Il existe 2 périodes de 69 chiffres pour n/139 en base 4.

Pour toutes les fractions de n/139 en base 4, la période de 1/139 revient alors 69 fois (en orange)

1/139=0,000131131323121110232002300303210113330110100210311122033221321203131...

2/139=0,000322323312302221130011201213020233320220201021222310133103303012322...

3/139=0,001120121302023332022020102122231013310330301232200032232331230222113...

4/139=0,001311313231211102320023003032101133301101002103111220332213212031310...

5/139=0,002103111220332213212031310001311313231211102320023003032101133301101...

6/139=0,002300303210113330110100210311122033221321203131000131131323121110232...

7/139=0,003032101133301101002103111220332213212031310001311313231211102320023...

8/139=0,003223233123022211300112012130202333202202010212223101331033030123220...

9/139=0,010021031112203322132120313100013113132312111023200230030321011333011...

10/139=0,010212223101331033030123220003223233123022211300112012130202333202202...

11/139=0,011010021031112203322132120313100013113132312111023200230030321011333...

12/139=0,011201213020233320220201021222310133103303012322000322323312302221130...

13/139=0,011333011010021031112203322132120313100013113132312111023200230030321...

14/139=0,012130202333202202010212223101331033030123220003223233123022211300112...

15/139=0,012322000322323312302221130011201213020233320220201021222310133103303...

16/139=0,013113132312111023200230030321011333011010021031112203322132120313100...

17/139=0,013310330301232200032232331230222113001120121302023332022020102122231...

18/139=0,020102122231013310330301232200032232331230222113001120121302023332022...

19/139=0,020233320220201021222310133103303012322000322323312302221130011201213...

20/139=0,021031112203322132120313100013113132312111023200230030321011333011010...

21/139=0,021222310133103303012322000322323312302221130011201213020233320220201...

22/139=0,022020102122231013310330301232200032232331230222113001120121302023332...

23/139=0,022211300112012130202333202202010212223101331033030123220003223233123...

24/139=0,023003032101133301101002103111220332213212031310001311313231211102320...

25/139=0,023200230030321011333011010021031112203322132120313100013113132312111...

26/139=0,023332022020102122231013310330301232200032232331230222113001120121302...

27/139=0,030123220003223233123022211300112012130202333202202010212223101331033...

28/139=0,030321011333011010021031112203322132120313100013113132312111023200230...

29/139=0,031112203322132120313100013113132312111023200230030321011333011010021...

30/139=0,031310001311313231211102320023003032101133301101002103111220332213212...

31/139=0,032101133301101002103111220332213212031310001311313231211102320023003...

32/139=0,032232331230222113001120121302023332022020102122231013310330301232200...

33/139=0,033030123220003223233123022211300112012130202333202202010212223101331...

34/139=0,033221321203131000131131323121110232002300303210113330110100210311122...

35/139=0,100013113132312111023200230030321011333011010021031112203322132120313...

36/139=0,100210311122033221321203131000131131323121110232002300303210113330110...

37/139=0,101002103111220332213212031310001311313231211102320023003032101133301...

38/139=0,101133301101002103111220332213212031310001311313231211102320023003032...

39/139=0,101331033030123220003223233123022211300112012130202333202202010212223...

40/139=0,102122231013310330301232200032232331230222113001120121302023332022020...

41/139=0,102320023003032101133301101002103111220332213212031310001311313231211...

42/139=0,103111220332213212031310001311313231211102320023003032101133301101002...

43/139=0,103303012322000322323312302221130011201213020233320220201021222310133...

44/139=0,110100210311122033221321203131000131131323121110232002300303210113330...

45/139=0,110232002300303210113330110100210311122033221321203131000131131323121...

46/139=0,111023200230030321011333011010021031112203322132120313100013113132312...

47/139=0,111220332213212031310001311313231211102320023003032101133301101002103...

48/139=0,112012130202333202202010212223101331033030123220003223233123022211300...

49/139=0,112203322132120313100013113132312111023200230030321011333011010021031...

50/139=0,113001120121302023332022020102122231013310330301232200032232331230222...

51/139=0,113132312111023200230030321011333011010021031112203322132120313100013...

52/139=0,113330110100210311122033221321203131000131131323121110232002300303210...

53/139=0,120121302023332022020102122231013310330301232200032232331230222113001...

54/139=0,120313100013113132312111023200230030321011333011010021031112203322132...

55/139=0,121110232002300303210113330110100210311122033221321203131000131131323...

56/139=0,121302023332022020102122231013310330301232200032232331230222113001120...

57/139=0,122033221321203131000131131323121110232002300303210113330110100210311...

58/139=0,122231013310330301232200032232331230222113001120121302023332022020102...

59/139=0,123022211300112012130202333202202010212223101331033030123220003223233...

60/139=0,123220003223233123022211300112012130202333202202010212223101331033030...

61/139=0,130011201213020233320220201021222310133103303012322000322323312302221...

62/139=0,130202333202202010212223101331033030123220003223233123022211300112012...

63/139=0,131000131131323121110232002300303210113330110100210311122033221321203...

64/139=0,131131323121110232002300303210113330110100210311122033221321203131000...

65/139=0,131323121110232002300303210113330110100210311122033221321203131000131...

66/139=0,132120313100013113132312111023200230030321011333011010021031112203322...

67/139=0,132312111023200230030321011333011010021031112203322132120313100013113...

68/139=0,133103303012322000322323312302221130011201213020233320220201021222310...

