Il existe 4 périodes de 45 chiffres pour n/181 en base 3.

Pour toutes les fractions de n/181 en base 3, la période de 1/181 revient alors 45 fois (en orange)

1/181=0,000011000202010201200122110020021011022210122...

2/181=0,000022001111021110101021220110112022122121021...

3/181=0,000110002020102012001221100200210110222101220...

4/181=0,000121002222112220202120210221001122022012112...

5/181=0,000202010201200122110020021011022210122000011...

6/181=0,000220011110211101010212201101120221221210210...

7/181=0,001001012012222002211112011121212010021121102...

8/181=0,001012012222002211112011121212010021121102001...

9/181=0,001100020201020120012211002002101102221012200...

10/181=0,001111021110101021220110112022122121021000022...

11/181=0,001122022012112000121002222112220202120210221...

12/181=0,001210022221122202021202102210011220220121120...

13/181=0,001221100200210110222101220000110002020102012...

14/181=0,002002101102221012200001100020201020120012211...

15/181=0,002020102012001221100200210110222101220000110...

16/181=0,002101102221012200001100020201020120012211002...

17/181=0,002112110200100101201222200221111201112121201...

18/181=0,002200111102111010102122011011202212212102100...

19/181=0,002211112011121212010021121102001001012012222...

20/181=0,002222112220202120210221001122022012112000121...

21/181=0,010010120122220022111120111212120100211211020...

22/181=0,010021121102001001012012222002211112011121212...

23/181=0,010102122011011202212212102100002200111102111...

24/181=0,010120122220022111120111212120100211211020010...

25/181=0,010201200122110020021011022210122000011000202...

26/181=0,010212201101120221221210210000220011110211101...

27/181=0,011000202010201200122110020021011022210122000...

28/181=0,011011202212212102100002200111102111010102122...

29/181=0,011022210122000011000202010201200122110020021...

30/181=0,011110211101010212201101120221221210210000220...

31/181=0,011121212010021121102001001012012222002211112...

32/181=0,011202212212102100002200111102111010102122011...

33/181=0,011220220121120001210022221122202021202102210...

34/181=0,012001221100200210110222101220000110002020102...

35/181=0,012012222002211112011121212010021121102001001...

36/181=0,012100222211222020212021022100112202201211200...

37/181=0,012112000121002222112220202120210221001122022...

38/181=0,012200001100020201020120012211002002101102221...

39/181=0,012211002002101102221012200001100020201020120...

40/181=0,012222002211112011121212010021121102001001012...

41/181=0,020010010120122220022111120111212120100211211...

42/181=0,020021011022210122000011000202010201200122110...

43/181=0,020102012001221100200210110222101220000110002...

44/181=0,020120012211002002101102221012200001100020201...

45/181=0,020201020120012211002002101102221012200001100...

46/181=0,020212021022100112202201211200012100222211222...

47/181=0,021000022001111021110101021220110112022122121...

48/181=0,021011022210122000011000202010201200122110020...

49/181=0,021022100112202201211200012100222211222020212...

50/181=0,021110101021220110112022122121021000022001111...

51/181=0,021121102001001012012222002211112011121212010...

52/181=0,021202102210011220220121120001210022221122202...

53/181=0,021220110112022122121021000022001111021110101...

54/181=0,022001111021110101021220110112022122121021000...

55/181=0,022012112000121002222112220202120210221001122...

56/181=0,022100112202201211200012100222211222020212021...

57/181=0,022111120111212120100211211020010010120122220...

58/181=0,022122121021000022001111021110101021220110112...

59/181=0,022210122000011000202010201200122110020021011...

60/181=0,022221122202021202102210011220220121120001210...

61/181=0,100002200111102111010102122011011202212212102...

62/181=0,100020201020120012211002002101102221012200001...

63/181=0,100101201222200221111201112121201002112110200...

64/181=0,100112202201211200012100222211222020212021022...

65/181=0,100200210110222101220000110002020102012001221...

66/181=0,100211211020010010120122220022111120111212120...

67/181=0,100222211222020212021022100112202201211200012...

68/181=0,101010212201101120221221210210000220011110211...

69/181=0,101021220110112022122121021000022001111021110...

70/181=0,101102221012200001100020201020120012211002002...

71/181=0,101120221221210210000220011110211101010212201...

72/181=0,101201222200221111201112121201002112110200100...

73/181=0,101220000110002020102012001221100200210110222...

74/181=0,102001001012012222002211112011121212010021121...

75/181=0,102012001221100200210110222101220000110002020...

76/181=0,102100002200111102111010102122011011202212212...

77/181=0,102111010102122011011202212212102100002200111...

78/181=0,102122011011202212212102100002200111102111010...

79/181=0,102210011220220121120001210022221122202021202...

80/181=0,102221012200001100020201020120012211002002101...

81/181=0,110002020102012001221100200210110222101220000...

82/181=0,110020021011022210122000011000202010201200122...

83/181=0,110101021220110112022122121021000022001111021...

84/181=0,110112022122121021000022001111021110101021220...

85/181=0,110200100101201222200221111201112121201002112...

86/181=0,110211101010212201101120221221210210000220011...

87/181=0,110222101220000110002020102012001221100200210...

88/181=0,111010102122011011202212212102100002200111102...

89/181=0,111021110101021220110112022122121021000022001...

