/* Function that returns a list of digits given a nonnegative integer */
decompose(num) := block([digits, remainder],
  digits: [],
  while num > 0 do
   (remainder: mod(num, 10),
    digits: cons(remainder, digits),
    num: floor(num/10)),
  digits
)$

/* Function that given a positive integer returns the sum of their digits */
auxdig(n):=block(decompose(n),apply("+",%%));

/* Function that given a positive integer returns a list of two: the additive persistence and the digital root */
digrt(n):=block([additive_persistence:0,digital_root:n],
    while length(decompose(digital_root))>1 do (digital_root:auxdig(digital_root),additive_persistence:additive_persistence+1),
    [additive_persistence,digital_root]);

/* Examples */
digrt(627615);
digrt(39390);
digrt(588225);
digrt(393900588225);