A362840 a(n) is the smallest number x between 1 and n-1 for which the number 1/x achieves the longest cycle of repeating digits in its expansion in base n.

2, 3, 3, 5, 5, 5, 7, 7, 9, 7, 11, 9, 13, 11, 11, 11, 13, 17, 19, 19, 17, 17, 23, 23, 25, 23, 19, 23, 29, 29, 23, 31, 29, 23, 29, 23, 37, 29, 19, 37, 31, 31, 17, 43, 41, 43, 47, 37, 47, 47, 41, 49, 53, 53, 47, 53, 49, 47, 59, 47, 61, 59, 59, 47, 61, 61, 67, 59, 61, 59

Offset

3,1

Comments

Terminating expansions, in any base, are considered to have a cycle period of length 0.

It appears by observation that all terms in the sequence are either primes or powers of primes.

Links

Table of n, a(n) for n=3..72.

Example

a(3)=2 since in base 3, 1/2 is represented by 0.111... with a cycle of 1 repeating digit, which is the longest cycle among 1/x for x = 1..2.
a(10)=7 since in base 10, 1/7 is represented by 0.142857... with a cycle of 6 repeating digits, which is the longest cycle among 1/x for x = 1..9.

Crossrefs

Cf. A362865 (corresponding cycle lengths).

Cf. A051626.

Sequence in context: A280740 A156350 A076367 * A302607 A098567 A086162

Adjacent sequences: A362837 A362838 A362839 * A362841 A362842 A362843

Keyword

nonn,base

Author

Itamar Zamir, May 05 2023

Status

approved