A121090 Period of unit fractions having periodic decimal expansions.

1, 1, 6, 1, 2, 1, 6, 6, 1, 16, 1, 18, 6, 2, 22, 1, 6, 3, 6, 28, 1, 15, 2, 16, 6, 1, 3, 18, 6, 5, 6, 21, 2, 1, 22, 46, 1, 42, 16, 6, 13, 3, 2, 6, 18, 28, 58, 1, 60, 15, 6, 6, 2, 33, 16, 22, 6, 35, 1, 8, 3, 1, 18, 6, 6, 13, 9, 5, 41, 6, 16, 21, 28, 2, 44, 1, 6, 22, 15, 46, 18, 1, 96, 42, 2, 4, 16

Offset: 0

Author

Gil Broussard, Aug 11 2006

Keywords

• nonn
• base

Comments

See A007732, which is the main entry for this sequence.

Examples

			The first unit fraction considered is 1/3 because both 1/1 and 1/2 have finite decimal expansions.
a(1) = 1 because 1/3=.33333... whose repeating portion, 3, is of length 1.
Note: 1/4 and 1/5 are skipped because their decimal expansions are finite.
a(2) = 1 because 1/6=.166666... whose repeating portion, 6, is of length 1.
a(3) = 6 because 1/7 =.142857142857... whose repeating portion, 142857, is of length 6.
		

Crossrefs

Cf. A085837, A007732.

Formula

a(n) = A007732(A085837(n)). - Kevin Ryde, May 05 2023