The number is divisible by 3 if the sum of digits is divisible by 3. 1221 is the first number with a sum of digits divisible by 3. Adding 3 more 2s to the sequence will result in another number divisible by 3.
So, every 3rd term from n=2 to n=98 will be divisible by 3, for a total of 33 terms out of the first 100 in the sequence.
and . 3 divides both 12 and 21, so and 21 contribute no remainder.
This leaves us with
Recall that a decimal integer is divisible by 3 if its digits add to a multiple of 3. The digits in are copies of 2 and one 0, so the digital sum is .
If for , then the digital sum is , which is not divisible by 3.
If , then the sum is , which is not divisible by 3.
If , then the sum is , which is always divisble by 3.
This means that roughly 1/3 of the first numbers in this sequence are divisible by 3; among the first 100 terms, they occur for , of which there are 33.
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