Il existe 4 périodes de 43 chiffres pour n/173 en base 6.

Pour toutes les fractions de n/173 en base 6, la période de 1/173 revient alors 43 fois (en orange)

1/173=0,0011254043245044414453143402025251344031551...

2/173=0,0022552130534133233350331204054543132103542...

3/173=0,0034250214223222052243515010124234520135533...

4/173=0,0045544301512310511141102412153530304211524...

5/173=0,0101242345201355330034250214223222052243515...

6/173=0,0112540432450444144531434020252513440315510...

7/173=0,0124234520135533003425021422322205224351501...

8/173=0,0135533003425021422322205224351501012423452...

9/173=0,0151231051114110241215353030421152400455443...

10/173=0,0202525134403155100112540432450444144531434...

11/173=0,0214223222052243515010124234520135533003425...

12/173=0,0225521305341332333503312040545431321035420...

13/173=0,0241215353030421152400455443015123105111411...

14/173=0,0252513440315510011254043245044414453143402...

15/173=0,0304211524004554430151231051114110241215353...

16/173=0,0315510011254043245044414453143402025251344...

17/173=0,0331204054543132103542002255213053413323335...

18/173=0,0342502142232220522435150101242345201355330...

19/173=0,0354200225521305341332333503312040545431321...

20/173=0,0405454313210354200225521305341332333503312...

21/173=0,0421152400455443015123105111411024121535303...

22/173=0,0432450444144531434020252513440315510011254...

23/173=0,0444144531434020252513440315510011254043245...

24/173=0,0455443015123105111411024121535303042115240...

25/173=0,0511141102412153530304211524004554430151231...

26/173=0,0522435150101242345201355330034250214223222...

27/173=0,0534133233350331204054543132103542002255213...

28/173=0,0545431321035420022552130534133233350331204...

29/173=0,1001125404324504441445314340202525134403155...

30/173=0,1012423452013553300342502142232220522435150...

31/173=0,1024121535303042115240045544301512310511141...

32/173=0,1035420022552130534133233350331204054543132...

33/173=0,1051114110241215353030421152400455443015123...

34/173=0,1102412153530304211524004554430151231051114...

35/173=0,1114110241215353030421152400455443015123105...

36/173=0,1125404324504441445314340202525134403155100...

37/173=0,1141102412153530304211524004554430151231051...

38/173=0,1152400455443015123105111411024121535303042...

39/173=0,1204054543132103542002255213053413323335033...

40/173=0,1215353030421152400455443015123105111411024...

41/173=0,1231051114110241215353030421152400455443015...

42/173=0,1242345201355330034250214223222052243515010...

43/173=0,1254043245044414453143402025251344031551001...

44/173=0,1305341332333503312040545431321035420022552...

45/173=0,1321035420022552130534133233350331204054543...

46/173=0,1332333503312040545431321035420022552130534...

47/173=0,1344031551001125404324504441445314340202525...

48/173=0,1355330034250214223222052243515010124234520...

49/173=0,1411024121535303042115240045544301512310511...

50/173=0,1422322205224351501012423452013553300342502...

51/173=0,1434020252513440315510011254043245044414453...

52/173=0,1445314340202525134403155100112540432450444...

53/173=0,1501012423452013553300342502142232220522435...

54/173=0,1512310511141102412153530304211524004554430...

55/173=0,1524004554430151231051114110241215353030421...

56/173=0,1535303042115240045544301512310511141102412...

57/173=0,1551001125404324504441445314340202525134403...

58/173=0,2002255213053413323335033120405454313210354...

59/173=0,2013553300342502142232220522435150101242345...

60/173=0,2025251344031551001125404324504441445314340...

61/173=0,2040545431321035420022552130534133233350331...

62/173=0,2052243515010124234520135533003425021422322...

63/173=0,2103542002255213053413323335033120405454313...

64/173=0,2115240045544301512310511141102412153530304...

65/173=0,2130534133233350331204054543132103542002255...

66/173=0,2142232220522435150101242345201355330034250...

67/173=0,2153530304211524004554430151231051114110241...

68/173=0,2205224351501012423452013553300342502142232...

69/173=0,2220522435150101242345201355330034250214223...

70/173=0,2232220522435150101242345201355330034250214...

71/173=0,2243515010124234520135533003425021422322205...

72/173=0,2255213053413323335033120405454313210354200...

73/173=0,2310511141102412153530304211524004554430151...

74/173=0,2322205224351501012423452013553300342502142...

75/173=0,2333503312040545431321035420022552130534133...

76/173=0,2345201355330034250214223222052243515010124...

77/173=0,2400455443015123105111411024121535303042115...

78/173=0,2412153530304211524004554430151231051114110...

79/173=0,2423452013553300342502142232220522435150101...

80/173=0,2435150101242345201355330034250214223222052...

81/173=0,2450444144531434020252513440315510011254043...

82/173=0,2502142232220522435150101242345201355330034...

83/173=0,2513440315510011254043245044414453143402025...

84/173=0,2525134403155100112540432450444144531434020...

85/173=0,2540432450444144531434020252513440315510011...

