A338753 Number of integers less than n with the same period of reciprocal as n.

0, 1, 0, 2, 3, 1, 0, 4, 2, 5, 0, 3, 1, 2, 4, 6, 0, 5, 0, 7, 3, 1, 0, 6, 8, 4, 0, 5, 0, 7, 0, 9, 2, 1, 6, 8, 1, 1, 7, 10, 0, 8, 0, 3, 9, 1, 0, 10, 0, 11, 2, 9, 0, 2, 4, 10, 2, 1, 0, 11, 0, 1, 11, 12, 12, 5, 0, 3, 2, 13, 0, 12, 0, 3, 13, 3, 14, 15, 1, 13, 0, 1, 0, 16, 4, 1, 2, 6, 0, 14

Offset: 1

Author

Ilya Gutkovskiy, Nov 06 2020

Keywords

• nonn
• base

Examples

			a(14) = 2 because A051626(14) = 6 and also A051626(7) = A051626(13) = 6.
More specifically,
1/7  = 0.142857(142857)...  (period 6),
1/13 = 0.076923(076923)...  (period 6),
1/14 = 0.0714285(714285)... (period 6).
		

Links

• Eric Weisstein's World of Mathematics, Repeating Decimal
• Index entries for sequences related to decimal expansion of 1/n

Crossrefs

Cf. A051626.

Programs

Mathematica

Table[Length[Select[Range[n - 1], Length[RealDigits[1/#][[1, -1]]] == Length[RealDigits[1/n][[1, -1]]] &]], {n, 90}]

Formula

a(n) = |{j < n : A051626(j) = A051626(n)}|.