MathDB

CNCM Online R1P3

Source:

September 2, 2020

Problem Statement

Define

S(N)

to be the sum of the digits of

N

when it is written in base

10

, and take

S^k(N) = S(S(\dots(N)\dots))

with

k

applications of

S

. The stability of a number

N

is defined to be the smallest positive integer

K

where

S^K(N) = S^{K+1}(N) = S^{K+2}(N) = \dots

. Let

T_3

be the set of all natural numbers with stability

3

. Compute the sum of the two least entries of

T_3

.
Proposed by Albert Wang (awang11)

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