Il existe 2 périodes de 29 chiffres pour n/59 en base 7.

Pour toutes les fractions de n/59 en base 7, la période de 1/59 revient alors 29 fois (en orange)

1/59=0,00554602330410321531265224162...

2/59=0,01442504661120643362563451354...

3/59=0,02330410321531265224162005546...

4/59=0,03215312652241620055460233041...

5/59=0,04103215312652241620055460233...

6/59=0,04661120643362563451354014425...

7/59=0,05546023304103215312652241620...

8/59=0,06433625634513540144250466112...

9/59=0,10321531265224162005546023304...

10/59=0,11206433625634513540144250466...

11/59=0,12064336256345135401442504661...

12/59=0,12652241620055460233041032153...

13/59=0,13540144250466112064336256345...

14/59=0,14425046611206433625634513540...

15/59=0,15312652241620055460233041032...

16/59=0,16200554602330410321531265224...

17/59=0,20055460233041032153126522416...

18/59=0,20643362563451354014425046611...

19/59=0,21531265224162005546023304103...

20/59=0,22416200554602330410321531265...

21/59=0,23304103215312652241620055460...

22/59=0,24162005546023304103215312652...

23/59=0,25046611206433625634513540144...

24/59=0,25634513540144250466112064336...

25/59=0,26522416200554602330410321531...

26/59=0,30410321531265224162005546023...

27/59=0,31265224162005546023304103215...

28/59=0,32153126522416200554602330410...

29/59=0,33041032153126522416200554602...

30/59=0,33625634513540144250466112064...

31/59=0,34513540144250466112064336256...

32/59=0,35401442504661120643362563451...

33/59=0,36256345135401442504661120643...

34/59=0,40144250466112064336256345135...

35/59=0,41032153126522416200554602330...

36/59=0,41620055460233041032153126522...

37/59=0,42504661120643362563451354014...

38/59=0,43362563451354014425046611206...

39/59=0,44250466112064336256345135401...

40/59=0,45135401442504661120643362563...

41/59=0,46023304103215312652241620055...

42/59=0,46611206433625634513540144250...

43/59=0,50466112064336256345135401442...

44/59=0,51354014425046611206433625634...

45/59=0,52241620055460233041032153126...

46/59=0,53126522416200554602330410321...

47/59=0,54014425046611206433625634513...

48/59=0,54602330410321531265224162005...

49/59=0,55460233041032153126522416200...

50/59=0,56345135401442504661120643362...

51/59=0,60233041032153126522416200554...

52/59=0,61120643362563451354014425046...

53/59=0,62005546023304103215312652241...

54/59=0,62563451354014425046611206433...

55/59=0,63451354014425046611206433625...

56/59=0,64336256345135401442504661120...

57/59=0,65224162005546023304103215312...

58/59=0,66112064336256345135401442504...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (29) est égal à 58 et donc au premier -1.