Il existe 6 périodes de 37 chiffres pour n/223 en base 4.

Pour toutes les fractions de n/223 en base 4, la période de 1/223 revient alors 37 fois (en orange)

1/223=0,0001021132020213002000210233010103201...

2/223=0,0002102330101032010001021132020213002...

3/223=0,0003130122121311012001232031030322203...

4/223=0,0010211320202130020002102330101032010...

5/223=0,0011233112223003022002313223111201211...

6/223=0,0012320310303222030003130122121311012...

7/223=0,0020002102330101032010001021132020213...

8/223=0,0021023301010320100010211320202130020...

9/223=0,0022111033031133102011022213212233221...

10/223=0,0023132231112012110011233112223003022...

11/223=0,0030220023132231112012110011233112223...

12/223=0,0031301221213110120012320310303222030...

13/223=0,0032323013233323122013131203313331231...

14/223=0,0100010211320202130020002102330101032...

15/223=0,0101032010001021132020213002000210233...

16/223=0,0102113202021300200021023301010320100...

17/223=0,0103201000102113202021300200021023301...

18/223=0,0110222132122332210022111033031133102...

19/223=0,0111303330203211212022321332101302303...

20/223=0,0112331122230030220023132231112012110...

21/223=0,0120012320310303222030003130122121311...

22/223=0,0121100112331122230030220023132231112...

23/223=0,0122121311012001232031030322203000313...

24/223=0,0123203103032220300031301221213110120...

25/223=0,0130230301113033302032112120223213321...

26/223=0,0131312033133312310032323013233323122...

27/223=0,0132333231220131312033133312310032323...

28/223=0,0200021023301010320100010211320202130...

29/223=0,0201102221321223322100221110330311331...

30/223=0,0202130020002102330101032010001021132...

31/223=0,0203211212022321332101302303011130333...

32/223=0,0210233010103201000102113202021300200...

33/223=0,0211320202130020002102330101032010001...

34/223=0,0213002000210233010103201000102113202...

35/223=0,0220023132231112012110011233112223003...

36/223=0,0221110330311331020110222132122332210...

37/223=0,0222132122332210022111033031133102011...

38/223=0,0223213321013023030111303330203211212...

39/223=0,0230301113033302032112120223213321013...

40/223=0,0231322311120121100112331122230030220...

41/223=0,0233010103201000102113202021300200021...

42/223=0,0300031301221213110120012320310303222...

43/223=0,0301113033302032112120223213321013023...

44/223=0,0302200231322311120121100112331122230...

45/223=0,0303222030003130122121311012001232031...

46/223=0,0310303222030003130122121311012001232...

47/223=0,0311331020110222132122332210022111033...

48/223=0,0313012212131101200123203103032220300...

49/223=0,0320100010211320202130020002102330101...

50/223=0,0321121202232133210130230301113033302...

51/223=0,0322203000313012212131101200123203103...

52/223=0,0323230132333231220131312033133312310...

53/223=0,0330311331020110222132122332210022111...

54/223=0,0331333123100323230132333231220131312...

55/223=0,0333020321121202232133210130230301113...

56/223=0,1000102113202021300200021023301010320...

57/223=0,1001123311222300302200231322311120121...

58/223=0,1002211103303113310201102221321223322...

59/223=0,1003232301323332312201313120331333123...

60/223=0,1010320100010211320202130020002102330...

61/223=0,1012001232031030322203000313012212131...

62/223=0,1013023030111303330203211212022321332...

63/223=0,1020110222132122332210022111033031133...

64/223=0,1021132020213002000210233010103201000...

65/223=0,1022213212233221002211103303113310201...

66/223=0,1023301010320100010211320202130020002...

67/223=0,1030322203000313012212131101200123203...

68/223=0,1032010001021132020213002000210233010...

69/223=0,1033031133102011022213212233221002211...

70/223=0,1100112331122230030220023132231112012...

71/223=0,1101200123203103032220300031301221213...

72/223=0,1102221321223322100221110330311331020...

