Il existe 4 périodes de 48 chiffres pour n/193 en base 4.

Pour toutes les fractions de n/193 en base 4, la période de 1/193 revient alors 48 fois (en orange)

1/193=0,000111032100211020331000333222301233122313002333...

2/193=0,000222130201022101322001333111203132311232011332...

3/193=0,000333222301233122313002333000111032100211020331...

4/193=0,001110321002110203310003332223012331223130023330...

5/193=0,001222013102321230301010332111320231012103032323...

6/193=0,001333111203132311232011332000222130201022101322...

7/193=0,002110203310003332223012331223130023330001110321...

8/193=0,002221302010221013220013331112031323112320113320...

9/193=0,002333000111032100211020331000333222301233122313...

10/193=0,003110032211303121202021330223301122030212131312...

11/193=0,003221130312120202133022330112203021213131200311...

12/193=0,003332223012331223130023330001110321002110203310...

13/193=0,010103321113202310121030323230012220131023212303...

14/193=0,010221013220013331112031323112320113320002221302...

15/193=0,010332111320231012103032323001222013102321230301...

16/193=0,011103210021102033100033322230123312231300233300...

17/193=0,011220302121313120031100322113031212020213302233...

18/193=0,011332000222130201022101322001333111203132311232...

19/193=0,012103032323001222013102321230301010332111320231...

20/193=0,012220131023212303010103321113202310121030323230...

21/193=0,012331223130023330001110321002110203310003332223...

22/193=0,013102321230301010332111320231012103032323001222...

23/193=0,013220013331112031323112320113320002221302010221...

24/193=0,013331112031323112320113320002221302010221013220...

25/193=0,020102210132200133311120313231123201133200022213...

26/193=0,020213302233011220302121313120031100322113031212...

27/193=0,020331000333222301233122313002333000111032100211...

28/193=0,021102033100033322230123312231300233300011103210...

29/193=0,021213131200311003221130312120202133022330112203...

30/193=0,021330223301122030212131312003110032211303121202...

31/193=0,022101322001333111203132311232011332000222130201...

32/193=0,022213020102210132200133311120313231123201133200...

33/193=0,022330112203021213131200311003221130312120202133...

34/193=0,023101210303232300122201310232123030101033211132...

35/193=0,023212303010103321113202310121030323230012220131...

36/193=0,023330001110321002110203310003332223012331223130...

37/193=0,030101033211132023101210303232300122201310232123...

38/193=0,030212131312003110032211303121202021330223301122...

39/193=0,030323230012220131023212303010103321113202310121...

40/193=0,031100322113031212020213302233011220302121313120...

41/193=0,031212020213302233011220302121313120031100322113...

42/193=0,031323112320113320002221302010221013220013331112...

43/193=0,032100211020331000333222301233122313002333000111...

44/193=0,032211303121202021330223301122030212131312003110...

45/193=0,032323001222013102321230301010332111320231012103...

46/193=0,033100033322230123312231300233300011103210021102...

47/193=0,033211132023101210303232300122201310232123030101...

48/193=0,033322230123312231300233300011103210021102033100...

49/193=0,100033322230123312231300233300011103210021102033...

50/193=0,100211020331000333222301233122313002333000111032...

51/193=0,100322113031212020213302233011220302121313120031...

52/193=0,101033211132023101210303232300122201310232123030...

53/193=0,101210303232300122201310232123030101033211132023...

54/193=0,101322001333111203132311232011332000222130201022...

55/193=0,102033100033322230123312231300233300011103210021...

56/193=0,102210132200133311120313231123201133200022213020...

57/193=0,102321230301010332111320231012103032323001222013...

58/193=0,103032323001222013102321230301010332111320231012...

59/193=0,103210021102033100033322230123312231300233300011...

60/193=0,103321113202310121030323230012220131023212303010...

61/193=0,110032211303121202021330223301122030212131312003...

62/193=0,110203310003332223012331223130023330001110321002...

