What is the sum of these three natural numbers

What is the sum of these three natural numbers


(a-1)+a+(a+1)=3a



1-3000 the sum of all the 3000 consecutive natural numbers


(1+3000)×1500=4501500



There is a kind of natural number, starting from the third number, each number is just the sum of the two numbers in front of it, such as 246, 1347, etc
What is the largest natural number in this kind of numbers?


3369