Il existe 2 périodes de 39 chiffres pour n/79 en base 5.

Pour toutes les fractions de n/79 en base 5, la période de 1/79 revient alors 39 fois (en orange)

1/79=0,001242343022312114401113103220030402411...

2/79=0,003040241100124234302231211440111310322...

3/79=0,004333134122441404203344320210142213233...

4/79=0,011131032200304024110012423430223121144...

5/79=0,012423430223121144011131032200304024110...

6/79=0,014221323300433313412244140420334432021...

7/79=0,021014221323300433313412244140420334432...

8/79=0,022312114401113103220030402411001242343...

9/79=0,024110012423430223121144011131032200304...

10/79=0,030402411001242343022312114401113103220...

11/79=0,032200304024110012423430223121144011131...

12/79=0,033443202101422132330043331341224414042...

13/79=0,040241100124234302231211440111310322003...

14/79=0,042033443202101422132330043331341224414...

15/79=0,043331341224414042033443202101422132330...

16/79=0,100124234302231211440111310322003040241...

17/79=0,101422132330043331341224414042033443202...

18/79=0,103220030402411001242343022312114401113...

19/79=0,110012423430223121144011131032200304024...

20/79=0,111310322003040241100124234302231211440...

21/79=0,113103220030402411001242343022312114401...

22/79=0,114401113103220030402411001242343022312...

23/79=0,121144011131032200304024110012423430223...

24/79=0,122441404203344320210142213233004333134...

25/79=0,124234302231211440111310322003040241100...

26/79=0,131032200304024110012423430223121144011...

27/79=0,132330043331341224414042033443202101422...

28/79=0,134122441404203344320210142213233004333...

29/79=0,140420334432021014221323300433313412244...

30/79=0,142213233004333134122441404203344320210...

31/79=0,144011131032200304024110012423430223121...

32/79=0,200304024110012423430223121144011131032...

33/79=0,202101422132330043331341224414042033443...

34/79=0,203344320210142213233004333134122441404...

35/79=0,210142213233004333134122441404203344320...

36/79=0,211440111310322003040241100124234302231...

37/79=0,213233004333134122441404203344320210142...

38/79=0,220030402411001242343022312114401113103...

39/79=0,221323300433313412244140420334432021014...

40/79=0,223121144011131032200304024110012423430...

41/79=0,224414042033443202101422132330043331341...

42/79=0,231211440111310322003040241100124234302...

43/79=0,233004333134122441404203344320210142213...

44/79=0,234302231211440111310322003040241100124...

45/79=0,241100124234302231211440111310322003040...

46/79=0,242343022312114401113103220030402411001...

47/79=0,244140420334432021014221323300433313412...

48/79=0,300433313412244140420334432021014221323...

49/79=0,302231211440111310322003040241100124234...

50/79=0,304024110012423430223121144011131032200...

51/79=0,310322003040241100124234302231211440111...

52/79=0,312114401113103220030402411001242343022...

53/79=0,313412244140420334432021014221323300433...

54/79=0,320210142213233004333134122441404203344...

55/79=0,322003040241100124234302231211440111310...

56/79=0,323300433313412244140420334432021014221...

57/79=0,330043331341224414042033443202101422132...

58/79=0,331341224414042033443202101422132330043...

59/79=0,333134122441404203344320210142213233004...

60/79=0,334432021014221323300433313412244140420...

61/79=0,341224414042033443202101422132330043331...

62/79=0,343022312114401113103220030402411001242...

63/79=0,344320210142213233004333134122441404203...

64/79=0,401113103220030402411001242343022312114...

65/79=0,402411001242343022312114401113103220030...

66/79=0,404203344320210142213233004333134122441...

67/79=0,411001242343022312114401113103220030402...

68/79=0,412244140420334432021014221323300433313...

69/79=0,414042033443202101422132330043331341224...

70/79=0,420334432021014221323300433313412244140...

71/79=0,422132330043331341224414042033443202101...

72/79=0,423430223121144011131032200304024110012...

73/79=0,430223121144011131032200304024110012423...

74/79=0,432021014221323300433313412244140420334...

75/79=0,433313412244140420334432021014221323300...

76/79=0,440111310322003040241100124234302231211...

77/79=0,441404203344320210142213233004333134122...

78/79=0,443202101422132330043331341224414042033...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (39) est égal à 78 et donc au premier -1.