Making 100 starting with two 1s

Question

You have an empty blackboard. At each step, you can either write two ones on the blackboard,
or erase two copies of a number n and replace them with n−1 and n+1.
What is the fewest number of steps it takes to write 100 on the board?

WhatsUp · Accepted Answer

I think the answer is

The closed formula solution is

tehtmi · Answer

Taking the algorithm of @WhatsUp for granted, counting more constructively:

Making 100 starting with two 1s

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