#JavaScript (ES6), 43 bytes

###Why doing it this way?

###Commented

JavaScript (ES6), 43 bytes

Why doing it this way?

Commented

For example, this would work for 45 bytes:

It turns out to be shorter to skip all values of \$n\$ that contain a \$2\$.

For example, this would work for 45 bytes:

Or this would work for 44 bytes, if a leading comma is acceptable:

f=(n=100)=>n?f(n-1)+(/2/.test(n)?'':[,n]):''

All in all (and until proven otherwise), it turns out to be shorter to skip right away all values of \$n\$ that contain a \$2\$.

###Commented

###Why doing it this way?

We could iterate from \$1\$ to \$100\$ and test each number with /2/.test(n), which is a rather concise statement. But in this scenario, we'd have to handle empty entries with something like (/2/.test(n)?'':...), which adds a couple more bytes.

For example, this would work for 45 bytes:

f=(n=1)=>n>99?n:(/2/.test(n)?'':[n,,])+f(n+1)

It turns out to be shorter to skip all values of \$n\$ that contain a \$2\$.

###Commented