Integers sorted by their digital roots
Python 2, 78 60 52 46 45 bytes

-6 bytes thanks to G B.
-1 byte thanks to Jakob.



n=input()
b=10**~-len(`n`)
print~-b+n/b+n%b*9


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Finally reached a closed form, 1-indexed.



Python 2, 78 bytes

0-indexed.



d=10;k=1
exec'\nk+=9\nif k&gt;d+7:k=d;d*=10\nif k&gt;=d:k-=d/10*9-1'*input()
print k


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