f57v Summation of sequences

[ReneZ]

Summation of the digits of a number is equivalent with taking the remainder while dividing by 9.
In mathematical terms, the number, and the sum of its digits are the same, modulo 9.


Example: 147 = 16 x 9 + 3,  so the remainder is 3.
1+4+7= 12; 1+2 = 3.

When adding three series of numbers, of which one goes down by one (modulo 9) and the other two go up by one, the result is a series going up by one (always modulo 9).
Therefore, nothing surprising happened.