MathDB
d(n), d(d(n)), d(d(d(n))), ... , sum of digits , limit

Source: LIMIT 2020 Cat 2 Obj P13

June 9, 2020
sum of digitslimit

Problem Statement

For every n∈Nn \in N , let d(n)d(n) denote the sum of digits of nn. It is easy to see that the sequence d(n),d(d(n))d(n), d(d(n)), d(d(d(n))),...d(d(d(n))), ... will eventually become a constant integer between 11 and 99 (both inclusive). This number is called the digital root of nn . Denote it by b(n)b(n). Then for how many natural numbers k<1000,lim⁡n→∞b(kn)k<1000 , \lim_{n \to \infty} b(k^n) exists.
Back to ProblemsView on AoPS