Il existe 2 périodes de 105 chiffres pour n/211 en base 6.

Pour toutes les fractions de n/211 en base 6, la période de 1/211 revient alors 105 fois (en orange)

1/211=0,001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445...

2/211=0,002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334...

3/211=0,003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223...

4/211=0,004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112...

5/211=0,005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001...

6/211=0,010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450...

7/211=0,011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335...

8/211=0,012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224...

9/211=0,013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113...

10/211=0,014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002...

11/211=0,015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451...

12/211=0,020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340...

13/211=0,021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225...

14/211=0,022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114...

15/211=0,023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003...

16/211=0,024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452...

17/211=0,025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341...

18/211=0,030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230...

19/211=0,031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115...

20/211=0,032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004...

21/211=0,033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453...

22/211=0,034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342...

23/211=0,035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231...

24/211=0,040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120...

25/211=0,041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005...

26/211=0,042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454...

27/211=0,043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343...

28/211=0,044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232...

29/211=0,045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121...

30/211=0,050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010...

31/211=0,051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455...

32/211=0,052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344...

33/211=0,053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233...

34/211=0,054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122...

35/211=0,055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011...

36/211=0,100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500...

37/211=0,101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345...

38/211=0,102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234...

39/211=0,103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123...

40/211=0,104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012...

41/211=0,105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501...

42/211=0,110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350...

43/211=0,112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235...

44/211=0,113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124...

45/211=0,114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013...

46/211=0,115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502...

47/211=0,120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351...

48/211=0,121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240...

49/211=0,122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125...

50/211=0,123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014...

51/211=0,124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503...

52/211=0,125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352...

53/211=0,130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241...

54/211=0,131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130...

55/211=0,132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015...

56/211=0,133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504...

57/211=0,134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353...

58/211=0,135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242...

59/211=0,140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131...

60/211=0,141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020...

61/211=0,142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505...

62/211=0,143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354...

63/211=0,144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243...

64/211=0,145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132...

65/211=0,150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021...

66/211=0,151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510...

67/211=0,152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355...

68/211=0,153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244...

69/211=0,154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133...

70/211=0,155354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022...

71/211=0,200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511...

72/211=0,201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400...

73/211=0,202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245...

74/211=0,203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134...

75/211=0,204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023...

76/211=0,205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512...

77/211=0,210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401...

78/211=0,211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250...

79/211=0,212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135...

80/211=0,213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024...

81/211=0,214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513...

82/211=0,215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402...

83/211=0,220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251...

84/211=0,221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140...

85/211=0,223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025...

86/211=0,224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514...

87/211=0,225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403...

88/211=0,230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252...

89/211=0,231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141...

90/211=0,232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030...

91/211=0,233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515...

92/211=0,234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404...

93/211=0,235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253...

94/211=0,240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142...

95/211=0,241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031...

96/211=0,242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520...

97/211=0,243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405...

98/211=0,244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254...

99/211=0,245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143...

100/211=0,250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032...

101/211=0,251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521...

102/211=0,252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410...

103/211=0,253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033255...

104/211=0,254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144...

105/211=0,255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321453033...

106/211=0,300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522...

107/211=0,301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411...

108/211=0,302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300...

109/211=0,303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145...

110/211=0,304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034...

111/211=0,305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523...

112/211=0,310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412...

113/211=0,311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301...

114/211=0,312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150...

115/211=0,313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035...

116/211=0,314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524...

117/211=0,315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413...

118/211=0,320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302...

119/211=0,321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151...

120/211=0,322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040...

121/211=0,323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525...

122/211=0,324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414...

123/211=0,325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303...

124/211=0,330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152...

125/211=0,331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041...

126/211=0,332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530...

127/211=0,334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415...

128/211=0,335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304...

129/211=0,340020141231035313420343043350110554550514224012104540423410252230030232044355152330534405243144254244153...

130/211=0,341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210454042...

131/211=0,342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103531...

132/211=0,343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420...

133/211=0,344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305...

134/211=0,345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154...

135/211=0,350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043...

136/211=0,351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532...

137/211=0,352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421...

138/211=0,353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310...

139/211=0,354143245202421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155...

140/211=0,355152330534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044...

141/211=0,400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533...

142/211=0,401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422...

143/211=0,402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311...

144/211=0,403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200...

145/211=0,404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045...

146/211=0,405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330534...

147/211=0,410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540423...

148/211=0,411301311402215535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312...

149/211=0,412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201...

150/211=0,413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050...

151/211=0,414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535...

152/211=0,415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425424...

153/211=0,420343043350110554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313...

154/211=0,421352125122054450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202...

155/211=0,422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051...

156/211=0,423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104540...

157/211=0,424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314425...

158/211=0,425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440524314...

159/211=0,430433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203...

160/211=0,431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052...

161/211=0,432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541...

162/211=0,433501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430...

163/211=0,434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315...

164/211=0,435515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204...

165/211=0,440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053...

166/211=0,441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542...

167/211=0,442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431...

168/211=0,443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320...

169/211=0,445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205...

170/211=0,450010050413315434510151321453033255253235112004032250211503124113013114022155354143245202421352125122054...

171/211=0,451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331543...

172/211=0,452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432...

173/211=0,453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434510151321...

174/211=0,454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055455051422401210...

175/211=0,455051422401210454042341025223003023204435515233053440524314425424415334002014123103531342034304335011055...

176/211=0,500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544...

177/211=0,501105545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433...

178/211=0,502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552532351120040322...

179/211=0,503124113013114022155354143245202421352125122054450010050413315434510151321453033255253235112004032250211...

180/211=0,504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100...

181/211=0,505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105545...

182/211=0,510151321453033255253235112004032250211503124113013114022155354143245202421352125122054450010050413315434...

183/211=0,511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325525323...

184/211=0,512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324520242135212...

185/211=0,513214530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101...

186/211=0,514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550...

187/211=0,515233053440524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435...

188/211=0,520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215535414324...

189/211=0,521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213...

190/211=0,522300302320443551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102...

191/211=0,523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443551...

192/211=0,524314425424415334002014123103531342034304335011055455051422401210454042341025223003023204435515233053440...

193/211=0,525323511200403225021150312411301311402215535414324520242135212512205445001005041331543451015132145303325...

194/211=0,530332552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214...

195/211=0,531342034304335011055455051422401210454042341025223003023204435515233053440524314425424415334002014123103...

196/211=0,532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332552...

197/211=0,533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442542441...

198/211=0,534405243144254244153340020141231035313420343043350110554550514224012104540423410252230030232044355152330...

199/211=0,535414324520242135212512205445001005041331543451015132145303325525323511200403225021150312411301311402215...

200/211=0,540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554550514224012104...

201/211=0,541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221553...

202/211=0,542441533400201412310353134203430433501105545505142240121045404234102522300302320443551523305344052431442...

203/211=0,543451015132145303325525323511200403225021150312411301311402215535414324520242135212512205445001005041331...

204/211=0,544500100504133154345101513214530332552532351120040322502115031241130131140221553541432452024213521251220...

205/211=0,545505142240121045404234102522300302320443551523305344052431442542441533400201412310353134203430433501105...

206/211=0,550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110554...

207/211=0,551523305344052431442542441533400201412310353134203430433501105545505142240121045404234102522300302320443...

208/211=0,552532351120040322502115031241130131140221553541432452024213521251220544500100504133154345101513214530332...

209/211=0,553541432452024213521251220544500100504133154345101513214530332552532351120040322502115031241130131140221...

210/211=0,554550514224012104540423410252230030232044355152330534405243144254244153340020141231035313420343043350110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (105) est égal à 210 et donc au premier -1.