86/173=0,2552130534133233350331204054543132103542002...

87/173=0,3003425021422322205224351501012423452013553...

88/173=0,3015123105111411024121535303042115240045544...

89/173=0,3030421152400455443015123105111411024121535...

90/173=0,3042115240045544301512310511141102412153530...

91/173=0,3053413323335033120405454313210354200225521...

92/173=0,3105111411024121535303042115240045544301512...

93/173=0,3120405454313210354200225521305341332333503...

94/173=0,3132103542002255213053413323335033120405454...

95/173=0,3143402025251344031551001125404324504441445...

96/173=0,3155100112540432450444144531434020252513440...

97/173=0,3210354200225521305341332333503312040545431...

98/173=0,3222052243515010124234520135533003425021422...

99/173=0,3233350331204054543132103542002255213053413...

100/173=0,3245044414453143402025251344031551001125404...

101/173=0,3300342502142232220522435150101242345201355...

102/173=0,3312040545431321035420022552130534133233350...

103/173=0,3323335033120405454313210354200225521305341...

104/173=0,3335033120405454313210354200225521305341332...

105/173=0,3350331204054543132103542002255213053413323...

106/173=0,3402025251344031551001125404324504441445314...

107/173=0,3413323335033120405454313210354200225521305...

108/173=0,3425021422322205224351501012423452013553300...

109/173=0,3440315510011254043245044414453143402025251...

110/173=0,3452013553300342502142232220522435150101242...

111/173=0,3503312040545431321035420022552130534133233...

112/173=0,3515010124234520135533003425021422322205224...

113/173=0,3530304211524004554430151231051114110241215...

114/173=0,3542002255213053413323335033120405454313210...

115/173=0,3553300342502142232220522435150101242345201...

116/173=0,4004554430151231051114110241215353030421152...

117/173=0,4020252513440315510011254043245044414453143...

118/173=0,4031551001125404324504441445314340202525134...

119/173=0,4043245044414453143402025251344031551001125...

120/173=0,4054543132103542002255213053413323335033120...

121/173=0,4110241215353030421152400455443015123105111...

122/173=0,4121535303042115240045544301512310511141102...

123/173=0,4133233350331204054543132103542002255213053...

124/173=0,4144531434020252513440315510011254043245044...

125/173=0,4200225521305341332333503312040545431321035...

126/173=0,4211524004554430151231051114110241215353030...

127/173=0,4223222052243515010124234520135533003425021...

128/173=0,4234520135533003425021422322205224351501012...

129/173=0,4250214223222052243515010124234520135533003...

130/173=0,4301512310511141102412153530304211524004554...

131/173=0,4313210354200225521305341332333503312040545...

132/173=0,4324504441445314340202525134403155100112540...

133/173=0,4340202525134403155100112540432450444144531...

134/173=0,4351501012423452013553300342502142232220522...

135/173=0,4403155100112540432450444144531434020252513...

136/173=0,4414453143402025251344031551001125404324504...

137/173=0,4430151231051114110241215353030421152400455...

138/173=0,4441445314340202525134403155100112540432450...

139/173=0,4453143402025251344031551001125404324504441...

140/173=0,4504441445314340202525134403155100112540432...

141/173=0,4520135533003425021422322205224351501012423...

142/173=0,4531434020252513440315510011254043245044414...

143/173=0,4543132103542002255213053413323335033120405...

144/173=0,4554430151231051114110241215353030421152400...

145/173=0,5010124234520135533003425021422322205224351...

146/173=0,5021422322205224351501012423452013553300342...

147/173=0,5033120405454313210354200225521305341332333...

148/173=0,5044414453143402025251344031551001125404324...

149/173=0,5100112540432450444144531434020252513440315...

150/173=0,5111411024121535303042115240045544301512310...

151/173=0,5123105111411024121535303042115240045544301...

152/173=0,5134403155100112540432450444144531434020252...

153/173=0,5150101242345201355330034250214223222052243...

154/173=0,5201355330034250214223222052243515010124234...

155/173=0,5213053413323335033120405454313210354200225...

156/173=0,5224351501012423452013553300342502142232220...

157/173=0,5240045544301512310511141102412153530304211...

158/173=0,5251344031551001125404324504441445314340202...

159/173=0,5303042115240045544301512310511141102412153...

160/173=0,5314340202525134403155100112540432450444144...

161/173=0,5330034250214223222052243515010124234520135...

162/173=0,5341332333503312040545431321035420022552130...

163/173=0,5353030421152400455443015123105111411024121...

164/173=0,5404324504441445314340202525134403155100112...

165/173=0,5420022552130534133233350331204054543132103...

166/173=0,5431321035420022552130534133233350331204054...

167/173=0,5443015123105111411024121535303042115240045...

168/173=0,5454313210354200225521305341332333503312040...

169/173=0,5510011254043245044414453143402025251344031...

170/173=0,5521305341332333503312040545431321035420022...

171/173=0,5533003425021422322205224351501012423452013...

172/173=0,5544301512310511141102412153530304211524004...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (43) est égal à 172 et donc au premier -1.