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A positive integer may be represented in an integer base 1 <= b < inf.

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.

code-golf sequence number-theory base-conversion