THE NUMBER 13

 Two interesting facts about the number 13: 

(i)  (1 / 13 )   =     0.076923076923076923076923...

                 (rational periodic infinite decimal)

On multiplying the periodic number 76923 by successive multiples of 13, the following curious numerical pattern is obtained.

76923 * 013 = 0999999
76923 * 026 = 1999998 
76923 * 039 = 2999997 
76923 * 052 = 3999996
76923 * 065 = 4999995

76923 * 078 = 5999994

76923 * 091 = 6999993

76923 * 104 = 7999992

76923 * 117 = 8999991

76923 * 130 = 9999990

 (ii) The numerical pattern abcabc is divisible by 13.