A positive integer may be represented in an integer base \$1 \le b < \infty\$.
When converted to that base it has some number of distinct digits.
Any positive integer in base \$1\$ has \$1\$ distinct digit.
Most positive integers in base \$2\$ have \$2\$ distinct digits, the exceptions being those of the form \$2^n - 1\$, which only have \$1\$.
So the first positive integer that may be represented in an integer base with \$1\$ unique digit is \$1\$ and the first that may be represented with \$2\$ distinct digits is \$2\$.
We can say that \$1\$ is the first integer with digital diversity \$1\$ and \$2\$ is the first integer with digital diversity \$2\$.
Challenge:
Given a positive integer \$n\$ return the first positive integer (in base ten*) that has a digital diversity of \$n\$.
* if your language only supports a specific base (e.g. unary or binary) then you may output in that base.
Your algorithm must work in theory for any positive integer input: it may fail because the precision of your language's integer is too small for the output; but may not fail because base conversion is only defined up to some limit.
Test cases
input output
1 1
2 2
3 11
4 75
5 694
6 8345
7 123717
17 49030176097150555672
20 5271200265927977839335179
35 31553934355853606735562426636407089783813301667210139
63 3625251781415299613726919161860178255907794200133329465833974783321623703779312895623049180230543882191649073441
257 87678437238928144977867204156371666030574491195943247606217411725999221158137320290311206746021269051905957869964398955543865645836750532964676103309118517901711628268617642190891105089936701834562621017362909185346834491214407969530898724148629372941508591337423558645926764610261822387781382563338079572769909101879401794746607730261119588219922573912353523976018472514396317057486257150092160745928604277707892487794747938484196105308022626085969393774316283689089561353458798878282422725100360693093282006215082783023264045094700028196975508236300153490495688610733745982183150355962887110565055971546946484175232
This is code-golf, the shortest solution in bytes wins.
OEIS: A049363 - also smallest pandigital number in base n.