Il existe 10 périodes de 25 chiffres pour n/251 en base 4.

Pour toutes les fractions de n/251 en base 4, la période de 1/251 revient alors 25 fois (en orange)

1/251=0,0001001101211333133113031...

2/251=0,0002002203023332332232122...

3/251=0,0003003310301332132011213...

4/251=0,0010011012113331331130310...

5/251=0,0011012113331331130310001...

6/251=0,0012013221203330330023032...

7/251=0,0013020323021330123202123...

8/251=0,0020022030233323322321220...

9/251=0,0021023132111323122100311...

10/251=0,0022030233323322321220002...

11/251=0,0023032001201322120333033...

12/251=0,0030033103013321320112130...

13/251=0,0031100210231321113231221...

14/251=0,0032101312103320313010312...

15/251=0,0033103013321320112130003...

16/251=0,0100110121133313311303100...

17/251=0,0101111223011313111022131...

18/251=0,0102112330223312310201222...

19/251=0,0103120032101312103320313...

20/251=0,0110121133313311303100010...

21/251=0,0111122301131311102213101...

22/251=0,0112130003003310301332132...

23/251=0,0113131110221310101111223...

24/251=0,0120132212033303300230320...

25/251=0,0121133313311303100010011...

26/251=0,0122201021123302233123102...

27/251=0,0123202123001302032302133...

28/251=0,0130203230213301232021230...

29/251=0,0131210332031301031200321...

30/251=0,0132212033303300230320012...

31/251=0,0133213201121300030033103...

32/251=0,0200220302333233223212200...

33/251=0,0201222010211233022331231...

34/251=0,0202223112023232222110322...

35/251=0,0203230213301232021230013...

36/251=0,0210231321113231221003110...

37/251=0,0211233022331231020122201...

38/251=0,0212300130203230213301232...

39/251=0,0213301232021230013020323...

40/251=0,0220302333233223212200020...

41/251=0,0221310101111223011313111...

42/251=0,0222311202323222211032202...

43/251=0,0223312310201222010211233...

44/251=0,0230320012013221203330330...

45/251=0,0231321113231221003110021...

46/251=0,0232322221103220202223112...

47/251=0,0233323322321220002002203...

48/251=0,0300331030133213201121300...

49/251=0,0301332132011213000300331...

50/251=0,0302333233223212200020022...

51/251=0,0310001001101211333133113...

52/251=0,0311002102313211132312210...

53/251=0,0312003210131210332031301...

54/251=0,0313010312003210131210332...

55/251=0,0320012013221203330330023...

56/251=0,0321013121033203130103120...

57/251=0,0322020222311202323222211...

58/251=0,0323021330123202123001302...

59/251=0,0330023032001201322120333...

60/251=0,0331030133213201121300030...

61/251=0,0332031301031200321013121...

62/251=0,0333033002303200120132212...

63/251=0,1000100110121133313311303...

64/251=0,1001101211333133113031000...

65/251=0,1002102313211132312210031...

66/251=0,1003110021023132111323122...

67/251=0,1010111122301131311102213...

68/251=0,1011112230113131110221310...

69/251=0,1012113331331130310001001...

70/251=0,1013121033203130103120032...

71/251=0,1020122201021123302233123...

72/251=0,1021123302233123102012220...

73/251=0,1022131010111122301131311...

74/251=0,1023132111323122100311002...

75/251=0,1030133213201121300030033...

76/251=0,1031200321013121033203130...

77/251=0,1032202022231120232322221...

78/251=0,1033203130103120032101312...

79/251=0,1100210231321113231221003...

80/251=0,1101211333133113031000100...

81/251=0,1102213101011112230113131...

82/251=0,1103220202223112023232222...

83/251=0,1110221310101111223011313...

84/251=0,1111223011313111022131010...

85/251=0,1112230113131110221310101...

86/251=0,1113231221003110021023132...

87/251=0,1120232322221103220202223...

88/251=0,1121300030033103013321320...

89/251=0,1122301131311102213101011...

90/251=0,1123302233123102012220102...

91/251=0,1130310001001101211333133...

92/251=0,1131311102213101011112230...

93/251=0,1132312210031100210231321...

94/251=0,1133313311303100010011012...

95/251=0,1200321013121033203130103...

96/251=0,1201322120333033002303200...

97/251=0,1202323222211032202022231...

98/251=0,1203330330023032001201322...

99/251=0,1210332031301031200321013...

100/251=0,1211333133113031000100110...

101/251=0,1213000300331030133213201...

102/251=0,1220002002203023332332232...

103/251=0,1221003110021023132111323...

104/251=0,1222010211233022331231020...

105/251=0,1223011313111022131010111...

106/251=0,1230013020323021330123202...

107/251=0,1231020122201021123302233...

108/251=0,1232021230013020323021330...

109/251=0,1233022331231020122201021...

110/251=0,1300030033103013321320112...

111/251=0,1301031200321013121033203...

112/251=0,1302032302133012320212300...

113/251=0,1303100010011012113331331...

114/251=0,1310101111223011313111022...

115/251=0,1311102213101011112230113...

116/251=0,1312103320313010312003210...

117/251=0,1313111022131010111122301...

118/251=0,1320112130003003310301332...

119/251=0,1321113231221003110021023...

120/251=0,1322120333033002303200120...

121/251=0,1323122100311002102313211...

122/251=0,1330123202123001302032302...

123/251=0,1331130310001001101211333...

124/251=0,1332132011213000300331030...

