Il existe 8 périodes de 30 chiffres pour n/241 en base 10.

Pour toutes les fractions de n/241 en base 10, la période de 1/241 revient alors 30 fois (en orange)

1/241=0,004149377593360995850622406639...

2/241=0,008298755186721991701244813278...

3/241=0,012448132780082987551867219917...

4/241=0,016597510373443983402489626556...

5/241=0,020746887966804979253112033195...

6/241=0,024896265560165975103734439834...

7/241=0,029045643153526970954356846473...

8/241=0,033195020746887966804979253112...

9/241=0,037344398340248962655601659751...

10/241=0,041493775933609958506224066390...

11/241=0,045643153526970954356846473029...

12/241=0,049792531120331950207468879668...

13/241=0,053941908713692946058091286307...

14/241=0,058091286307053941908713692946...

15/241=0,062240663900414937759336099585...

16/241=0,066390041493775933609958506224...

17/241=0,070539419087136929460580912863...

18/241=0,074688796680497925311203319502...

19/241=0,078838174273858921161825726141...

20/241=0,082987551867219917012448132780...

21/241=0,087136929460580912863070539419...

22/241=0,091286307053941908713692946058...

23/241=0,095435684647302904564315352697...

24/241=0,099585062240663900414937759336...

25/241=0,103734439834024896265560165975...

26/241=0,107883817427385892116182572614...

27/241=0,112033195020746887966804979253...

28/241=0,116182572614107883817427385892...

29/241=0,120331950207468879668049792531...

30/241=0,124481327800829875518672199170...

31/241=0,128630705394190871369294605809...

32/241=0,132780082987551867219917012448...

33/241=0,136929460580912863070539419087...

34/241=0,141078838174273858921161825726...

35/241=0,145228215767634854771784232365...

36/241=0,149377593360995850622406639004...

37/241=0,153526970954356846473029045643...

38/241=0,157676348547717842323651452282...

39/241=0,161825726141078838174273858921...

40/241=0,165975103734439834024896265560...

41/241=0,170124481327800829875518672199...

42/241=0,174273858921161825726141078838...

43/241=0,178423236514522821576763485477...

44/241=0,182572614107883817427385892116...

45/241=0,186721991701244813278008298755...

46/241=0,190871369294605809128630705394...

47/241=0,195020746887966804979253112033...

48/241=0,199170124481327800829875518672...

49/241=0,203319502074688796680497925311...

50/241=0,207468879668049792531120331950...

51/241=0,211618257261410788381742738589...

52/241=0,215767634854771784232365145228...

53/241=0,219917012448132780082987551867...

54/241=0,224066390041493775933609958506...

55/241=0,228215767634854771784232365145...

56/241=0,232365145228215767634854771784...

57/241=0,236514522821576763485477178423...

58/241=0,240663900414937759336099585062...

59/241=0,244813278008298755186721991701...

60/241=0,248962655601659751037344398340...

61/241=0,253112033195020746887966804979...

62/241=0,257261410788381742738589211618...

63/241=0,261410788381742738589211618257...

64/241=0,265560165975103734439834024896...

65/241=0,269709543568464730290456431535...

66/241=0,273858921161825726141078838174...

67/241=0,278008298755186721991701244813...

68/241=0,282157676348547717842323651452...

69/241=0,286307053941908713692946058091...

70/241=0,290456431535269709543568464730...

71/241=0,294605809128630705394190871369...

72/241=0,298755186721991701244813278008...

73/241=0,302904564315352697095435684647...

74/241=0,307053941908713692946058091286...

75/241=0,311203319502074688796680497925...

76/241=0,315352697095435684647302904564...

77/241=0,319502074688796680497925311203...

78/241=0,323651452282157676348547717842...

79/241=0,327800829875518672199170124481...

80/241=0,331950207468879668049792531120...

81/241=0,336099585062240663900414937759...

82/241=0,340248962655601659751037344398...

83/241=0,344398340248962655601659751037...

84/241=0,348547717842323651452282157676...

85/241=0,352697095435684647302904564315...

86/241=0,356846473029045643153526970954...

87/241=0,360995850622406639004149377593...

88/241=0,365145228215767634854771784232...

89/241=0,369294605809128630705394190871...

90/241=0,373443983402489626556016597510...

91/241=0,377593360995850622406639004149...

92/241=0,381742738589211618257261410788...

93/241=0,385892116182572614107883817427...

94/241=0,390041493775933609958506224066...

95/241=0,394190871369294605809128630705...

96/241=0,398340248962655601659751037344...

97/241=0,402489626556016597510373443983...

98/241=0,406639004149377593360995850622...

99/241=0,410788381742738589211618257261...

100/241=0,414937759336099585062240663900...

101/241=0,419087136929460580912863070539...

102/241=0,423236514522821576763485477178...

103/241=0,427385892116182572614107883817...

104/241=0,431535269709543568464730290456...

105/241=0,435684647302904564315352697095...

106/241=0,439834024896265560165975103734...

107/241=0,443983402489626556016597510373...

108/241=0,448132780082987551867219917012...

109/241=0,452282157676348547717842323651...

110/241=0,456431535269709543568464730290...

111/241=0,460580912863070539419087136929...

112/241=0,464730290456431535269709543568...

113/241=0,468879668049792531120331950207...

114/241=0,473029045643153526970954356846...

115/241=0,477178423236514522821576763485...

116/241=0,481327800829875518672199170124...

117/241=0,485477178423236514522821576763...

118/241=0,489626556016597510373443983402...

119/241=0,493775933609958506224066390041...

