A179193 Sum of the number of repeating digits for each reciprocal of integer m, where 1 < m < n and n is the base.

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

Author

Will Nicholes, Jul 01 2010

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A051626.

Programs

Mathematica

a[n_] := Sum[Length[RealDigits[1/k, n][[1, -1]]], {k, 2, n-1}]; Array[a, 100, 2] (* Amiram Eldar, Jun 28 2024 *)

Extensions

Data corrected and extended by Amiram Eldar, Jun 28 2024