Is a general sequence possible for the given data?

[SithsNGiggles]

I finished exploring a family of functions

f_k(x) = {x^ksin(1/x) for x≠0
{0 for x=0
for an assignment in my Analysis course, and I'm supposed to determine the highest order derivative that exists and whether or not it's continuous.

I've noticed a pattern:
k = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}
n = {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...},
where k is a positive integer, and n is the highest order derivative that exists.

I want to save some space on my page by generalizing these results as a sequence. Is this possible, and if so what's the sequence? Thanks.

 

[Char. Limit]

Would n=floor((k-1)/2) work?

 

[SithsNGiggles]

Would n=floor((k-1)/2) work?

Yes, I figured it out very recently. Thank you.