121...

12/149=0,0200131433121014103230204231114144222...

13/149=0,0204231114144222020013143312101410323...

14/149=0,0213330300222424431301132343034121424...

15/149=0,0222424431301132343034121424021333030...

16/149=0,0232024112324340304322111010004044131...

17/149=0,0241123243403043221110100040441310232...

18/149=0,0300222424431301132343034121424021333...

19/149=0,0304322111010004044131023202411232434...

20/149=0,0313421242033212010414012233343444040...

21/149=0,0323020423111414422202001314331210141...

22/149=0,0332120104140122333434440400313421242...

23/149=0,0341214240213330300222424431301132343...

24/149=0,0400313421242033212010414012233343444...

25/149=0,0404413102320241123243403043221110100...

26/149=0,0414012233343444040031342124203321201...

27/149=0,0423111414422202001314331210141032302...

28/149=0,0432211101000404413102320241123243403...

29/149=0,0441310232024112324340304322111010004...

30/149=0,1000404413102320241123243403043221110...

31/149=0,1010004044131023202411232434030432211...

32/149=0,1014103230204231114144222020013143312...

33/149=0,1023202411232434030432211101000404413...

34/149=0,1032302042311141442220200131433121014...

35/149=0,1041401223334344404003134212420332120...

36/149=0,1101000404413102320241123243403043221...

37/149=0,1110100040441310232024112324340304322...

38/149=0,1114144222020013143312101410323020423...

39/149=0,1123243403043221110100040441310232024...

40/149=0,1132343034121424021333030022242443130...

41/149=0,1141442220200131433121014103230204231...

42/149=0,1201041401223334344404003134212420332...

43/149=0,1210141032302042311141442220200131433...

44/149=0,1214240213330300222424431301132343034...

45/149=0,1223334344404003134212420332120104140...

46/149=0,1232434030432211101000404413102320241...

47/149=0,1242033212010414012233343444040031342...

48/149=0,1301132343034121424021333030022242443...

49/149=0,1310232024112324340304322111010004044...

50/149=0,1314331210141032302042311141442220200...

51/149=0,1323430341214240213330300222424431301...

52/149=0,1333030022242443130113234303412142402...

53/149=0,1342124203321201041401223334344404003...

54/149=0,1401223334344404003134212420332120104...

55/149=0,1410323020423111414422202001314331210...

56/149=0,1414422202001314331210141032302042311...

57/149=0,1424021333030022242443130113234303412...

58/149=0,1433121014103230204231114144222020013...

59/149=0,1442220200131433121014103230204231114...

60/149=0,2001314331210141032302042311141442220...

61/149=0,2010414012233343444040031342124203321...

62/149=0,2020013143312101410323020423111414422...

63/149=0,2024112324340304322111010004044131023...

64/149=0,2033212010414012233343444040031342124...

65/149=0,2042311141442220200131433121014103230...

66/149=0,2101410323020423111414422202001314331...

67/149=0,2111010004044131023202411232434030432...

68/149=0,2120104140122333434440400313421242033...

69/149=0,2124203321201041401223334344404003134...

70/149=0,2133303002224244313011323430341214240...

71/149=0,2142402133303002224244313011323430341...

72/149=0,2202001314331210141032302042311141442...

73/149=0,2211101000404413102320241123243403043...

74/149=0,2220200131433121014103230204231114144...

75/149=0,2224244313011323430341214240213330300...

76/149=0,2233343444040031342124203321201041401...

77/149=0,2242443130113234303412142402133303002...

78/149=0,2302042311141442220200131433121014103...

79/149=0,2311141442220200131433121014103230204...

80/149=0,2320241123243403043221110100040441310...

81/149=0,2324340304322111010004044131023202411...

82/149=0,2333434440400313421242033212010414012...

83/149=0,2343034121424021333030022242443130113...

84/149=0,2402133303002224244313011323430341214...

85/149=0,2411232434030432211101000404413102320...

86/149=0,2420332120104140122333434440400313421...

87/149=0,2424431301132343034121424021333030022...

88/149=0,2434030432211101000404413102320241123...

89/149=0,2443130113234303412142402133303002224...

90/149=0,3002224244313011323430341214240213330...

91/149=0,3011323430341214240213330300222424431...

92/149=0,3020423111414422202001314331210141032...

93/149=0,3030022242443130113234303412142402133...

94/149=0,3034121424021333030022242443130113234...

95/149=0,3043221110100040441310232024112324340...

96/149=0,3102320241123243403043221110100040441...

97/149=0,3111414422202001314331210141032302042...

98/149=0,3121014103230204231114144222020013143...

99/149=0,3130113234303412142402133303002224244...

100/149=0,3134212420332120104140122333434440400...

101/149=0,3143312101410323020423111414422202001...

102/149=0,3202411232434030432211101000404413102...

103/149=0,3212010414012233343444040031342124203...

104/149=0,3221110100040441310232024112324340304...

105/149=0,3230204231114144222020013143312101410...

106/149=0,3234303412142402133303002224244313011...

107/149=0,3243403043221110100040441310232024112...

108/149=0,3303002224244313011323430341214240213...

109/149=0,3312101410323020423111414422202001314...

110/149=0,3321201041401223334344404003134212420...

111/149=0,3330300222424431301132343034121424021...

112/149=0,3334344404003134212420332120104140122...

113/149=0,3343444040031342124203321201041401223...

114/149=0,3403043221110100040441310232024112324...

115/149=0,3412142402133303002224244313011323430...

116/149=0,3421242033212010414012233343444040031...

117/149=0,3430341214240213330300222424431301132...

118/149=0,3434440400313421242033212010414012233...

119/149=0,3444040031342124203321201041401223334...

120/149=0,4003134212420332120104140122333434440...

121/149=0,4012233343444040031342124203321201041...

122/149=0,4021333030022242443130113234303412142...

123/149=0,4030432211101000404413102320241123243...

124/149=0,4040031342124203321201041401223334344...

125/149=0,4044131023202411232434030432211101000...

126/149=0,4103230204231114144222020013143312101...

127/149=0,4112324340304322111010004044131023202...

128/149=0,4121424021333030022242443130113234303...

129/149=0,4131023202411232434030432211101000404...

130/149=0,4140122333434440400313421242033212010...

131/149=0,4144222020013143312101410323020423111...

132/149=0,4203321201041401223334344404003134212...

133/149=0,4212420332120104140122333434440400313...

134/149=0,4222020013143312101410323020423111414...

135/149=0,4231114144222020013143312101410323020...

136/149=0,4240213330300222424431301132343034121...

137/149=0,4244313011323430341214240213330300222...

138/149=0,4303412142402133303002224244313011323...

139/149=0,4313011323430341214240213330300222424...

140/149=0,4322111010004044131023202411232434030...

141/149=0,4331210141032302042311141442220200131...

142/149=0,4340304322111010004044131023202411232...

143/149=0,4344404003134212420332120104140122333...

144/149=0,4404003134212420332120104140122333434...

145/149=0,4413102320241123243403043221110100040...

146/149=0,4422202001314331210141032302042311141...

147/149=0,4431301132343034121424021333030022242...

148/149=0,4440400313421242033212010414012233343...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (37) est égal à 148 et donc au premier -1.