120/241=0,497925311203319502074688796680...

121/241=0,502074688796680497925311203319...

122/241=0,506224066390041493775933609958...

123/241=0,510373443983402489626556016597...

124/241=0,514522821576763485477178423236...

125/241=0,518672199170124481327800829875...

126/241=0,522821576763485477178423236514...

127/241=0,526970954356846473029045643153...

128/241=0,531120331950207468879668049792...

129/241=0,535269709543568464730290456431...

130/241=0,539419087136929460580912863070...

131/241=0,543568464730290456431535269709...

132/241=0,547717842323651452282157676348...

133/241=0,551867219917012448132780082987...

134/241=0,556016597510373443983402489626...

135/241=0,560165975103734439834024896265...

136/241=0,564315352697095435684647302904...

137/241=0,568464730290456431535269709543...

138/241=0,572614107883817427385892116182...

139/241=0,576763485477178423236514522821...

140/241=0,580912863070539419087136929460...

141/241=0,585062240663900414937759336099...

142/241=0,589211618257261410788381742738...

143/241=0,593360995850622406639004149377...

144/241=0,597510373443983402489626556016...

145/241=0,601659751037344398340248962655...

146/241=0,605809128630705394190871369294...

147/241=0,609958506224066390041493775933...

148/241=0,614107883817427385892116182572...

149/241=0,618257261410788381742738589211...

150/241=0,622406639004149377593360995850...

151/241=0,626556016597510373443983402489...

152/241=0,630705394190871369294605809128...

153/241=0,634854771784232365145228215767...

154/241=0,639004149377593360995850622406...

155/241=0,643153526970954356846473029045...

156/241=0,647302904564315352697095435684...

157/241=0,651452282157676348547717842323...

158/241=0,655601659751037344398340248962...

159/241=0,659751037344398340248962655601...

160/241=0,663900414937759336099585062240...

161/241=0,668049792531120331950207468879...

162/241=0,672199170124481327800829875518...

163/241=0,676348547717842323651452282157...

164/241=0,680497925311203319502074688796...

165/241=0,684647302904564315352697095435...

166/241=0,688796680497925311203319502074...

167/241=0,692946058091286307053941908713...

168/241=0,697095435684647302904564315352...

169/241=0,701244813278008298755186721991...

170/241=0,705394190871369294605809128630...

171/241=0,709543568464730290456431535269...

172/241=0,713692946058091286307053941908...

173/241=0,717842323651452282157676348547...

174/241=0,721991701244813278008298755186...

175/241=0,726141078838174273858921161825...

176/241=0,730290456431535269709543568464...

177/241=0,734439834024896265560165975103...

178/241=0,738589211618257261410788381742...

179/241=0,742738589211618257261410788381...

180/241=0,746887966804979253112033195020...

181/241=0,751037344398340248962655601659...

182/241=0,755186721991701244813278008298...

183/241=0,759336099585062240663900414937...

184/241=0,763485477178423236514522821576...

185/241=0,767634854771784232365145228215...

186/241=0,771784232365145228215767634854...

187/241=0,775933609958506224066390041493...

188/241=0,780082987551867219917012448132...

189/241=0,784232365145228215767634854771...

190/241=0,788381742738589211618257261410...

191/241=0,792531120331950207468879668049...

192/241=0,796680497925311203319502074688...

193/241=0,800829875518672199170124481327...

194/241=0,804979253112033195020746887966...

195/241=0,809128630705394190871369294605...

196/241=0,813278008298755186721991701244...

197/241=0,817427385892116182572614107883...

198/241=0,821576763485477178423236514522...

199/241=0,825726141078838174273858921161...

200/241=0,829875518672199170124481327800...

201/241=0,834024896265560165975103734439...

202/241=0,838174273858921161825726141078...

203/241=0,842323651452282157676348547717...

204/241=0,846473029045643153526970954356...

205/241=0,850622406639004149377593360995...

206/241=0,854771784232365145228215767634...

207/241=0,858921161825726141078838174273...

208/241=0,863070539419087136929460580912...

209/241=0,867219917012448132780082987551...

210/241=0,871369294605809128630705394190...

211/241=0,875518672199170124481327800829...

212/241=0,879668049792531120331950207468...

213/241=0,883817427385892116182572614107...

214/241=0,887966804979253112033195020746...

215/241=0,892116182572614107883817427385...

216/241=0,896265560165975103734439834024...

217/241=0,900414937759336099585062240663...

218/241=0,904564315352697095435684647302...

219/241=0,908713692946058091286307053941...

220/241=0,912863070539419087136929460580...

221/241=0,917012448132780082987551867219...

222/241=0,921161825726141078838174273858...

223/241=0,925311203319502074688796680497...

224/241=0,929460580912863070539419087136...

225/241=0,933609958506224066390041493775...

226/241=0,937759336099585062240663900414...

227/241=0,941908713692946058091286307053...

228/241=0,946058091286307053941908713692...

229/241=0,950207468879668049792531120331...

230/241=0,954356846473029045643153526970...

231/241=0,958506224066390041493775933609...

232/241=0,962655601659751037344398340248...

233/241=0,966804979253112033195020746887...

234/241=0,970954356846473029045643153526...

235/241=0,975103734439834024896265560165...

236/241=0,979253112033195020746887966804...

237/241=0,983402489626556016597510373443...

238/241=0,987551867219917012448132780082...

239/241=0,991701244813278008298755186721...

240/241=0,995850622406639004149377593360...

On remarque que le produit du nombre de périodes (8) et de leurs longueurs (30) est égal à 240 et donc au premier -1.