A362865 a(n) is the length of the longest possible cycle of repeating digits in the digits expansion of 1/x, in base n, among all numbers x between 1 and n-1.

1, 1, 2, 1, 4, 4, 3, 6, 6, 6, 10, 6, 12, 5, 10, 10, 12, 16, 18, 18, 16, 16, 11, 11, 20, 22, 18, 22, 28, 28, 22, 30, 14, 11, 28, 22, 36, 28, 18, 36, 30, 30, 16, 42, 40, 42, 23, 36, 23, 46, 40, 42, 52, 52, 46, 52, 42, 46, 58, 46, 60, 29, 58, 46, 60, 60, 66, 58, 60

Offset: 3

Author

Itamar Zamir, May 06 2023

Keywords

• nonn
• base

Comments

This longest cycle may be attained by multiple values of x, among which x = A362840(n) is the smallest.

Examples

			a(10)=6 since in base 10, the longest possible cycle of recurrent digits for 1/x is of length 6, which appears for 1/7 = 0.142857...
		

Crossrefs

Cf. A362840.

Cf. A051626.