73/223=0,1103303113310201102221321223322100221...

74/223=0,1110330311331020110222132122332210022...

75/223=0,1112012110011233112223003022002313223...

76/223=0,1113033302032112120223213321013023030...

77/223=0,1120121100112331122230030220023132231...

78/223=0,1121202232133210130230301113033302032...

79/223=0,1122230030220023132231112012110011233...

80/223=0,1123311222300302200231322311120121100...

81/223=0,1130333020321121202232133210130230301...

82/223=0,1132020213002000210233010103201000102...

83/223=0,1133102011022213212233221002211103303...

84/223=0,1200123203103032220300031301221213110...

85/223=0,1201211001123311222300302200231322311...

86/223=0,1202232133210130230301113033302032112...

87/223=0,1203313331231003232301323332312201313...

88/223=0,1211001123311222300302200231322311120...

89/223=0,1212022321332101302303011130333020321...

90/223=0,1213110120012320310303222030003130122...

91/223=0,1220131312033133312310032323013233323...

92/223=0,1221213110120012320310303222030003130...

93/223=0,1222300302200231322311120121100112331...

94/223=0,1223322100221110330311331020110222132...

95/223=0,1231003232301323332312201313120331333...

96/223=0,1232031030322203000313012212131101200...

97/223=0,1233112223003022002313223111201211001...

98/223=0,1300200021023301010320100010211320202...

99/223=0,1301221213110120012320310303222030003...

100/223=0,1302303011130333020321121202232133210...

101/223=0,1303330203211212022321332101302303011...

102/223=0,1311012001232031030322203000313012212...

103/223=0,1312033133312310032323013233323122013...

104/223=0,1313120331333123100323230132333231220...

105/223=0,1320202130020002102330101032010001021...

106/223=0,1321223322100221110330311331020110222...

107/223=0,1322311120121100112331122230030220023...

108/223=0,1323332312201313120331333123100323230...

109/223=0,1331020110222132122332210022111033031...

110/223=0,1332101302303011130333020321121202232...

111/223=0,1333123100323230132333231220131312033...

112/223=0,2000210233010103201000102113202021300...

113/223=0,2001232031030322203000313012212131101...

114/223=0,2002313223111201211001123311222300302...

115/223=0,2010001021132020213002000210233010103...

116/223=0,2011022213212233221002211103303113310...

117/223=0,2012110011233112223003022002313223111...

118/223=0,2013131203313331231003232301323332312...

119/223=0,2020213002000210233010103201000102113...

120/223=0,2021300200021023301010320100010211320...

121/223=0,2022321332101302303011130333020321121...

122/223=0,2030003130122121311012001232031030322...

123/223=0,2031030322203000313012212131101200123...

124/223=0,2032112120223213321013023030111303330...

125/223=0,2033133312310032323013233323122013131...

126/223=0,2100221110330311331020110222132122332...

127/223=0,2101302303011130333020321121202232133...

128/223=0,2102330101032010001021132020213002000...

129/223=0,2110011233112223003022002313223111201...

130/223=0,2111033031133102011022213212233221002...

131/223=0,2112120223213321013023030111303330203...

132/223=0,2113202021300200021023301010320100010...

133/223=0,2120223213321013023030111303330203211...

134/223=0,2121311012001232031030322203000313012...

135/223=0,2122332210022111033031133102011022213...

136/223=0,2130020002102330101032010001021132020...

137/223=0,2131101200123203103032220300031301221...

138/223=0,2132122332210022111033031133102011022...

139/223=0,2133210130230301113033302032112120223...

140/223=0,2200231322311120121100112331122230030...

141/223=0,2201313120331333123100323230132333231...

142/223=0,2203000313012212131101200123203103032...

143/223=0,2210022111033031133102011022213212233...

144/223=0,2211103303113310201102221321223322100...

145/223=0,2212131101200123203103032220300031301...

146/223=0,2213212233221002211103303113310201102...

147/223=0,2220300031301221213110120012320310303...

