Fomin D:

Each member of the sequence, starting from the second, is obtained by adding to the previous number the sum of its digits. The first member of the sequence is one. Will the number 123456 appear in the sequence?

#
Obviously, a number and the sum of its digits give the same remainder when divided by 3. Therefore, the sequence of remainders when divided by 3 is: $1,2,1,2$, ..., and in it, 0 (the remainder of 123456 when divided by 3) will not appear.

## Answer

It will not appear.