Il existe 2 périodes de 20 chiffres pour n/41 en base 5.

Pour toutes les fractions de n/41 en base 5, la période de 1/41 revient alors 20 fois (en orange)

1/41=0,00301102204414334224...

2/41=0,01102204414334224003...

3/41=0,01403312124304113232...

4/41=0,02204414334224003011...

5/41=0,03011022044143342240...

6/41=0,03312124304113232014...

7/41=0,04113232014033121243...

8/41=0,04414334224003011022...

9/41=0,10220441433422400301...

10/41=0,11022044143342240030...

11/41=0,11323201403312124304...

12/41=0,12124304113232014033...

13/41=0,12430411323201403312...

14/41=0,13232014033121243041...

15/41=0,14033121243041132320...

16/41=0,14334224003011022044...

17/41=0,20140331212430411323...

18/41=0,20441433422400301102...

19/41=0,21243041132320140331...

20/41=0,22044143342240030110...

21/41=0,22400301102204414334...

22/41=0,23201403312124304113...

23/41=0,24003011022044143342...

24/41=0,24304113232014033121...

25/41=0,30110220441433422400...

26/41=0,30411323201403312124...

27/41=0,31212430411323201403...

28/41=0,32014033121243041132...

29/41=0,32320140331212430411...

30/41=0,33121243041132320140...

31/41=0,33422400301102204414...

32/41=0,34224003011022044143...

33/41=0,40030110220441433422...

34/41=0,40331212430411323201...

35/41=0,41132320140331212430...

36/41=0,41433422400301102204...

37/41=0,42240030110220441433...

38/41=0,43041132320140331212...

39/41=0,43342240030110220441...

40/41=0,44143342240030110220...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (20) est égal à 40 et donc au premier -1.