125/251=0,1333133113031000100110121...

126/251=0,2000200220302333233223212...

127/251=0,2001201322120333033002303...

128/251=0,2002203023332332232122000...

129/251=0,2003210131210332031301031...

130/251=0,2010211233022331231020122...

131/251=0,2011213000300331030133213...

132/251=0,2012220102112330223312310...

133/251=0,2013221203330330023032001...

134/251=0,2020222311202323222211032...

135/251=0,2021230013020323021330123...

136/251=0,2022231120232322221103220...

137/251=0,2023232222110322020222311...

138/251=0,2030233323322321220002002...

139/251=0,2031301031200321013121033...

140/251=0,2032302133012320212300130...

141/251=0,2033303300230320012013221...

142/251=0,2100311002102313211132312...

143/251=0,2101312103320313010312003...

144/251=0,2102313211132312210031100...

145/251=0,2103320313010312003210131...

146/251=0,2110322020222311202323222...

147/251=0,2111323122100311002102313...

148/251=0,2112330223312310201222010...

149/251=0,2113331331130310001001101...

150/251=0,2120333033002303200120132...

151/251=0,2122000200220302333233223...

152/251=0,2123001302032302133012320...

153/251=0,2130003003310301332132011...

154/251=0,2131010111122301131311102...

155/251=0,2132011213000300331030133...

156/251=0,2133012320212300130203230...

157/251=0,2200020022030233323322321...

158/251=0,2201021123302233123102012...

159/251=0,2202022231120232322221103...

160/251=0,2203023332332232122000200...

161/251=0,2210031100210231321113231...

162/251=0,2211032202022231120232322...

163/251=0,2212033303300230320012013...

164/251=0,2213101011112230113131110...

165/251=0,2220102112330223312310201...

166/251=0,2221103220202223112023232...

167/251=0,2222110322020222311202323...

168/251=0,2223112023232222110322020...

169/251=0,2230113131110221310101111...

170/251=0,2231120232322221103220202...

171/251=0,2232122000200220302333233...

172/251=0,2233123102012220102112330...

173/251=0,2300130203230213301232021...

174/251=0,2301131311102213101011112...

175/251=0,2302133012320212300130203...

176/251=0,2303200120132212033303300...

177/251=0,2310201222010211233022331...

178/251=0,2311202323222211032202022...

179/251=0,2312210031100210231321113...

180/251=0,2313211132312210031100210...

181/251=0,2320212300130203230213301...

182/251=0,2321220002002203023332332...

183/251=0,2322221103220202223112023...

184/251=0,2323222211032202022231120...

185/251=0,2330223312310201222010211...

186/251=0,2331231020122201021123302...

187/251=0,2332232122000200220302333...

188/251=0,2333233223212200020022030...

189/251=0,3000300331030133213201121...

190/251=0,3001302032302133012320212...

191/251=0,3002303200120132212033303...

192/251=0,3003310301332132011213000...

193/251=0,3010312003210131210332031...

194/251=0,3011313111022131010111122...

195/251=0,3012320212300130203230213...

196/251=0,3013321320112130003003310...

197/251=0,3020323021330123202123001...

198/251=0,3021330123202123001302032...

199/251=0,3022331231020122201021123...

200/251=0,3023332332232122000200220...

201/251=0,3031000100110121133313311...

202/251=0,3032001201322120333033002...

203/251=0,3033002303200120132212033...

204/251=0,3100010011012113331331130...

205/251=0,3101011112230113131110221...

206/251=0,3102012220102112330223312...

207/251=0,3103013321320112130003003...

208/251=0,3110021023132111323122100...

209/251=0,3111022131010111122301131...

210/251=0,3112023232222110322020222...

211/251=0,3113031000100110121133313...

212/251=0,3120032101312103320313010...

213/251=0,3121033203130103120032101...

214/251=0,3122100311002102313211132...

215/251=0,3123102012220102112330223...

216/251=0,3130103120032101312103320...

217/251=0,3131110221310101111223011...

218/251=0,3132111323122100311002102...

219/251=0,3133113031000100110121133...

220/251=0,3200120132212033303300230...

221/251=0,3201121300030033103013321...

222/251=0,3202123001302032302133012...

223/251=0,3203130103120032101312103...

224/251=0,3210131210332031301031200...

225/251=0,3211132312210031100210231...

226/251=0,3212200020022030233323322...

227/251=0,3213201121300030033103013...

228/251=0,3220202223112023232222110...

229/251=0,3221203330330023032001201...

230/251=0,3222211032202022231120232...

231/251=0,3223212200020022030233323...

232/251=0,3230213301232021230013020...

233/251=0,3231221003110021023132111...

234/251=0,3232222110322020222311202...

235/251=0,3233223212200020022030233...

236/251=0,3300230320012013221203330...

237/251=0,3301232021230013020323021...

238/251=0,3302233123102012220102112...

239/251=0,3303300230320012013221203...

240/251=0,3310301332132011213000300...

241/251=0,3311303100010011012113331...

242/251=0,3312310201222010211233022...

243/251=0,3313311303100010011012113...

244/251=0,3320313010312003210131210...

245/251=0,3321320112130003003310301...

246/251=0,3322321220002002203023332...

247/251=0,3323322321220002002203023...

248/251=0,3330330023032001201322120...

249/251=0,3331331130310001001101211...

250/251=0,3332332232122000200220302...

On remarque que le produit du nombre de périodes (10) et de leurs longueurs (25) est égal à 250 et donc au premier -1.