A382498 Smallest k such that the fractional part of 1/k is pandigital in base n.

3, 5, 13, 7, 11, 11, 11, 43, 17, 13, 17, 19, 17, 19, 79, 23, 29, 23, 23, 23, 31, 47, 31, 73, 29, 29, 41, 41, 41, 47, 37, 43, 41, 37, 137, 59, 47, 47, 47, 47, 59, 47, 47, 47, 67, 59, 53, 241, 53, 53, 59, 71, 59, 59, 59, 67, 73, 61, 73, 67, 71, 67, 383, 71, 79

Offset: 2

Author

Joshua Searle, Mar 29 2025

Keywords

• nonn
• base

Comments

It appears that for squarefree n, a(n) has a reptend of maximal length and for square n, a(n) has a reptend of half the maximal length.

Not every prime appears in this sequence - excluding 2, the first missing prime is 109.

The first composite term is a(81).

How many times can a term appear consecutively?

How does a(n) grow with n?

Examples

			a(10) = 17 because 1/17 = 0.(0588235294117647)... in base 10 where the brackets indicate the reptend. Every digit 0-9 appears within the reptend and is the smallest unit fraction where this is the case.
a(36) = 137 because 1/137 = 0.(09gjyy5s47cvj6khv9q0ix3xwbk8epr2d4zqjg11u7vsn4gtfi4q9zh2w23ofrla8xmv)... in base 36 where the digits 0-9 and letters a-z have been used as additional digits. Every character appears at least once.
		

Links

• SeqFans Mailing List, Smallest pandigital reptend of 1/n in base b

Crossrefs

Cf. A001913, A261773.