Crunchy Coconuts

Number Theory Level 4

A positive number \(n\) is called a coconut if the logarithm of \(n\) to the base 10 is in the interval \([2,3) \).

Moreover, a natural number \(n\) is called crunchy if it suffices the following condition \[\displaystyle \text{SOD}(3+n)=\dfrac{\text{SOD}(n)}{3}\]
,where \(\displaystyle \text{SOD}(n)\) is an operator which tells the sum of digits of the number \(\displaystyle n\).

What is the sum of all numbers that are both crunchy and coconuts'?


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