Il existe 2 périodes de 23 chiffres pour n/47 en base 4.

Pour toutes les fractions de n/47 en base 4, la période de 1/47 revient alors 23 fois (en orange)

1/47=0,00111302120200223210301...

2/47=0,00223210301001113021202...

3/47=0,01001113021202002232103...

4/47=0,01113021202002232103010...

5/47=0,01230323322203121313311...

6/47=0,02002232103010011130212...

7/47=0,02120200223210301001113...

8/47=0,02232103010011130212020...

9/47=0,03010011130212020022321...

10/47=0,03121313311012303233222...

11/47=0,03233222031213133110123...

12/47=0,10011130212020022321030...

13/47=0,10123032332220312131331...

14/47=0,10301001113021202002232...

15/47=0,11012303233222031213133...

16/47=0,11130212020022321030100...

17/47=0,11302120200223210301001...

18/47=0,12020022321030100111302...

19/47=0,12131331101230323322203...

20/47=0,12303233222031213133110...

21/47=0,13021202002232103010011...

22/47=0,13133110123032332220312...

23/47=0,13311012303233222031213...

24/47=0,20022321030100111302120...

25/47=0,20200223210301001113021...

26/47=0,20312131331101230323322...

27/47=0,21030100111302120200223...

28/47=0,21202002232103010011130...

29/47=0,21313311012303233222031...

30/47=0,22031213133110123032332...

31/47=0,22203121313311012303233...

32/47=0,22321030100111302120200...

33/47=0,23032332220312131331101...

34/47=0,23210301001113021202002...

35/47=0,23322203121313311012303...

36/47=0,30100111302120200223210...

37/47=0,30212020022321030100111...

38/47=0,30323322203121313311012...

39/47=0,31101230323322203121313...

40/47=0,31213133110123032332220...

41/47=0,31331101230323322203121...

42/47=0,32103010011130212020022...

43/47=0,32220312131331101230323...

44/47=0,32332220312131331101230...

45/47=0,33110123032332220312131...

46/47=0,33222031213133110123032...

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