For example, the sequence obtained from the starting number 9876 is (9876, 30, 3), so 9876 has an additive
persistence of 2 and a digital root of 3. The additive
persistences of the first few positive integers
are 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, ... (OEIS A031286).
The smallest numbers of additive persistence for , 1, ... are 0, 10, 19, 199,
19999999999999999999999, ... (OEIS A006050).
Hindin, H. J. "The Additive Persistence of a Number." J. Recr. Math.7, 134-135, 1974.Sloane, N. J. A.
"The Persistence of a Number." J. Recr. Math.6, 97-98, 1973.Sloane,
N. J. A. Sequences A006050/M4683
and A031286 in "The On-Line Encyclopedia
of Integer Sequences."
is the number of iterations of summing
its decimal digits required
to obtain a single digit. The digit
obtained is called the digital root of 
.
for 
, 1, ... are 0, 10, 19, 199,
19999999999999999999999, ... (OEIS A006050).
