Liste des fractions de n/47 en base 3.

Il existe 2 périodes de 23 chiffres pour n/47 en base 3.

Pour toutes les fractions de n/47 en base 3, la période de 1/47 revient alors 23 fois (en orange)

1/47=0,00012011121002022001011...

2/47=0,00101100012011121002022...

3/47=0,00120111210020220010110...

4/47=0,00202200101100012011121...

5/47=0,00221211222102111012202...

6/47=0,01011000120111210020220...

7/47=0,01100012011121002022001...

8/47=0,01112100202200101100012...

9/47=0,01201112100202200101100...

10/47=0,01220200221211222102111...

11/47=0,02002212112221021110122...

12/47=0,02022001011000120111210...

13/47=0,02111012202002212112221...

14/47=0,02200101100012011121002...

15/47=0,02212112221021110122020...

16/47=0,10001201112100202200101...

17/47=0,10020220010110001201112...

18/47=0,10110001201112100202200...

19/47=0,10122020022121122210211...

20/47=0,10211101220200221211222...

21/47=0,11000120111210020220010...

22/47=0,11012202002212112221021...

23/47=0,11101220200221211222102...

24/47=0,11121002022001011000120...

25/47=0,11210020220010110001201...

26/47=0,11222102111012202002212...

27/47=0,12011121002022001011000...

28/47=0,12100202200101100012011...

29/47=0,12112221021110122020022...

30/47=0,12202002212112221021110...

31/47=0,12221021110122020022121...

32/47=0,20010110001201112100202...

33/47=0,20022121122210211101220...

34/47=0,20111210020220010110001...

35/47=0,20200221211222102111012...

36/47=0,20220010110001201112100...

37/47=0,21002022001011000120111...

38/47=0,21021110122020022121122...

39/47=0,21110122020022121122210...

40/47=0,21122210211101220200221...

41/47=0,21211222102111012202002...

42/47=0,22001011000120111210020...

43/47=0,22020022121122210211101...

44/47=0,22102111012202002212112...

45/47=0,22121122210211101220200...

46/47=0,22210211101220200221211...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (23) est égal à 46 et donc au premier -1.