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A179193
Sum of the number of repeating digits for each reciprocal of integer m, where 1 < m < n and n is the base.
1
0, 1, 1, 4, 1, 9, 9, 9, 9, 20, 15, 30, 22, 28, 23, 52, 33, 63, 58, 44, 65, 86, 84, 67, 68, 102, 135, 140, 74, 142, 171, 159, 142, 124, 88, 220, 204, 205, 238, 258, 209, 244, 231, 201, 245, 304, 328, 214, 291, 292, 465, 422, 380, 350, 422, 381, 507, 507, 417, 627
OFFSET
2,4
COMMENTS
No digits are counted as repeating for 1/m if 1/m terminates.
Equivalent to 1 <= m <= n, since 1/n and 1/1 do not have repeating digits in any integer base n.
LINKS
EXAMPLE
7th term considers octal: the fractions 1/2, 1/3, 1/4, 1/5, 1/6 and 1/7 have 0, 2, 0, 4, 2 and 1 repeating (octal) digits respectively, for a total of 9.
9th term considers decimal: the fractions 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8 and 1/9 have 0, 1, 0, 0, 1, 6, 0 and 1 repeating (decimal) digits respectively, for a total of 9.
MATHEMATICA
a[n_] := Sum[Length[RealDigits[1/k, n][[1, -1]]], {k, 2, n-1}]; Array[a, 100, 2] (* Amiram Eldar, Jun 28 2024 *)
CROSSREFS
Cf. A051626.
Sequence in context: A084887 A367025 A067015 * A158199 A091885 A069606
KEYWORD
nonn,base
AUTHOR
Will Nicholes, Jul 01 2010
EXTENSIONS
Data corrected and extended by Amiram Eldar, Jun 28 2024
STATUS
approved