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
Examples
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.
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