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

2,1

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?

Links

Table of n, a(n) for n=2..66.

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

Example

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.

Crossrefs

Cf. A001913, A261773.

Sequence in context: A099791 A301901 A351225 * A348744 A263829 A028268

Adjacent sequences: A382495 A382496 A382497 * A382499 A382500 A382501

Keyword

nonn,base

Author

Joshua Searle, Mar 29 2025

Status

approved