Billy writes out all of the numbers from 1 to 103 on the

Last updated: 7/12/2022

Billy writes out all of the numbers from 1 to 103 on the board, in order from smallest to largest from left to right. He then goes down the board, starting from 1, up to 100, erasing each number and replacing it with the sum of the next two numbers on the right. For example, he replaces 1 with 2 + 3 = 5, 2 with 7, 3 with 9, and 4 with 11. He then goes back to the beginning, starting with 5, then replaces each number with the sum of the next three numbers on the right, until this is not possible anymore. For example, the 5 he wrote on the very left gets replaced with 7+9+ 11 = 27. What is the sum of the first 100 numbers on the board?