Il existe 2 périodes de 35 chiffres pour n/71 en base 3.

Pour toutes les fractions de n/71 en base 3, la période de 1/71 revient alors 35 fois (en orange)

1/71=0,00010102102000202112110011120012201...

2/71=0,00020211211001112001220100010102102...

3/71=0,00101021020002021121100111200122010...

4/71=0,00111200122010001010210200020211211...

5/71=0,00122010001010210200020211211001112...

6/71=0,00202112110011120012201000101021020...

7/71=0,00212221212012022202011011221110221...

8/71=0,01000101021020002021121100111200122...

9/71=0,01010210200020211211001112001220100...

10/71=0,01021020002021121100111200122010001...

11/71=0,01101122111022100212221212012022202...

12/71=0,01112001220100010102102000202112110...

13/71=0,01122111022100212221212012022202011...

14/71=0,01202220201101122111022100212221212...

15/71=0,01220100010102102000202112110011120...

16/71=0,02000202112110011120012201000101021...

17/71=0,02011011221110221002122212120120222...

18/71=0,02021121100111200122010001010210200...

19/71=0,02102000202112110011120012201000101...

20/71=0,02112110011120012201000101021020002...

21/71=0,02122212120120222020110112211102210...

22/71=0,02210021222121201202220201101122111...

23/71=0,02220201101122111022100212221212012...

24/71=0,10001010210200020211211001112001220...

25/71=0,10011120012201000101021020002021121...

26/71=0,10021222121201202220201101122111022...

27/71=0,10102102000202112110011120012201000...

28/71=0,10112211102210021222121201202220201...

29/71=0,10200020211211001112001220100010102...

30/71=0,10210200020211211001112001220100010...

31/71=0,10221002122212120120222020110112211...

32/71=0,11001112001220100010102102000202112...

33/71=0,11011221110221002122212120120222020...

34/71=0,11022100212221212012022202011011221...

35/71=0,11102210021222121201202220201101122...

36/71=0,11120012201000101021020002021121100...

37/71=0,11200122010001010210200020211211001...

38/71=0,11211001112001220100010102102000202...

39/71=0,11221110221002122212120120222020110...

40/71=0,12001220100010102102000202112110011...

41/71=0,12012022202011011221110221002122212...

42/71=0,12022202011011221110221002122212120...

43/71=0,12110011120012201000101021020002021...

44/71=0,12120120222020110112211102210021222...

45/71=0,12201000101021020002021121100111200...

46/71=0,12211102210021222121201202220201101...

47/71=0,12221212012022202011011221110221002...

48/71=0,20002021121100111200122010001010210...

49/71=0,20012201000101021020002021121100111...

50/71=0,20100010102102000202112110011120012...

51/71=0,20110112211102210021222121201202220...

52/71=0,20120222020110112211102210021222121...

53/71=0,20201101122111022100212221212012022...

54/71=0,20211211001112001220100010102102000...

55/71=0,20222020110112211102210021222121201...

56/71=0,21002122212120120222020110112211102...

57/71=0,21020002021121100111200122010001010...

58/71=0,21100111200122010001010210200020211...

59/71=0,21110221002122212120120222020110112...

60/71=0,21121100111200122010001010210200020...

61/71=0,21201202220201101122111022100212221...

62/71=0,21212012022202011011221110221002122...

63/71=0,21222121201202220201101122111022100...

64/71=0,22010001010210200020211211001112001...

65/71=0,22020110112211102210021222121201202...

66/71=0,22100212221212012022202011011221110...

67/71=0,22111022100212221212012022202011011...

68/71=0,22121201202220201101122111022100212...

69/71=0,22202011011221110221002122212120120...

70/71=0,22212120120222020110112211102210021...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (35) est égal à 70 et donc au premier -1.