What is the next number in the sequence: $24, 30, 33 , 39 , 51,...$ [closed]

What is the next number in the sequence:

$24, 30, 33 , 39 , 51,...$

Here all numbers are divisible by $3$, difference between numbers are $6,3,6,12,...$ but I can't find common relationship in the sequence.

Solution 1:

Looks to me like each term is the preceding term, plus the preceding term's sum of digits. The sequence would then be: $24, 30, 33, 39, 51, 57, 69, 84, 96,...$

Note that if a number is divisible by 3, then the sum of its digits is also divisible by 3, resulting in all of the numbers in the sequence being divisible by 3. Because of this, there are probably many other ways to define the sequence, but I find the one I gave to be fairly natural.

Edit: Just noticed @DavidMitra's earlier comment which links to an OEIS page which includes the answer I gave, but I'll leave my answer here as reference.

Solution 2:

24 or 45 or 1000 or 286575! Perhaps anything will work. A theorem states that given any values, a polynomial exists which takes all those values. So this question has a pretty basic flaw in it!