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

0,3

Comments

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

Links

Table of n, a(n) for n=0..86.

Formula

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

Example

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.

Sequence in context: A002950 A324046 A244059 * A321991 A010135 A176401

Adjacent sequences: A121087 A121088 A121089 * A121091 A121092 A121093

Keyword

nonn,base

Author

Gil Broussard, Aug 11 2006

Status

approved