63/193=0,110321002110203310003332223012331223130023330001...

64/193=0,111032100211020331000333222301233122313002333000...

65/193=0,111203132311232011332000222130201022101322001333...

66/193=0,111320231012103032323001222013102321230301010332...

67/193=0,112031323112320113320002221302010221013220013331...

68/193=0,112203021213131200311003221130312120202133022330...

69/193=0,112320113320002221302010221013220013331112031323...

70/193=0,113031212020213302233011220302121313120031100322...

71/193=0,113202310121030323230012220131023212303010103321...

72/193=0,113320002221302010221013220013331112031323112320...

73/193=0,120031100322113031212020213302233011220302121313...

74/193=0,120202133022330112203021213131200311003221130312...

75/193=0,120313231123201133200022213020102210132200133311...

76/193=0,121030323230012220131023212303010103321113202310...

77/193=0,121202021330223301122030212131312003110032211303...

78/193=0,121313120031100322113031212020213302233011220302...

79/193=0,122030212131312003110032211303121202021330223301...

80/193=0,122201310232123030101033211132023101210303232300...

81/193=0,122313002333000111032100211020331000333222301233...

82/193=0,123030101033211132023101210303232300122201310232...

83/193=0,123201133200022213020102210132200133311120313231...

84/193=0,123312231300233300011103210021102033100033322230...

85/193=0,130023330001110321002110203310003332223012331223...

86/193=0,130201022101322001333111203132311232011332000222...

87/193=0,130312120202133022330112203021213131200311003221...

88/193=0,131023212303010103321113202310121030323230012220...

89/193=0,131200311003221130312120202133022330112203021213...

90/193=0,131312003110032211303121202021330223301122030212...

91/193=0,132023101210303232300122201310232123030101033211...

92/193=0,132200133311120313231123201133200022213020102210...

93/193=0,132311232011332000222130201022101322001333111203...

94/193=0,133022330112203021213131200311003221130312120202...

95/193=0,133200022213020102210132200133311120313231123201...

96/193=0,133311120313231123201133200022213020102210132200...

97/193=0,200022213020102210132200133311120313231123201133...

98/193=0,200133311120313231123201133200022213020102210132...

99/193=0,200311003221130312120202133022330112203021213131...

100/193=0,201022101322001333111203132311232011332000222130...

101/193=0,201133200022213020102210132200133311120313231123...

102/193=0,201310232123030101033211132023101210303232300122...

103/193=0,202021330223301122030212131312003110032211303121...

104/193=0,202133022330112203021213131200311003221130312120...

105/193=0,202310121030323230012220131023212303010103321113...

106/193=0,203021213131200311003221130312120202133022330112...

107/193=0,203132311232011332000222130201022101322001333111...

108/193=0,203310003332223012331223130023330001110321002110...

109/193=0,210021102033100033322230123312231300233300011103...

110/193=0,210132200133311120313231123201133200022213020102...

111/193=0,210303232300122201310232123030101033211132023101...

112/193=0,211020331000333222301233122313002333000111032100...

113/193=0,211132023101210303232300122201310232123030101033...

114/193=0,211303121202021330223301122030212131312003110032...

115/193=0,212020213302233011220302121313120031100322113031...

116/193=0,212131312003110032211303121202021330223301122030...

117/193=0,212303010103321113202310121030323230012220131023...

118/193=0,213020102210132200133311120313231123201133200022...

119/193=0,213131200311003221130312120202133022330112203021...

120/193=0,213302233011220302121313120031100322113031212020...

121/193=0,220013331112031323112320113320002221302010221013...

122/193=0,220131023212303010103321113202310121030323230012...

123/193=0,220302121313120031100322113031212020213302233011...

124/193=0,221013220013331112031323112320113320002221302010...

125/193=0,221130312120202133022330112203021213131200311003...

126/193=0,221302010221013220013331112031323112320113320002...

127/193=0,222013102321230301010332111320231012103032323001...

128/193=0,222130201022101322001333111203132311232011332000...