148/223=0,2221321223322100221110330311331020110...

149/223=0,2223003022002313223111201211001123311...

150/223=0,2230030220023132231112012110011233112...

151/223=0,2231112012110011233112223003022002313...

152/223=0,2232133210130230301113033302032112120...

153/223=0,2233221002211103303113310201102221321...

154/223=0,2300302200231322311120121100112331122...

155/223=0,2301323332312201313120331333123100323...

156/223=0,2303011130333020321121202232133210130...

157/223=0,2310032323013233323122013131203313331...

158/223=0,2311120121100112331122230030220023132...

159/223=0,2312201313120331333123100323230132333...

160/223=0,2313223111201211001123311222300302200...

161/223=0,2320310303222030003130122121311012001...

162/223=0,2321332101302303011130333020321121202...

163/223=0,2323013233323122013131203313331231003...

164/223=0,2330101032010001021132020213002000210...

165/223=0,2331122230030220023132231112012110011...

166/223=0,2332210022111033031133102011022213212...

167/223=0,2333231220131312033133312310032323013...

168/223=0,3000313012212131101200123203103032220...

169/223=0,3002000210233010103201000102113202021...

170/223=0,3003022002313223111201211001123311222...

171/223=0,3010103201000102113202021300200021023...

172/223=0,3011130333020321121202232133210130230...

173/223=0,3012212131101200123203103032220300031...

174/223=0,3013233323122013131203313331231003232...

175/223=0,3020321121202232133210130230301113033...

176/223=0,3022002313223111201211001123311222300...

177/223=0,3023030111303330203211212022321332101...

178/223=0,3030111303330203211212022321332101302...

179/223=0,3031133102011022213212233221002211103...

180/223=0,3032220300031301221213110120012320310...

181/223=0,3033302032112120223213321013023030111...

182/223=0,3100323230132333231220131312033133312...

183/223=0,3102011022213212233221002211103303113...

184/223=0,3103032220300031301221213110120012320...

185/223=0,3110120012320310303222030003130122121...

186/223=0,3111201211001123311222300302200231322...

187/223=0,3112223003022002313223111201211001123...

188/223=0,3113310201102221321223322100221110330...

189/223=0,3120331333123100323230132333231220131...

190/223=0,3122013131203313331231003232301323332...

191/223=0,3123100323230132333231220131312033133...

192/223=0,3130122121311012001232031030322203000...

193/223=0,3131203313331231003232301323332312201...

194/223=0,3132231112012110011233112223003022002...

195/223=0,3133312310032323013233323122013131203...

196/223=0,3201000102113202021300200021023301010...

197/223=0,3202021300200021023301010320100010211...

198/223=0,3203103032220300031301221213110120012...

199/223=0,3210130230301113033302032112120223213...

200/223=0,3211212022321332101302303011130333020...

201/223=0,3212233221002211103303113310201102221...

202/223=0,3213321013023030111303330203211212022...

203/223=0,3221002211103303113310201102221321223...

204/223=0,3222030003130122121311012001232031030...

205/223=0,3223111201211001123311222300302200231...

206/223=0,3230132333231220131312033133312310032...

207/223=0,3231220131312033133312310032323013233...

208/223=0,3232301323332312201313120331333123100...

209/223=0,3233323122013131203313331231003232301...

210/223=0,3301010320100010211320202130020002102...

211/223=0,3302032112120223213321013023030111303...

212/223=0,3303113310201102221321223322100221110...

213/223=0,3310201102221321223322100221110330311...

214/223=0,3311222300302200231322311120121100112...

215/223=0,3312310032323013233323122013131203313...

216/223=0,3313331231003232301323332312201313120...

217/223=0,3321013023030111303330203211212022321...

218/223=0,3322100221110330311331020110222132122...

219/223=0,3323122013131203313331231003232301323...

220/223=0,3330203211212022321332101302303011130...

221/223=0,3331231003232301323332312201313120331...

222/223=0,3332312201313120331333123100323230132...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (37) est égal à 222 et donc au premier -1.