69/139=0,133301101002103111220332213212031310001311313231211102320023003032101...

70/139=0,200032232331230222113001120121302023332022020102122231013310330301232...

71/139=0,200230030321011333011010021031112203322132120313100013113132312111023...

72/139=0,201021222310133103303012322000322323312302221130011201213020233320220...

73/139=0,201213020233320220201021222310133103303012322000322323312302221130011...

74/139=0,202010212223101331033030123220003223233123022211300112012130202333202...

75/139=0,202202010212223101331033030123220003223233123022211300112012130202333...

76/139=0,202333202202010212223101331033030123220003223233123022211300112012130...

77/139=0,203131000131131323121110232002300303210113330110100210311122033221321...

78/139=0,203322132120313100013113132312111023200230030321011333011010021031112...

79/139=0,210113330110100210311122033221321203131000131131323121110232002300303...

80/139=0,210311122033221321203131000131131323121110232002300303210113330110100...

81/139=0,211102320023003032101133301101002103111220332213212031310001311313231...

82/139=0,211300112012130202333202202010212223101331033030123220003223233123022...

83/139=0,212031310001311313231211102320023003032101133301101002103111220332213...

84/139=0,212223101331033030123220003223233123022211300112012130202333202202010...

85/139=0,213020233320220201021222310133103303012322000322323312302221130011201...

86/139=0,213212031310001311313231211102320023003032101133301101002103111220332...

87/139=0,220003223233123022211300112012130202333202202010212223101331033030123...

88/139=0,220201021222310133103303012322000322323312302221130011201213020233320...

89/139=0,220332213212031310001311313231211102320023003032101133301101002103111...

90/139=0,221130011201213020233320220201021222310133103303012322000322323312302...

91/139=0,221321203131000131131323121110232002300303210113330110100210311122033...

92/139=0,222113001120121302023332022020102122231013310330301232200032232331230...

93/139=0,222310133103303012322000322323312302221130011201213020233320220201021...

94/139=0,223101331033030123220003223233123022211300112012130202333202202010212...

95/139=0,223233123022211300112012130202333202202010212223101331033030123220003...

96/139=0,230030321011333011010021031112203322132120313100013113132312111023200...

97/139=0,230222113001120121302023332022020102122231013310330301232200032232331...

98/139=0,231013310330301232200032232331230222113001120121302023332022020102122...

99/139=0,231211102320023003032101133301101002103111220332213212031310001311313...

100/139=0,232002300303210113330110100210311122033221321203131000131131323121110...

101/139=0,232200032232331230222113001120121302023332022020102122231013310330301...

102/139=0,232331230222113001120121302023332022020102122231013310330301232200032...

103/139=0,233123022211300112012130202333202202010212223101331033030123220003223...

104/139=0,233320220201021222310133103303012322000322323312302221130011201213020...

105/139=0,300112012130202333202202010212223101331033030123220003223233123022211...

106/139=0,300303210113330110100210311122033221321203131000131131323121110232002...

107/139=0,301101002103111220332213212031310001311313231211102320023003032101133...

108/139=0,301232200032232331230222113001120121302023332022020102122231013310330...

109/139=0,302023332022020102122231013310330301232200032232331230222113001120121...

110/139=0,302221130011201213020233320220201021222310133103303012322000322323312...

111/139=0,303012322000322323312302221130011201213020233320220201021222310133103...

112/139=0,303210113330110100210311122033221321203131000131131323121110232002300...

113/139=0,310001311313231211102320023003032101133301101002103111220332213212031...

114/139=0,310133103303012322000322323312302221130011201213020233320220201021222...

115/139=0,310330301232200032232331230222113001120121302023332022020102122231013...

116/139=0,311122033221321203131000131131323121110232002300303210113330110100210...

117/139=0,311313231211102320023003032101133301101002103111220332213212031310001...

118/139=0,312111023200230030321011333011010021031112203322132120313100013113132...

119/139=0,312302221130011201213020233320220201021222310133103303012322000322323...

120/139=0,313100013113132312111023200230030321011333011010021031112203322132120...

121/139=0,313231211102320023003032101133301101002103111220332213212031310001311...

122/139=0,320023003032101133301101002103111220332213212031310001311313231211102...

123/139=0,320220201021222310133103303012322000322323312302221130011201213020233...

124/139=0,321011333011010021031112203322132120313100013113132312111023200230030...

125/139=0,321203131000131131323121110232002300303210113330110100210311122033221...

126/139=0,322000322323312302221130011201213020233320220201021222310133103303012...

127/139=0,322132120313100013113132312111023200230030321011333011010021031112203...

128/139=0,322323312302221130011201213020233320220201021222310133103303012322000...

129/139=0,323121110232002300303210113330110100210311122033221321203131000131131...

130/139=0,323312302221130011201213020233320220201021222310133103303012322000322...

131/139=0,330110100210311122033221321203131000131131323121110232002300303210113...

132/139=0,330301232200032232331230222113001120121302023332022020102122231013310...

133/139=0,331033030123220003223233123022211300112012130202333202202010212223101...

134/139=0,331230222113001120121302023332022020102122231013310330301232200032232...

135/139=0,332022020102122231013310330301232200032232331230222113001120121302023...

136/139=0,332213212031310001311313231211102320023003032101133301101002103111220...

137/139=0,333011010021031112203322132120313100013113132312111023200230030321011...

138/139=0,333202202010212223101331033030123220003223233123022211300112012130202...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (69) est égal à 138 et donc au premier -1.