129/193=0,222301233122313002333000111032100211020331000333...

130/193=0,223012331223130023330001110321002110203310003332...

131/193=0,223130023330001110321002110203310003332223012331...

132/193=0,223301122030212131312003110032211303121202021330...

133/193=0,230012220131023212303010103321113202310121030323...

134/193=0,230123312231300233300011103210021102033100033322...

135/193=0,230301010332111320231012103032323001222013102321...

136/193=0,231012103032323001222013102321230301010332111320...

137/193=0,231123201133200022213020102210132200133311120313...

138/193=0,231300233300011103210021102033100033322230123312...

139/193=0,232011332000222130201022101322001333111203132311...

140/193=0,232123030101033211132023101210303232300122201310...

141/193=0,232300122201310232123030101033211132023101210303...

142/193=0,233011220302121313120031100322113031212020213302...

143/193=0,233122313002333000111032100211020331000333222301...

144/193=0,233300011103210021102033100033322230123312231300...

145/193=0,300011103210021102033100033322230123312231300233...

146/193=0,300122201310232123030101033211132023101210303232...

147/193=0,300233300011103210021102033100033322230123312231...

148/193=0,301010332111320231012103032323001222013102321230...

149/193=0,301122030212131312003110032211303121202021330223...

150/193=0,301233122313002333000111032100211020331000333222...

151/193=0,302010221013220013331112031323112320113320002221...

152/193=0,302121313120031100322113031212020213302233011220...

153/193=0,302233011220302121313120031100322113031212020213...

154/193=0,303010103321113202310121030323230012220131023212...

155/193=0,303121202021330223301122030212131312003110032211...

156/193=0,303232300122201310232123030101033211132023101210...

157/193=0,310003332223012331223130023330001110321002110203...

158/193=0,310121030323230012220131023212303010103321113202...

159/193=0,310232123030101033211132023101210303232300122201...

160/193=0,311003221130312120202133022330112203021213131200...

161/193=0,311120313231123201133200022213020102210132200133...

162/193=0,311232011332000222130201022101322001333111203132...

163/193=0,312003110032211303121202021330223301122030212131...

164/193=0,312120202133022330112203021213131200311003221130...

165/193=0,312231300233300011103210021102033100033322230123...

166/193=0,313002333000111032100211020331000333222301233122...

167/193=0,313120031100322113031212020213302233011220302121...

168/193=0,313231123201133200022213020102210132200133311120...

169/193=0,320002221302010221013220013331112031323112320113...

170/193=0,320113320002221302010221013220013331112031323112...

171/193=0,320231012103032323001222013102321230301010332111...

172/193=0,321002110203310003332223012331223130023330001110...

173/193=0,321113202310121030323230012220131023212303010103...

174/193=0,321230301010332111320231012103032323001222013102...

175/193=0,322001333111203132311232011332000222130201022101...

176/193=0,322113031212020213302233011220302121313120031100...

177/193=0,322230123312231300233300011103210021102033100033...

178/193=0,323001222013102321230301010332111320231012103032...

179/193=0,323112320113320002221302010221013220013331112031...

180/193=0,323230012220131023212303010103321113202310121030...

181/193=0,330001110321002110203310003332223012331223130023...

182/193=0,330112203021213131200311003221130312120202133022...

183/193=0,330223301122030212131312003110032211303121202021...

184/193=0,331000333222301233122313002333000111032100211020...

185/193=0,331112031323112320113320002221302010221013220013...

186/193=0,331223130023330001110321002110203310003332223012...

187/193=0,332000222130201022101322001333111203132311232011...

188/193=0,332111320231012103032323001222013102321230301010...

189/193=0,332223012331223130023330001110321002110203310003...

190/193=0,333000111032100211020331000333222301233122313002...

191/193=0,333111203132311232011332000222130201022101322001...

192/193=0,333222301233122313002333000111032100211020331000...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (48) est égal à 192 et donc au premier -1.