What is the logic for solving this sequence?

Question

The sequence goes like this.. `7,8,77,78,87,88,777,778,787,788` and so on.. What can be the logic for finding the nth number of the sequence? I tried that by dividing it by 2 and then by 4 and hence, but it doesn't seem to work.

Answer 1

If its a seven, make it an 8,

then make the PREVIOUS 7 and 8 and change the 8 in the lower position back to 7...

Basically, the 8's change back to sevens when they overflow

(kind of like when 9's change to zeros when they overflow)

7

8

77

78

87 <--- overflow

88

777 <--- overflow

778

787 <--- overflow

788

877 <---- every other term overflows in the next digit

878

887

888

7777

7778

7787

7788

7877

7878

7887

7888

8777

8778

8787

8788

8877

8878

8887

8888

77777

77778

77787

77788

77877

77878

77887

77888

78777

78778

78787

78788

78877

78878

78887

78888

87777

87778

etc

etc

Answer 2

7777, 7778, 7787, 7788,

77777, 77778, 77787, 77788