Il existe 2 périodes de 23 chiffres pour n/47 en base 7.

Pour toutes les fractions de n/47 en base 7, la période de 1/47 revient alors 23 fois (en orange)

1/47=0,01020411224523503061534...

2/47=0,02041122452350306153401...

3/47=0,03061534010204112245235...

4/47=0,04112245235030615340102...

5/47=0,05132656462554421431636...

6/47=0,06153401020411224523503...

7/47=0,10204112245235030615340...

8/47=0,11224523503061534010204...

9/47=0,12245235030615340102041...

10/47=0,13265646255442143163605...

11/47=0,14316360513265646255442...

12/47=0,15340102041122452350306...

13/47=0,16360513265646255442143...

14/47=0,20411224523503061534010...

15/47=0,21431636051326564625544...

16/47=0,22452350306153401020411...

17/47=0,23503061534010204112245...

18/47=0,24523503061534010204112...

19/47=0,25544214316360513265646...

20/47=0,26564625544214316360513...

21/47=0,30615340102041122452350...

22/47=0,31636051326564625544214...

23/47=0,32656462554421431636051...

24/47=0,34010204112245235030615...

25/47=0,35030615340102041122452...

26/47=0,36051326564625544214316...

27/47=0,40102041122452350306153...

28/47=0,41122452350306153401020...

29/47=0,42143163605132656462554...

30/47=0,43163605132656462554421...

31/47=0,44214316360513265646255...

32/47=0,45235030615340102041122...

33/47=0,46255442143163605132656...

34/47=0,50306153401020411224523...

35/47=0,51326564625544214316360...

36/47=0,52350306153401020411224...

37/47=0,53401020411224523503061...

38/47=0,54421431636051326564625...

39/47=0,55442143163605132656462...

40/47=0,56462554421431636051326...

41/47=0,60513265646255442143163...

42/47=0,61534010204112245235030...

43/47=0,62554421431636051326564...

44/47=0,63605132656462554421431...

45/47=0,64625544214316360513265...

46/47=0,65646255442143163605132...

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