90/181=0,111102111010102122011011202212212102100002200...

91/181=0,111120111212120100211211020010010120122220022...

92/181=0,111201112121201002112110200100101201222200221...

93/181=0,111212120100211211020010010120122220022111120...

94/181=0,112000121002222112220202120210221001122022012...

95/181=0,112011121212010021121102001001012012222002211...

96/181=0,112022122121021000022001111021110101021220110...

97/181=0,112110200100101201222200221111201112121201002...

98/181=0,112121201002112110200100101201222200221111201...

99/181=0,112202201211200012100222211222020212021022100...

100/181=0,112220202120210221001122022012112000121002222...

101/181=0,120001210022221122202021202102210011220220121...

102/181=0,120012211002002101102221012200001100020201020...

103/181=0,120100211211020010010120122220022111120111212...

104/181=0,120111212120100211211020010010120122220022111...

105/181=0,120122220022111120111212120100211211020010010...

106/181=0,120210221001122022012112000121002222112220202...

107/181=0,120221221210210000220011110211101010212201101...

108/181=0,121002222112220202120210221001122022012112000...

109/181=0,121021000022001111021110101021220110112022122...

110/181=0,121102001001012012222002211112011121212010021...

111/181=0,121120001210022221122202021202102210011220220...

112/181=0,121201002112110200100101201222200221111201112...

113/181=0,121212010021121102001001012012222002211112011...

114/181=0,122000011000202010201200122110020021011022210...

115/181=0,122011011202212212102100002200111102111010102...

116/181=0,122022012112000121002222112220202120210221001...

117/181=0,122110020021011022210122000011000202010201200...

118/181=0,122121021000022001111021110101021220110112022...

119/181=0,122202021202102210011220220121120001210022221...

120/181=0,122220022111120111212120100211211020010010120...

121/181=0,200001100020201020120012211002002101102221012...

122/181=0,200012100222211222020212021022100112202201211...

123/181=0,200100101201222200221111201112121201002112110...

124/181=0,200111102111010102122011011202212212102100002...

125/181=0,200122110020021011022210122000011000202010201...

126/181=0,200210110222101220000110002020102012001221100...

127/181=0,200221111201112121201002112110200100101201222...

128/181=0,201002112110200100101201222200221111201112121...

129/181=0,201020120012211002002101102221012200001100020...

130/181=0,201101120221221210210000220011110211101010212...

131/181=0,201112121201002112110200100101201222200221111...

132/181=0,201200122110020021011022210122000011000202010...

133/181=0,201211200012100222211222020212021022100112202...

134/181=0,201222200221111201112121201002112110200100101...

135/181=0,202010201200122110020021011022210122000011000...

136/181=0,202021202102210011220220121120001210022221122...

137/181=0,202102210011220220121120001210022221122202021...

138/181=0,202120210221001122022012112000121002222112220...

139/181=0,202201211200012100222211222020212021022100112...

140/181=0,202212212102100002200111102111010102122011011...

141/181=0,210000220011110211101010212201101120221221210...

142/181=0,210011220220121120001210022221122202021202102...

143/181=0,210022221122202021202102210011220220121120001...

144/181=0,210110222101220000110002020102012001221100200...

145/181=0,210122000011000202010201200122110020021011022...

146/181=0,210210000220011110211101010212201101120221221...

147/181=0,210221001122022012112000121002222112220202120...

148/181=0,211002002101102221012200001100020201020120012...

149/181=0,211020010010120122220022111120111212120100211...

150/181=0,211101010212201101120221221210210000220011110...

151/181=0,211112011121212010021121102001001012012222002...

152/181=0,211200012100222211222020212021022100112202201...

153/181=0,211211020010010120122220022111120111212120100...

154/181=0,211222020212021022100112202201211200012100222...

155/181=0,212010021121102001001012012222002211112011121...

156/181=0,212021022100112202201211200012100222211222020...

157/181=0,212102100002200111102111010102122011011202212...

158/181=0,212120100211211020010010120122220022111120111...

159/181=0,212201101120221221210210000220011110211101010...

160/181=0,212212102100002200111102111010102122011011202...

161/181=0,220000110002020102012001221100200210110222101...

162/181=0,220011110211101010212201101120221221210210000...

163/181=0,220022111120111212120100211211020010010120122...

164/181=0,220110112022122121021000022001111021110101021...

165/181=0,220121120001210022221122202021202102210011220...

166/181=0,220202120210221001122022012112000121002222112...

167/181=0,220220121120001210022221122202021202102210011...

168/181=0,221001122022012112000121002222112220202120210...

169/181=0,221012200001100020201020120012211002002101102...

170/181=0,221100200210110222101220000110002020102012001...

171/181=0,221111201112121201002112110200100101201222200...

172/181=0,221122202021202102210011220220121120001210022...

173/181=0,221210210000220011110211101010212201101120221...

174/181=0,221221210210000220011110211101010212201101120...

175/181=0,222002211112011121212010021121102001001012012...

176/181=0,222020212021022100112202201211200012100222211...

177/181=0,222101220000110002020102012001221100200210110...

178/181=0,222112220202120210221001122022012112000121002...

179/181=0,222200221111201112121201002112110200100101201...

180/181=0,222211222020212021022100112202201211200012100...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (45) est égal à 180 et donc au premier -1.