The natural numbers not divisible by 3 are those that leave a remainder of 1 or 2 when divided by 3.
Here's a breakdown:
-
Natural Numbers: These are the positive whole numbers (1, 2, 3, 4, ...).
-
Divisibility by 3: A number is divisible by 3 if, when divided by 3, the remainder is 0.
Therefore, we're looking for natural numbers that, when divided by 3, have a remainder of either 1 or 2.
Here's a list of the first few natural numbers not divisible by 3:
1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, ...
These numbers can be represented by the formulas 3n + 1 and 3n + 2, where n is any non-negative integer (0, 1, 2, 3, ...).
Examples:
- If n = 0, 3n + 1 = 1 and 3n + 2 = 2
- If n = 1, 3n + 1 = 4 and 3n + 2 = 5
- If n = 2, 3n + 1 = 7 and 3n + 2 = 8
- If n = 3, 3n + 1 = 10 and 3n + 2 = 11
In essence, you can generate the sequence of natural numbers not divisible by 3 by starting with 1 and 2, and then successively adding 3 to each to get the next numbers in the sequence.
